TSTP Solution File: ITP213^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP213^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n007.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 03:20:07 EDT 2023
% Result : Timeout 299.79s 300.14s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.68/2.74 % Problem : ITP213^3 : TPTP v8.1.2. Released v8.1.0.
% 2.68/2.75 % Command : do_cvc5 %s %d
% 2.75/2.96 % Computer : n007.cluster.edu
% 2.75/2.96 % Model : x86_64 x86_64
% 2.75/2.96 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.75/2.96 % Memory : 8042.1875MB
% 2.75/2.96 % OS : Linux 3.10.0-693.el7.x86_64
% 2.75/2.96 % CPULimit : 300
% 2.75/2.96 % WCLimit : 300
% 2.75/2.96 % DateTime : Sun Aug 27 12:22:44 EDT 2023
% 2.75/2.96 % CPUTime :
% 5.42/5.61 %----Proving TH0
% 5.45/5.62 %------------------------------------------------------------------------------
% 5.45/5.62 % File : ITP213^3 : TPTP v8.1.2. Released v8.1.0.
% 5.45/5.62 % Domain : Interactive Theorem Proving
% 5.45/5.62 % Problem : Sledgehammer problem Hoare_Triple 00154_004690
% 5.45/5.62 % Version : [Des22] axioms.
% 5.45/5.62 % English :
% 5.45/5.62
% 5.45/5.62 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.45/5.62 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.45/5.62 % Source : [Des22]
% 5.45/5.62 % Names : 0025_Hoare_Triple_00154_004690 [Des22]
% 5.45/5.62
% 5.45/5.62 % Status : Theorem
% 5.45/5.62 % Rating : 0.92 v8.1.0
% 5.45/5.62 % Syntax : Number of formulae : 11206 (4947 unt;1462 typ; 0 def)
% 5.45/5.62 % Number of atoms : 27472 (10209 equ; 0 cnn)
% 5.45/5.62 % Maximal formula atoms : 48 ( 2 avg)
% 5.45/5.62 % Number of connectives : 103086 (2290 ~; 424 |;1813 &;87938 @)
% 5.45/5.62 % ( 0 <=>;10621 =>; 0 <=; 0 <~>)
% 5.45/5.62 % Maximal formula depth : 25 ( 6 avg)
% 5.45/5.62 % Number of types : 143 ( 142 usr)
% 5.45/5.62 % Number of type conns : 7235 (7235 >; 0 *; 0 +; 0 <<)
% 5.45/5.62 % Number of symbols : 1323 (1320 usr; 103 con; 0-5 aty)
% 5.45/5.62 % Number of variables : 27832 (3429 ^;23861 !; 542 ?;27832 :)
% 5.45/5.62 % SPC : TH0_THM_EQU_NAR
% 5.45/5.62
% 5.45/5.62 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.45/5.62 % from the van Emde Boas Trees session in the Archive of Formal
% 5.45/5.62 % proofs -
% 5.45/5.62 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.45/5.62 % 2022-02-17 15:20:47.194
% 5.45/5.62 %------------------------------------------------------------------------------
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% 5.45/5.62 thf(ty_n_t__Set__Oset_I_Eo_J,type,
% 5.45/5.62 set_o: $tType ).
% 5.45/5.62
% 5.45/5.62 thf(ty_n_t__Rat__Orat,type,
% 5.45/5.62 rat: $tType ).
% 5.45/5.62
% 5.45/5.62 thf(ty_n_t__Num__Onum,type,
% 5.45/5.62 num: $tType ).
% 5.45/5.62
% 5.45/5.62 thf(ty_n_t__Nat__Onat,type,
% 5.45/5.62 nat: $tType ).
% 5.45/5.62
% 5.45/5.62 thf(ty_n_t__Int__Oint,type,
% 5.45/5.62 int: $tType ).
% 5.45/5.62
% 5.45/5.62 thf(ty_n_tf__a,type,
% 5.45/5.62 a: $tType ).
% 5.45/5.62
% 5.45/5.62 % Explicit typings (1320)
% 5.45/5.62 thf(sy_c_Archimedean__Field_Oceiling_001t__Rat__Orat,type,
% 5.45/5.62 archim2889992004027027881ng_rat: rat > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_001t__Rat__Orat,type,
% 5.45/5.62 archim3151403230148437115or_rat: rat > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Archimedean__Field_Ofrac_001t__Rat__Orat,type,
% 5.45/5.62 archimedean_frac_rat: rat > rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Archimedean__Field_Oround_001t__Rat__Orat,type,
% 5.45/5.62 archim7778729529865785530nd_rat: rat > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oassn_OAbs__assn,type,
% 5.45/5.62 abs_assn: ( produc3658429121746597890et_nat > $o ) > assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oassn_ORep__assn,type,
% 5.45/5.62 rep_assn: assn > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oentails,type,
% 5.45/5.62 entails: assn > assn > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oin__range,type,
% 5.45/5.62 in_range: produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oin__range__rel,type,
% 5.45/5.62 in_range_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oone__assn__raw,type,
% 5.45/5.62 one_assn_raw: produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Oone__assn__raw__rel,type,
% 5.45/5.62 one_assn_raw_rel: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Opure__assn,type,
% 5.45/5.62 pure_assn: $o > assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Opure__assn__raw_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Opure__assn__raw__rel_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat,type,
% 5.45/5.62 pure_a6022498039421069578it_nat: produc6197004810343482825et_nat > produc6197004810343482825et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_OrelH,type,
% 5.45/5.62 relH: set_nat > heap_e7401611519738050253t_unit > heap_e7401611519738050253t_unit > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Otimes__assn__raw,type,
% 5.45/5.62 times_assn_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Otimes__assn__raw__rel,type,
% 5.45/5.62 times_assn_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Owand__assn,type,
% 5.45/5.62 wand_assn: assn > assn > assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Owand__raw,type,
% 5.45/5.62 wand_raw: ( produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Assertions_Owand__raw__rel,type,
% 5.45/5.62 wand_raw_rel: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Arithmetic_Ocone,type,
% 5.45/5.62 bNF_Cardinal_cone: set_Pr5094982260447487303t_unit ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Arithmetic_Octwo,type,
% 5.45/5.62 bNF_Cardinal_ctwo: set_Product_prod_o_o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Arithmetic_Oczero_001_Eo,type,
% 5.45/5.62 bNF_Cardinal_czero_o: set_Product_prod_o_o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__of_001t__Product____Type__Ounit,type,
% 5.45/5.62 bNF_Ca7083678892733797993t_unit: set_Product_unit > set_Pr5094982260447487303t_unit ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_Ocard__order__on_001_Eo,type,
% 5.45/5.62 bNF_Ca8331644756375544342r_on_o: set_o > set_Product_prod_o_o > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLeq,type,
% 5.45/5.62 bNF_Ca8665028551170535155natLeq: set_Pr1261947904930325089at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Cardinal__Order__Relation_OnatLess,type,
% 5.45/5.62 bNF_Ca8459412986667044542atLess: set_Pr1261947904930325089at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.45/5.62 bNF_re3403563459893282935_int_o: ( int > int > $o ) > ( ( int > $o ) > ( int > $o ) > $o ) > ( int > int > $o ) > ( int > int > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.45/5.62 bNF_re157797125943740599nt_int: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > product_prod_int_int ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
% 5.45/5.62 bNF_re3461391660133120880nt_rat: ( int > int > $o ) > ( ( int > product_prod_int_int ) > ( int > rat ) > $o ) > ( int > int > product_prod_int_int ) > ( int > int > rat ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001_Eo_001_Eo,type,
% 5.45/5.62 bNF_re5089333283451836215nt_o_o: ( int > int > $o ) > ( $o > $o > $o ) > ( int > $o ) > ( int > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.45/5.62 bNF_re4712519889275205905nt_int: ( int > int > $o ) > ( int > int > $o ) > ( int > int ) > ( int > int ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.45/5.62 bNF_re6250860962936578807nt_int: ( int > int > $o ) > ( product_prod_int_int > product_prod_int_int > $o ) > ( int > product_prod_int_int ) > ( int > product_prod_int_int ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
% 5.45/5.62 bNF_re2214769303045360666nt_rat: ( int > int > $o ) > ( product_prod_int_int > rat > $o ) > ( int > product_prod_int_int ) > ( int > rat ) > $o ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 bNF_re578469030762574527_nat_o: ( nat > nat > $o ) > ( ( nat > $o ) > ( nat > $o ) > $o ) > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Nat__Onat_001t__Nat__Onat_001_Eo_001_Eo,type,
% 5.45/5.62 bNF_re4705727531993890431at_o_o: ( nat > nat > $o ) > ( $o > $o > $o ) > ( nat > $o ) > ( nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 bNF_re6830278522597306478at_int: ( nat > nat > $o ) > ( product_prod_nat_nat > int > $o ) > ( nat > product_prod_nat_nat ) > ( nat > int ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001_062_It__Num__Onum_Mt__Int__Oint_J_001_062_It__Num__Onum_Mt__Int__Oint_J,type,
% 5.45/5.62 bNF_re8402795839162346335um_int: ( num > num > $o ) > ( ( num > int ) > ( num > int ) > $o ) > ( num > num > int ) > ( num > num > int ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Num__Onum_001t__Num__Onum_001t__Int__Oint_001t__Int__Oint,type,
% 5.45/5.62 bNF_re1822329894187522285nt_int: ( num > num > $o ) > ( int > int > $o ) > ( num > int ) > ( num > int ) > $o ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 bNF_re1494630372529172596at_o_o: ( product_prod_int_int > rat > $o ) > ( $o > $o > $o ) > ( product_prod_int_int > $o ) > ( rat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 bNF_re6644619430987730960nt_o_o: ( product_prod_nat_nat > int > $o ) > ( $o > $o > $o ) > ( product_prod_nat_nat > $o ) > ( int > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_BNF__Def_Orel__fun_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.45/5.62 bNF_re4555766996558763186at_nat: ( product_prod_nat_nat > int > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( int > nat ) > $o ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 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 ).
% 5.45/5.62
% 5.45/5.62 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__Nat__Onat_001t__Nat__Onat,type,
% 5.45/5.62 bNF_re8246922863344978751at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > ( nat > nat > $o ) > ( product_prod_nat_nat > nat ) > ( product_prod_nat_nat > nat ) > $o ).
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% 5.45/5.62 thf(sy_c_Filter_Ofinite__subsets__at__top_001t__Nat__Onat,type,
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% 5.45/5.62
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% 5.45/5.62 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.45/5.62 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
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% 5.45/5.62 thf(sy_c_Finite__Set_Ofinite_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,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
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% 5.45/5.62 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.45/5.62 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.45/5.62 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.45/5.62
% 5.45/5.62 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,
% 5.45/5.62 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Nat__Onat_001t__Int__Oint,type,
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% 5.45/5.62 thf(sy_c_Fun_Oid_001_Eo,type,
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% 5.45/5.62 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_062_It__Int__Oint_M_Eo_J_001_062_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.45/5.62 map_fu2496120808607739376eger_o: ( code_integer > int ) > ( ( int > $o ) > code_integer > $o ) > ( int > int > $o ) > code_integer > code_integer > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001_Eo_001_Eo,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Ointeger_001t__Int__Oint_001t__Int__Oint_001t__Code____Numeral__Ointeger,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_062_It__Nat__Onat_M_Eo_J_001_062_It__Code____Numeral__Onatural_M_Eo_J,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Code____Numeral__Onatural_001t__Nat__Onat_001_Eo_001_Eo,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001_062_It__Int__Oint_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_001_062_It__Int__Oint_Mt__Rat__Orat_J,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Rat__Orat,type,
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
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% 5.45/5.62
% 5.45/5.62 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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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.45/5.62 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.45/5.62 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
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% 5.45/5.62 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.45/5.62 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.45/5.62
% 5.45/5.62 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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% 5.45/5.62
% 5.45/5.62 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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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.45/5.62
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% 5.45/5.62 thf(sy_c_Fun__Def_Omax__weak,type,
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% 5.45/5.62 thf(sy_c_Fun__Def_Omin__strict,type,
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% 5.45/5.62 thf(sy_c_Fun__Def_Omin__weak,type,
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% 5.45/5.62 thf(sy_c_Fun__Def_Opair__leq,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Fun__Def_Opair__less,type,
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% 5.45/5.62 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_GCD_Obezw,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_GCD_Obezw__rel,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
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% 5.45/5.62
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% 5.45/5.62 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Ointrel,type,
% 5.45/5.62 intrel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Onat,type,
% 5.45/5.62 nat2: int > nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Opcr__int,type,
% 5.45/5.62 pcr_int: product_prod_nat_nat > int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Code____Numeral__Ointeger,type,
% 5.45/5.62 ring_11222124179247155820nteger: set_Code_integer ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Int__Oint,type,
% 5.45/5.62 ring_1_Ints_int: set_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_OInts_001t__Rat__Orat,type,
% 5.45/5.62 ring_1_Ints_rat: set_rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.45/5.62 ring_18347121197199848620nteger: int > code_integer ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.45/5.62 ring_1_of_int_int: int > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.45/5.62 ring_1_of_int_rat: int > rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 5.45/5.62 inf_in8201999774870019094_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 5.45/5.62 inf_in2641120393918057659_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 5.45/5.62 inf_in3295504058751909687_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 5.45/5.62 inf_in8045883074377559328_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_I_Eo_M_Eo_J,type,
% 5.45/5.62 inf_inf_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Int__Oint_M_Eo_J,type,
% 5.45/5.62 inf_inf_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 inf_inf_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 5.45/5.62 inf_inf_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.45/5.62 inf_inf_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 5.45/5.62 inf_in3604695632404883862_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 inf_in5163264567034779214_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 inf_inf_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001_062_Itf__a_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 5.45/5.62 inf_in8051596381320575356_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Assertions__Oassn,type,
% 5.45/5.62 inf_inf_assn: assn > assn > assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Int__Oint,type,
% 5.45/5.62 inf_inf_int: int > int > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 5.45/5.62 inf_inf_nat: nat > nat > nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Assertions__Oassn_J,type,
% 5.45/5.62 inf_inf_option_assn: option_assn > option_assn > option_assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.45/5.62 inf_inf_option_nat: option_nat > option_nat > option_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Product____Type__Ounit_J,type,
% 5.45/5.62 inf_in5800606384722953409t_unit: option_Product_unit > option_Product_unit > option_Product_unit ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.45/5.62 inf_in7812914138253463912et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.62 inf_in777885744494410645at_nat: option8963830502488799655at_nat > option8963830502488799655at_nat > option8963830502488799655at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Product____Type__Ounit,type,
% 5.45/5.62 inf_inf_Product_unit: product_unit > product_unit > product_unit ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Rat__Orat,type,
% 5.45/5.62 inf_inf_rat: rat > rat > rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_I_Eo_J,type,
% 5.45/5.62 inf_inf_set_o: set_o > set_o > set_o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.45/5.62 inf_in1364745209274528805nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Int__Oint_J,type,
% 5.45/5.62 inf_inf_set_int: set_int > set_int > set_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.45/5.62 inf_inf_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.45/5.62 inf_inf_set_nat: set_nat > set_nat > set_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 5.45/5.62 inf_in8806012763027673301nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 5.45/5.62 inf_in3088352823822785602et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 5.45/5.62 inf_in1768905781608824518et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 5.45/5.62 inf_in2576786181675586251nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.45/5.62 inf_in2269163501485487111nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.45/5.62 inf_in1697001100524423349at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.45/5.62 inf_in2572325071724192079at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 inf_in4302113700860409141at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 inf_in7913087082777306421at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.62 inf_in3493107508024165057it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Rat__Orat_J,type,
% 5.45/5.62 inf_inf_set_rat: set_rat > set_rat > set_rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.45/5.62 inf_inf_set_set_nat: set_set_nat > set_set_nat > set_set_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Assertions__Oassn,type,
% 5.45/5.62 semila8603258263270017530r_assn: ( assn > assn > assn ) > assn > ( assn > assn > $o ) > ( assn > assn > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.45/5.62 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_I_Eo_J,type,
% 5.45/5.62 semila2554085542299052326_set_o: ( set_o > set_o > set_o ) > set_o > ( set_o > set_o > $o ) > ( set_o > set_o > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Int__Oint_J,type,
% 5.45/5.62 semila6712789903965657268et_int: ( set_int > set_int > set_int ) > set_int > ( set_int > set_int > $o ) > ( set_int > set_int > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.45/5.62 semila1667268886620078168et_nat: ( set_nat > set_nat > set_nat ) > set_nat > ( set_nat > set_nat > $o ) > ( set_nat > set_nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.45/5.62 semila5207306265035627125at_nat: ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ) > set_Pr8551490117392284871at_nat > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > ( set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.45/5.62 semila4918476307565957903at_nat: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ) > set_Pr1261947904930325089at_nat > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 semila1307241728879085301at_nat: ( set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ) > set_Pr8693737435421807431at_nat > ( set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > $o ) > ( set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 semila6534579987270727413at_nat: ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ) > set_Pr4329608150637261639at_nat > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > ( set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > $o ) > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su600977994968626096_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su6535292691877529429_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su1630790145277462993_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_M_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su4182031696650224058_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_I_Eo_M_Eo_J,type,
% 5.45/5.62 sup_sup_o_o: ( $o > $o ) > ( $o > $o ) > $o > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Int__Oint_M_Eo_J,type,
% 5.45/5.62 sup_sup_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__List__Olist_It__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 sup_sup_list_nat_o: ( list_nat > $o ) > ( list_nat > $o ) > list_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su2200014604384089602_nat_o: ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > ( multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ) > multis2468970476368604999at_nat > multis2468970476368604999at_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J,type,
% 5.45/5.62 sup_sup_nat_nat_o: ( nat > nat > $o ) > ( nat > nat > $o ) > nat > nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.45/5.62 sup_sup_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 5.45/5.62 sup_su8463660629351352368_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_M_Eo_J,type,
% 5.45/5.62 sup_su6256023009775730178_nat_o: ( produc4166570645942440679at_nat > $o ) > ( produc4166570645942440679at_nat > $o ) > produc4166570645942440679at_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su362511073950362882_nat_o: ( 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 > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 sup_su798857527126471912_nat_o: ( product_prod_nat_nat > $o ) > ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__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_M_Eo_J,type,
% 5.45/5.62 sup_su8986005896011022210_nat_o: ( produc859450856879609959at_nat > $o ) > ( produc859450856879609959at_nat > $o ) > produc859450856879609959at_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__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_M_Eo_J,type,
% 5.45/5.62 sup_su2080679670758317954_nat_o: ( produc3843707927480180839at_nat > $o ) > ( produc3843707927480180839at_nat > $o ) > produc3843707927480180839at_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
% 5.45/5.62 sup_sup_set_nat_o: ( set_nat > $o ) > ( set_nat > $o ) > set_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_062_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su7519161239522478338_nat_o: ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > ( set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ) > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001_062_Itf__a_M_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_M_Eo_J_J,type,
% 5.45/5.62 sup_su2191776239474528790_nat_o: ( a > produc6653097349344004940it_nat > $o ) > ( a > produc6653097349344004940it_nat > $o ) > a > produc6653097349344004940it_nat > $o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Assertions__Oassn,type,
% 5.45/5.62 sup_sup_assn: assn > assn > assn ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Int__Oint,type,
% 5.45/5.62 sup_sup_int: int > int > int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.45/5.62 sup_sup_nat: nat > nat > nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.45/5.62 sup_sup_option_nat: option_nat > option_nat > option_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.45/5.62 sup_su3598758113090618626et_nat: option_set_nat > option_set_nat > option_set_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J_J,type,
% 5.45/5.62 sup_su5873096292857799009at_nat: option2498585697089621389at_nat > option2498585697089621389at_nat > option2498585697089621389at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__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_J_J,type,
% 5.45/5.62 sup_su1419176701018045153at_nat: option2158460348403737357at_nat > option2158460348403737357at_nat > option2158460348403737357at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Option__Ooption_It__Set__Oset_It__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_J_J,type,
% 5.45/5.62 sup_su2273273666271716065at_nat: option1583680563626158861at_nat > option1583680563626158861at_nat > option1583680563626158861at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Product____Type__Ounit,type,
% 5.45/5.62 sup_sup_Product_unit: product_unit > product_unit > product_unit ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Rat__Orat,type,
% 5.45/5.62 sup_sup_rat: rat > rat > rat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_I_Eo_J,type,
% 5.45/5.62 sup_sup_set_o: set_o > set_o > set_o ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.45/5.62 sup_su848401254843788991nteger: set_Code_integer > set_Code_integer > set_Code_integer ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Int__Oint_J,type,
% 5.45/5.62 sup_sup_set_int: set_int > set_int > set_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__List__Olist_It__Nat__Onat_J_J,type,
% 5.45/5.62 sup_sup_set_list_nat: set_list_nat > set_list_nat > set_list_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.45/5.62 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Num__Onum_J,type,
% 5.45/5.62 sup_sup_set_num: set_num > set_num > set_num ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 5.45/5.62 sup_su3298353300217089135nt_int: set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int > set_Pr1872883991513573699nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J_J,type,
% 5.45/5.62 sup_su8975264963432250076et_nat: set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat > set_Pr8536935166611901872et_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
% 5.45/5.62 sup_su7128418612487073120et_nat: set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat > set_Pr3286484037609594932et_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J_J,type,
% 5.45/5.62 sup_su3382966977382714213nt_int: set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int > set_Pr9222295170931077689nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.45/5.62 sup_su6024340866399070445nt_int: set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int > set_Pr958786334691620121nt_int ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_J,type,
% 5.45/5.62 sup_su3035147773818789531at_nat: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.45/5.62 sup_su6327502436637775413at_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 sup_su718114333110466843at_nat: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__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_J,type,
% 5.45/5.62 sup_su5525570899277871387at_nat: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.62 sup_su3211442154794319707it_nat: set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat > set_Pr7098220151150636591it_nat ).
% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Assertions__Oassn,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Nat__Onat,type,
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% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Product____Type__Ounit,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Rat__Orat,type,
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% 5.45/5.62
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_Lattices__Big_Osemilattice__order__set_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.45/5.62
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Oappend_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Obutlast_001t__Nat__Onat,type,
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% 5.45/5.62 thf(sy_c_List_Oenumerate_001_Eo,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Oenumerate_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Oenumerate_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Ofilter_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Olast_001t__Nat__Onat,type,
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% 5.45/5.62
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% 5.45/5.62
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
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% 5.45/5.62
% 5.45/5.62 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Onth_001_Eo,type,
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% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Onth_001t__Nat__Onat,type,
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% 5.45/5.63
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% 5.45/5.63 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Oproduct_001t__Int__Oint_001_Eo,type,
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% 5.45/5.63 thf(sy_c_List_Oproduct_001t__Int__Oint_001t__Nat__Onat,type,
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% 5.45/5.63 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_List_Orotate1_001t__Nat__Onat,type,
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% 5.45/5.63 thf(sy_c_List_Osorted__wrt_001_Eo,type,
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% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Nat__Onat_001t__Num__Onum,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Assertions__Oassn_J_001t__Assertions__Oassn,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Nat__Onat_J_001t__Nat__Onat,type,
% 5.45/5.63 case_o7429725398727453821at_nat: option_nat > ( nat > option_nat ) > option_nat > option_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 5.45/5.63 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Omap__option_001t__Num__Onum_001t__Num__Onum,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63
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% 5.45/5.63 produc4111701587417901774et_int: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int ) > produc7773217078559923341nt_int > set_int ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.45/5.63 produc3577156405726439208et_nat: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat ) > produc7773217078559923341nt_int > set_set_nat ).
% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J_J,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001_Eo,type,
% 5.45/5.63 produc1437786849005270451_nat_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_001t__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 5.45/5.63 produc4058941399401191971et_nat: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > produc3925858234332021118et_nat ) > produc3925858234332021118et_nat > produc3925858234332021118et_nat ).
% 5.45/5.63
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% 5.45/5.63 produc7715693535893868691_set_o: ( ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o ) > produc3925858234332021118et_nat > set_o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.45/5.63 produc8492565224438309093nt_int: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > produc2285326912895808259nt_int ) > produc2285326912895808259nt_int > produc2285326912895808259nt_int ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.45/5.63 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.45/5.63 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.45/5.63 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.45/5.63
% 5.45/5.63 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,
% 5.45/5.63 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.45/5.63
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% 5.45/5.63 produc7488178964372371019it_nat: ( heap_e7401611519738050253t_unit > nat > option8956607266484857688it_nat ) > produc6653097349344004940it_nat > option8956607266484857688it_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_001t__Nat__Onat_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.63 produc5645566021302314940it_nat: ( heap_e7401611519738050253t_unit > nat > option3562590408128118217it_nat ) > produc6653097349344004940it_nat > option3562590408128118217it_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.45/5.63 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.45/5.63 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 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,
% 5.45/5.63 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.45/5.63
% 5.45/5.63 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,
% 5.45/5.63 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.45/5.63 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.45/5.63 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.45/5.63 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.45/5.63 produc6189476227299908564et_nat: ( nat > nat > set_nat ) > product_prod_nat_nat > set_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.45/5.63 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.45/5.63
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Int__Oint_J_001t__Set__Oset_It__Int__Oint_J_001_Eo,type,
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% 5.45/5.63
% 5.45/5.63 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Set__Oset_It__Nat__Onat_J_001t__Set__Oset_It__Nat__Onat_J_001_Eo,type,
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% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_M_Eo_J_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Set__Oset_It__Nat__Onat_J_J_J,type,
% 5.45/5.63 member1996754912294343701et_nat: produc3925858234332021118et_nat > set_Pr3286484037609594932et_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_I_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_Mt__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_J,type,
% 5.45/5.63 member7618704894036264090nt_int: produc2285326912895808259nt_int > set_Pr9222295170931077689nt_int > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.45/5.63 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_Mt__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.63 member6689249552917799696at_nat: produc4166570645942440679at_nat > set_Pr8551490117392284871at_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.45/5.63 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.45/5.63 member8206827879206165904at_nat: produc859450856879609959at_nat > set_Pr8693737435421807431at_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Code____Numeral__Ointeger_J_Mt__Set__Oset_It__Code____Numeral__Ointeger_J_J,type,
% 5.45/5.63 member4307123515891402160nteger: produc6491284506569428743nteger > set_Pr7577011563204128103nteger > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Int__Oint_J_Mt__Set__Oset_It__Int__Oint_J_J,type,
% 5.45/5.63 member2572552093476627150et_int: produc2115011035271226405et_int > set_Pr2522554150109002629et_int > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Nat__Onat_J_Mt__Set__Oset_It__Nat__Onat_J_J,type,
% 5.45/5.63 member8277197624267554838et_nat: produc7819656566062154093et_nat > set_Pr5488025237498180813et_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_J,type,
% 5.45/5.63 member444158400953824016od_o_o: produc2934264451710624999od_o_o > set_Pr1932065953672099015od_o_o > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_It__Set__Oset_It__Product____Type__Oprod_I_Eo_M_Eo_J_J_Mt__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J,type,
% 5.45/5.63 member4095101504841534314at_nat: produc732395585841259969at_nat > set_Pr457366540195662369at_nat > $o ).
% 5.45/5.63
% 5.45/5.63 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,
% 5.45/5.63 member8757157785044589968at_nat: produc3843707927480180839at_nat > set_Pr4329608150637261639at_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J,type,
% 5.45/5.63 member4554412811331277712it_nat: produc3260487557148687353it_nat > set_Pr7098220151150636591it_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Rat__Orat,type,
% 5.45/5.63 member_rat: rat > set_rat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.45/5.63 member_set_int: set_int > set_set_int > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.45/5.63 member_set_nat: set_nat > set_set_nat > $o ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_P,type,
% 5.45/5.63 p: assn ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_Q,type,
% 5.45/5.63 q: a > assn ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_R,type,
% 5.45/5.63 r: assn ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_as1____,type,
% 5.45/5.63 as1: set_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_as2____,type,
% 5.45/5.63 as2: set_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_as____,type,
% 5.45/5.63 as: set_nat ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_c,type,
% 5.45/5.63 c: heap_Time_Heap_a ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_h_H____,type,
% 5.45/5.63 h: heap_e7401611519738050253t_unit ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_h____,type,
% 5.45/5.63 h2: heap_e7401611519738050253t_unit ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_r____,type,
% 5.45/5.63 r2: a ).
% 5.45/5.63
% 5.45/5.63 thf(sy_v_t____,type,
% 5.45/5.63 t: nat ).
% 5.45/5.63
% 5.45/5.63 % Relevant facts (9692)
% 5.45/5.63 thf(fact_0_DJ,axiom,
% 5.45/5.63 ( ( inf_inf_set_nat @ as1 @ as2 )
% 5.45/5.63 = bot_bot_set_nat ) ).
% 5.45/5.63
% 5.45/5.63 % DJ
% 5.45/5.63 thf(fact_1__092_060open_062_Ih_H_M_Aas2_J_A_092_060Turnstile_062_AR_092_060close_062,axiom,
% 5.45/5.63 rep_assn @ r @ ( produc7507926704131184380et_nat @ h @ as2 ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>(h', as2) \<Turnstile> R\<close>
% 5.45/5.63 thf(fact_2_M2,axiom,
% 5.45/5.63 rep_assn @ r @ ( produc7507926704131184380et_nat @ h2 @ as2 ) ).
% 5.45/5.63
% 5.45/5.63 % M2
% 5.45/5.63 thf(fact_3_DJN,axiom,
% 5.45/5.63 ( ( inf_inf_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) @ as2 )
% 5.45/5.63 = bot_bot_set_nat ) ).
% 5.45/5.63
% 5.45/5.63 % DJN
% 5.45/5.63 thf(fact_4__092_060open_062new__addrs_Ah_Aas_Ah_H_A_061_Anew__addrs_Ah_Aas1_Ah_H_A_092_060union_062_Aas2_092_060close_062,axiom,
% 5.45/5.63 ( ( hoare_new_addrs @ h2 @ as @ h )
% 5.45/5.63 = ( sup_sup_set_nat @ ( hoare_new_addrs @ h2 @ as1 @ h ) @ as2 ) ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>new_addrs h as h' = new_addrs h as1 h' \<union> as2\<close>
% 5.45/5.63 thf(fact_5_new__addr__refl,axiom,
% 5.45/5.63 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.63 ( ( hoare_new_addrs @ H @ As @ H )
% 5.45/5.63 = As ) ).
% 5.45/5.63
% 5.45/5.63 % new_addr_refl
% 5.45/5.63 thf(fact_6_M1,axiom,
% 5.45/5.63 rep_assn @ p @ ( produc7507926704131184380et_nat @ h2 @ as1 ) ).
% 5.45/5.63
% 5.45/5.63 % M1
% 5.45/5.63 thf(fact_7_MDL,axiom,
% 5.45/5.63 rep_assn @ ( q @ r2 ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as1 @ h ) ) ).
% 5.45/5.63
% 5.45/5.63 % MDL
% 5.45/5.63 thf(fact_8__092_060open_062_Ih_M_Aas_J_A_092_060Turnstile_062_AP_A_K_AR_092_060close_062,axiom,
% 5.45/5.63 rep_assn @ ( times_times_assn @ p @ r ) @ ( produc7507926704131184380et_nat @ h2 @ as ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>(h, as) \<Turnstile> P * R\<close>
% 5.45/5.63 thf(fact_9__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062as1_Aas2_O_A_092_060lbrakk_062as_A_061_Aas1_A_092_060union_062_Aas2_059_Aas1_A_092_060inter_062_Aas2_A_061_A_123_125_059_A_Ih_M_Aas1_J_A_092_060Turnstile_062_AP_059_A_Ih_M_Aas2_J_A_092_060Turnstile_062_AR_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.45/5.63 ~ ! [As1: set_nat,As2: set_nat] :
% 5.45/5.63 ( ( as
% 5.45/5.63 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 5.45/5.63 => ( ( ( inf_inf_set_nat @ As1 @ As2 )
% 5.45/5.63 = bot_bot_set_nat )
% 5.45/5.63 => ( ( rep_assn @ p @ ( produc7507926704131184380et_nat @ h2 @ As1 ) )
% 5.45/5.63 => ~ ( rep_assn @ r @ ( produc7507926704131184380et_nat @ h2 @ As2 ) ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>\<And>thesis. (\<And>as1 as2. \<lbrakk>as = as1 \<union> as2; as1 \<inter> as2 = {}; (h, as1) \<Turnstile> P; (h, as2) \<Turnstile> R\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.45/5.63 thf(fact_10_Rep__assn__inject,axiom,
% 5.45/5.63 ! [X: assn,Y: assn] :
% 5.45/5.63 ( ( ( rep_assn @ X )
% 5.45/5.63 = ( rep_assn @ Y ) )
% 5.45/5.63 = ( X = Y ) ) ).
% 5.45/5.63
% 5.45/5.63 % Rep_assn_inject
% 5.45/5.63 thf(fact_11_mod__h__bot__iff_I5_J,axiom,
% 5.45/5.63 ! [P: assn,Q: assn,H: heap_e7401611519738050253t_unit] :
% 5.45/5.63 ( ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.63 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.63 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_h_bot_iff(5)
% 5.45/5.63 thf(fact_12__092_060open_062relH_Aas2_Ah_Ah_H_092_060close_062,axiom,
% 5.45/5.63 relH @ as2 @ h2 @ h ).
% 5.45/5.63
% 5.45/5.63 % \<open>relH as2 h h'\<close>
% 5.45/5.63 thf(fact_13_prod_Oinject,axiom,
% 5.45/5.63 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3658429121746597890et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( ( produc5001842942810119800et_nat @ X1 @ X2 )
% 5.45/5.63 = ( produc5001842942810119800et_nat @ Y1 @ Y2 ) )
% 5.45/5.63 = ( ( X1 = Y1 )
% 5.45/5.63 & ( X2 = Y2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod.inject
% 5.45/5.63 thf(fact_14_prod_Oinject,axiom,
% 5.45/5.63 ! [X1: produc3658429121746597890et_nat > $o,X2: produc3925858234332021118et_nat,Y1: produc3658429121746597890et_nat > $o,Y2: produc3925858234332021118et_nat] :
% 5.45/5.63 ( ( ( produc2245416461498447860et_nat @ X1 @ X2 )
% 5.45/5.63 = ( produc2245416461498447860et_nat @ Y1 @ Y2 ) )
% 5.45/5.63 = ( ( X1 = Y1 )
% 5.45/5.63 & ( X2 = Y2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod.inject
% 5.45/5.63 thf(fact_15_prod_Oinject,axiom,
% 5.45/5.63 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X2: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc5700946648718959541nt_int @ X1 @ X2 )
% 5.45/5.63 = ( produc5700946648718959541nt_int @ Y1 @ Y2 ) )
% 5.45/5.63 = ( ( X1 = Y1 )
% 5.45/5.63 & ( X2 = Y2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod.inject
% 5.45/5.63 thf(fact_16_prod_Oinject,axiom,
% 5.45/5.63 ! [X1: int > option6357759511663192854e_term,X2: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc4305682042979456191nt_int @ X1 @ X2 )
% 5.45/5.63 = ( produc4305682042979456191nt_int @ Y1 @ Y2 ) )
% 5.45/5.63 = ( ( X1 = Y1 )
% 5.45/5.63 & ( X2 = Y2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod.inject
% 5.45/5.63 thf(fact_17_prod_Oinject,axiom,
% 5.45/5.63 ! [X1: a,X2: produc6653097349344004940it_nat,Y1: a,Y2: produc6653097349344004940it_nat] :
% 5.45/5.63 ( ( ( produc9178034014595674355it_nat @ X1 @ X2 )
% 5.45/5.63 = ( produc9178034014595674355it_nat @ Y1 @ Y2 ) )
% 5.45/5.63 = ( ( X1 = Y1 )
% 5.45/5.63 & ( X2 = Y2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod.inject
% 5.45/5.63 thf(fact_18_old_Oprod_Oinject,axiom,
% 5.45/5.63 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 5.45/5.63 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 5.45/5.63 = ( ( A = A2 )
% 5.45/5.63 & ( B = B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.inject
% 5.45/5.63 thf(fact_19_old_Oprod_Oinject,axiom,
% 5.45/5.63 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 5.45/5.63 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 5.45/5.63 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 5.45/5.63 = ( ( A = A2 )
% 5.45/5.63 & ( B = B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.inject
% 5.45/5.63 thf(fact_20_old_Oprod_Oinject,axiom,
% 5.45/5.63 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.45/5.63 = ( produc5700946648718959541nt_int @ A2 @ B2 ) )
% 5.45/5.63 = ( ( A = A2 )
% 5.45/5.63 & ( B = B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.inject
% 5.45/5.63 thf(fact_21_old_Oprod_Oinject,axiom,
% 5.45/5.63 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.45/5.63 = ( produc4305682042979456191nt_int @ A2 @ B2 ) )
% 5.45/5.63 = ( ( A = A2 )
% 5.45/5.63 & ( B = B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.inject
% 5.45/5.63 thf(fact_22_old_Oprod_Oinject,axiom,
% 5.45/5.63 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 5.45/5.63 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 5.45/5.63 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 5.45/5.63 = ( ( A = A2 )
% 5.45/5.63 & ( B = B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.inject
% 5.45/5.63 thf(fact_23_mod__starD,axiom,
% 5.45/5.63 ! [A3: assn,B3: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( rep_assn @ ( times_times_assn @ A3 @ B3 ) @ H )
% 5.45/5.63 => ? [H1: produc3658429121746597890et_nat,H2: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( rep_assn @ A3 @ H1 )
% 5.45/5.63 & ( rep_assn @ B3 @ H2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_starD
% 5.45/5.63 thf(fact_24_mod__starE,axiom,
% 5.45/5.63 ! [A: assn,B: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( rep_assn @ ( times_times_assn @ A @ B ) @ H )
% 5.45/5.63 => ~ ( ? [X_1: produc3658429121746597890et_nat] : ( rep_assn @ A @ X_1 )
% 5.45/5.63 => ! [H_2: produc3658429121746597890et_nat] :
% 5.45/5.63 ~ ( rep_assn @ B @ H_2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_starE
% 5.45/5.63 thf(fact_25_assms,axiom,
% 5.45/5.63 hoare_hoare_triple_a @ p @ c @ q ).
% 5.45/5.63
% 5.45/5.63 % assms
% 5.45/5.63 thf(fact_26__092_060open_062lim_Ah_A_092_060le_062_Alim_Ah_H_092_060close_062,axiom,
% 5.45/5.63 ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ h ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>lim h \<le> lim h'\<close>
% 5.45/5.63 thf(fact_27__092_060open_062as_A_061_Aas1_A_092_060union_062_Aas2_092_060close_062,axiom,
% 5.45/5.63 ( as
% 5.45/5.63 = ( sup_sup_set_nat @ as1 @ as2 ) ) ).
% 5.45/5.63
% 5.45/5.63 % \<open>as = as1 \<union> as2\<close>
% 5.45/5.63 thf(fact_28_mod__h__bot__indep,axiom,
% 5.45/5.63 ! [P: assn,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 5.45/5.63 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.63 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ bot_bot_set_nat ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_h_bot_indep
% 5.45/5.63 thf(fact_29_relH__dist__union,axiom,
% 5.45/5.63 ! [As: set_nat,As3: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 5.45/5.63 ( ( relH @ ( sup_sup_set_nat @ As @ As3 ) @ H @ H3 )
% 5.45/5.63 = ( ( relH @ As @ H @ H3 )
% 5.45/5.63 & ( relH @ As3 @ H @ H3 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % relH_dist_union
% 5.45/5.63 thf(fact_30_times__assn__raw_Ocases,axiom,
% 5.45/5.63 ! [X: produc2732055786443039994et_nat] :
% 5.45/5.63 ~ ! [P2: produc3658429121746597890et_nat > $o,Q2: produc3658429121746597890et_nat > $o,H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.63 ( X
% 5.45/5.63 != ( produc2245416461498447860et_nat @ P2 @ ( produc5001842942810119800et_nat @ Q2 @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % times_assn_raw.cases
% 5.45/5.63 thf(fact_31_relH__sym,axiom,
% 5.45/5.63 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 5.45/5.63 ( ( relH @ As @ H @ H3 )
% 5.45/5.63 => ( relH @ As @ H3 @ H ) ) ).
% 5.45/5.63
% 5.45/5.63 % relH_sym
% 5.45/5.63 thf(fact_32_relH__trans,axiom,
% 5.45/5.63 ! [As: set_nat,H12: heap_e7401611519738050253t_unit,H22: heap_e7401611519738050253t_unit,H32: heap_e7401611519738050253t_unit] :
% 5.45/5.63 ( ( relH @ As @ H12 @ H22 )
% 5.45/5.63 => ( ( relH @ As @ H22 @ H32 )
% 5.45/5.63 => ( relH @ As @ H12 @ H32 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % relH_trans
% 5.45/5.63 thf(fact_33_mod__relH,axiom,
% 5.45/5.63 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,P: assn] :
% 5.45/5.63 ( ( relH @ As @ H @ H3 )
% 5.45/5.63 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.63 = ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_relH
% 5.45/5.63 thf(fact_34_hoare__triple__preI,axiom,
% 5.45/5.63 ! [P: assn,C: heap_Time_Heap_a,Q: a > assn] :
% 5.45/5.63 ( ! [H4: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( rep_assn @ P @ H4 )
% 5.45/5.63 => ( hoare_hoare_triple_a @ P @ C @ Q ) )
% 5.45/5.63 => ( hoare_hoare_triple_a @ P @ C @ Q ) ) ).
% 5.45/5.63
% 5.45/5.63 % hoare_triple_preI
% 5.45/5.63 thf(fact_35_mod__star__conv,axiom,
% 5.45/5.63 ! [A3: assn,B3: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( rep_assn @ ( times_times_assn @ A3 @ B3 ) @ H )
% 5.45/5.63 = ( ? [Hr: heap_e7401611519738050253t_unit,As12: set_nat,As22: set_nat] :
% 5.45/5.63 ( ( H
% 5.45/5.63 = ( produc7507926704131184380et_nat @ Hr @ ( sup_sup_set_nat @ As12 @ As22 ) ) )
% 5.45/5.63 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 5.45/5.63 = bot_bot_set_nat )
% 5.45/5.63 & ( rep_assn @ A3 @ ( produc7507926704131184380et_nat @ Hr @ As12 ) )
% 5.45/5.63 & ( rep_assn @ B3 @ ( produc7507926704131184380et_nat @ Hr @ As22 ) ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % mod_star_conv
% 5.45/5.63 thf(fact_36_star__assnI,axiom,
% 5.45/5.63 ! [P: assn,H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,As3: set_nat] :
% 5.45/5.63 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.63 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H @ As3 ) )
% 5.45/5.63 => ( ( ( inf_inf_set_nat @ As @ As3 )
% 5.45/5.63 = bot_bot_set_nat )
% 5.45/5.63 => ( rep_assn @ ( times_times_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H @ ( sup_sup_set_nat @ As @ As3 ) ) ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % star_assnI
% 5.45/5.63 thf(fact_37_prod__induct4,axiom,
% 5.45/5.63 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 5.45/5.63 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C2: heap_e7401611519738050253t_unit,D: set_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ ( produc7507926704131184380et_nat @ C2 @ D ) ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct4
% 5.45/5.63 thf(fact_38_prod__induct3,axiom,
% 5.45/5.63 ! [P: produc3925858234332021118et_nat > $o,X: produc3925858234332021118et_nat] :
% 5.45/5.63 ( ! [A4: produc3658429121746597890et_nat > $o,B4: heap_e7401611519738050253t_unit,C2: set_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B4 @ C2 ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct3
% 5.45/5.63 thf(fact_39_prod__induct3,axiom,
% 5.45/5.63 ! [P: produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat] :
% 5.45/5.63 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C2: produc3658429121746597890et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ C2 ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct3
% 5.45/5.63 thf(fact_40_prod__induct3,axiom,
% 5.45/5.63 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 5.45/5.63 ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C2 ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct3
% 5.45/5.63 thf(fact_41_prod__induct3,axiom,
% 5.45/5.63 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 5.45/5.63 ( ! [A4: int > option6357759511663192854e_term,B4: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C2 ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct3
% 5.45/5.63 thf(fact_42_prod__induct3,axiom,
% 5.45/5.63 ! [P: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 5.45/5.63 ( ! [A4: a,B4: heap_e7401611519738050253t_unit,C2: nat] : ( P @ ( produc9178034014595674355it_nat @ A4 @ ( produc584006145561248582it_nat @ B4 @ C2 ) ) )
% 5.45/5.63 => ( P @ X ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_induct3
% 5.45/5.63 thf(fact_43_prod__cases4,axiom,
% 5.45/5.63 ! [Y: produc2732055786443039994et_nat] :
% 5.45/5.63 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C2: heap_e7401611519738050253t_unit,D: set_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ ( produc7507926704131184380et_nat @ C2 @ D ) ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases4
% 5.45/5.63 thf(fact_44_prod__cases3,axiom,
% 5.45/5.63 ! [Y: produc3925858234332021118et_nat] :
% 5.45/5.63 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: heap_e7401611519738050253t_unit,C2: set_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc5001842942810119800et_nat @ A4 @ ( produc7507926704131184380et_nat @ B4 @ C2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases3
% 5.45/5.63 thf(fact_45_prod__cases3,axiom,
% 5.45/5.63 ! [Y: produc2732055786443039994et_nat] :
% 5.45/5.63 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat > $o,C2: produc3658429121746597890et_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc2245416461498447860et_nat @ A4 @ ( produc5001842942810119800et_nat @ B4 @ C2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases3
% 5.45/5.63 thf(fact_46_prod__cases3,axiom,
% 5.45/5.63 ! [Y: produc2285326912895808259nt_int] :
% 5.45/5.63 ~ ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: int,C2: int] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc5700946648718959541nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases3
% 5.45/5.63 thf(fact_47_prod__cases3,axiom,
% 5.45/5.63 ! [Y: produc7773217078559923341nt_int] :
% 5.45/5.63 ~ ! [A4: int > option6357759511663192854e_term,B4: int,C2: int] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc4305682042979456191nt_int @ A4 @ ( product_Pair_int_int @ B4 @ C2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases3
% 5.45/5.63 thf(fact_48_prod__cases3,axiom,
% 5.45/5.63 ! [Y: produc3260487557148687353it_nat] :
% 5.45/5.63 ~ ! [A4: a,B4: heap_e7401611519738050253t_unit,C2: nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc9178034014595674355it_nat @ A4 @ ( produc584006145561248582it_nat @ B4 @ C2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases3
% 5.45/5.63 thf(fact_49_Pair__inject,axiom,
% 5.45/5.63 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3658429121746597890et_nat] :
% 5.45/5.63 ( ( ( produc5001842942810119800et_nat @ A @ B )
% 5.45/5.63 = ( produc5001842942810119800et_nat @ A2 @ B2 ) )
% 5.45/5.63 => ~ ( ( A = A2 )
% 5.45/5.63 => ( B != B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Pair_inject
% 5.45/5.63 thf(fact_50_Pair__inject,axiom,
% 5.45/5.63 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,A2: produc3658429121746597890et_nat > $o,B2: produc3925858234332021118et_nat] :
% 5.45/5.63 ( ( ( produc2245416461498447860et_nat @ A @ B )
% 5.45/5.63 = ( produc2245416461498447860et_nat @ A2 @ B2 ) )
% 5.45/5.63 => ~ ( ( A = A2 )
% 5.45/5.63 => ( B != B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Pair_inject
% 5.45/5.63 thf(fact_51_Pair__inject,axiom,
% 5.45/5.63 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A2: produc8551481072490612790e_term > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.45/5.63 = ( produc5700946648718959541nt_int @ A2 @ B2 ) )
% 5.45/5.63 => ~ ( ( A = A2 )
% 5.45/5.63 => ( B != B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Pair_inject
% 5.45/5.63 thf(fact_52_Pair__inject,axiom,
% 5.45/5.63 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A2: int > option6357759511663192854e_term,B2: product_prod_int_int] :
% 5.45/5.63 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.45/5.63 = ( produc4305682042979456191nt_int @ A2 @ B2 ) )
% 5.45/5.63 => ~ ( ( A = A2 )
% 5.45/5.63 => ( B != B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Pair_inject
% 5.45/5.63 thf(fact_53_Pair__inject,axiom,
% 5.45/5.63 ! [A: a,B: produc6653097349344004940it_nat,A2: a,B2: produc6653097349344004940it_nat] :
% 5.45/5.63 ( ( ( produc9178034014595674355it_nat @ A @ B )
% 5.45/5.63 = ( produc9178034014595674355it_nat @ A2 @ B2 ) )
% 5.45/5.63 => ~ ( ( A = A2 )
% 5.45/5.63 => ( B != B2 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Pair_inject
% 5.45/5.63 thf(fact_54_prod__cases,axiom,
% 5.45/5.63 ! [P: produc3925858234332021118et_nat > $o,P3: produc3925858234332021118et_nat] :
% 5.45/5.63 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] : ( P @ ( produc5001842942810119800et_nat @ A4 @ B4 ) )
% 5.45/5.63 => ( P @ P3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases
% 5.45/5.63 thf(fact_55_prod__cases,axiom,
% 5.45/5.63 ! [P: produc2732055786443039994et_nat > $o,P3: produc2732055786443039994et_nat] :
% 5.45/5.63 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] : ( P @ ( produc2245416461498447860et_nat @ A4 @ B4 ) )
% 5.45/5.63 => ( P @ P3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases
% 5.45/5.63 thf(fact_56_prod__cases,axiom,
% 5.45/5.63 ! [P: produc2285326912895808259nt_int > $o,P3: produc2285326912895808259nt_int] :
% 5.45/5.63 ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 5.45/5.63 => ( P @ P3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases
% 5.45/5.63 thf(fact_57_prod__cases,axiom,
% 5.45/5.63 ! [P: produc7773217078559923341nt_int > $o,P3: produc7773217078559923341nt_int] :
% 5.45/5.63 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.45/5.63 => ( P @ P3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases
% 5.45/5.63 thf(fact_58_prod__cases,axiom,
% 5.45/5.63 ! [P: produc3260487557148687353it_nat > $o,P3: produc3260487557148687353it_nat] :
% 5.45/5.63 ( ! [A4: a,B4: produc6653097349344004940it_nat] : ( P @ ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.45/5.63 => ( P @ P3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % prod_cases
% 5.45/5.63 thf(fact_59_surj__pair,axiom,
% 5.45/5.63 ! [P3: produc3925858234332021118et_nat] :
% 5.45/5.63 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 5.45/5.63 ( P3
% 5.45/5.63 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % surj_pair
% 5.45/5.63 thf(fact_60_surj__pair,axiom,
% 5.45/5.63 ! [P3: produc2732055786443039994et_nat] :
% 5.45/5.63 ? [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 5.45/5.63 ( P3
% 5.45/5.63 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % surj_pair
% 5.45/5.63 thf(fact_61_surj__pair,axiom,
% 5.45/5.63 ! [P3: produc2285326912895808259nt_int] :
% 5.45/5.63 ? [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.45/5.63 ( P3
% 5.45/5.63 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % surj_pair
% 5.45/5.63 thf(fact_62_surj__pair,axiom,
% 5.45/5.63 ! [P3: produc7773217078559923341nt_int] :
% 5.45/5.63 ? [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.45/5.63 ( P3
% 5.45/5.63 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % surj_pair
% 5.45/5.63 thf(fact_63_surj__pair,axiom,
% 5.45/5.63 ! [P3: produc3260487557148687353it_nat] :
% 5.45/5.63 ? [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.45/5.63 ( P3
% 5.45/5.63 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) ) ).
% 5.45/5.63
% 5.45/5.63 % surj_pair
% 5.45/5.63 thf(fact_64_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.63 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_65_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: $o,P: $o > $o] :
% 5.45/5.63 ( ( member_o @ A @ ( collect_o @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_66_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.45/5.63 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_67_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: list_nat,P: list_nat > $o] :
% 5.45/5.63 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_68_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: set_nat,P: set_nat > $o] :
% 5.45/5.63 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_69_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: nat,P: nat > $o] :
% 5.45/5.63 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_70_mem__Collect__eq,axiom,
% 5.45/5.63 ! [A: int,P: int > $o] :
% 5.45/5.63 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.45/5.63 = ( P @ A ) ) ).
% 5.45/5.63
% 5.45/5.63 % mem_Collect_eq
% 5.45/5.63 thf(fact_71_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( collec3392354462482085612at_nat
% 5.45/5.63 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_72_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_o] :
% 5.45/5.63 ( ( collect_o
% 5.45/5.63 @ ^ [X4: $o] : ( member_o @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_73_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_Pr958786334691620121nt_int] :
% 5.45/5.63 ( ( collec213857154873943460nt_int
% 5.45/5.63 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_74_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_list_nat] :
% 5.45/5.63 ( ( collect_list_nat
% 5.45/5.63 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_75_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_set_nat] :
% 5.45/5.63 ( ( collect_set_nat
% 5.45/5.63 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_76_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_nat] :
% 5.45/5.63 ( ( collect_nat
% 5.45/5.63 @ ^ [X4: nat] : ( member_nat @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_77_Collect__mem__eq,axiom,
% 5.45/5.63 ! [A3: set_int] :
% 5.45/5.63 ( ( collect_int
% 5.45/5.63 @ ^ [X4: int] : ( member_int @ X4 @ A3 ) )
% 5.45/5.63 = A3 ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_mem_eq
% 5.45/5.63 thf(fact_78_Collect__cong,axiom,
% 5.45/5.63 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.63 ( ! [X3: product_prod_int_int] :
% 5.45/5.63 ( ( P @ X3 )
% 5.45/5.63 = ( Q @ X3 ) )
% 5.45/5.63 => ( ( collec213857154873943460nt_int @ P )
% 5.45/5.63 = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_cong
% 5.45/5.63 thf(fact_79_Collect__cong,axiom,
% 5.45/5.63 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.63 ( ! [X3: list_nat] :
% 5.45/5.63 ( ( P @ X3 )
% 5.45/5.63 = ( Q @ X3 ) )
% 5.45/5.63 => ( ( collect_list_nat @ P )
% 5.45/5.63 = ( collect_list_nat @ Q ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_cong
% 5.45/5.63 thf(fact_80_Collect__cong,axiom,
% 5.45/5.63 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.63 ( ! [X3: set_nat] :
% 5.45/5.63 ( ( P @ X3 )
% 5.45/5.63 = ( Q @ X3 ) )
% 5.45/5.63 => ( ( collect_set_nat @ P )
% 5.45/5.63 = ( collect_set_nat @ Q ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_cong
% 5.45/5.63 thf(fact_81_Collect__cong,axiom,
% 5.45/5.63 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.63 ( ! [X3: nat] :
% 5.45/5.63 ( ( P @ X3 )
% 5.45/5.63 = ( Q @ X3 ) )
% 5.45/5.63 => ( ( collect_nat @ P )
% 5.45/5.63 = ( collect_nat @ Q ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_cong
% 5.45/5.63 thf(fact_82_Collect__cong,axiom,
% 5.45/5.63 ! [P: int > $o,Q: int > $o] :
% 5.45/5.63 ( ! [X3: int] :
% 5.45/5.63 ( ( P @ X3 )
% 5.45/5.63 = ( Q @ X3 ) )
% 5.45/5.63 => ( ( collect_int @ P )
% 5.45/5.63 = ( collect_int @ Q ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % Collect_cong
% 5.45/5.63 thf(fact_83_old_Oprod_Oexhaust,axiom,
% 5.45/5.63 ! [Y: produc3925858234332021118et_nat] :
% 5.45/5.63 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc5001842942810119800et_nat @ A4 @ B4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.exhaust
% 5.45/5.63 thf(fact_84_old_Oprod_Oexhaust,axiom,
% 5.45/5.63 ! [Y: produc2732055786443039994et_nat] :
% 5.45/5.63 ~ ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc2245416461498447860et_nat @ A4 @ B4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.exhaust
% 5.45/5.63 thf(fact_85_old_Oprod_Oexhaust,axiom,
% 5.45/5.63 ! [Y: produc2285326912895808259nt_int] :
% 5.45/5.63 ~ ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc5700946648718959541nt_int @ A4 @ B4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.exhaust
% 5.45/5.63 thf(fact_86_old_Oprod_Oexhaust,axiom,
% 5.45/5.63 ! [Y: produc7773217078559923341nt_int] :
% 5.45/5.63 ~ ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc4305682042979456191nt_int @ A4 @ B4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.exhaust
% 5.45/5.63 thf(fact_87_old_Oprod_Oexhaust,axiom,
% 5.45/5.63 ! [Y: produc3260487557148687353it_nat] :
% 5.45/5.63 ~ ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.45/5.63 ( Y
% 5.45/5.63 != ( produc9178034014595674355it_nat @ A4 @ B4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % old.prod.exhaust
% 5.45/5.63 thf(fact_88_one__assn__raw_Ocases,axiom,
% 5.45/5.63 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.63 ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.63 ( X
% 5.45/5.63 != ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ).
% 5.45/5.63
% 5.45/5.63 % one_assn_raw.cases
% 5.45/5.63 thf(fact_89_assn__times__assoc,axiom,
% 5.45/5.63 ! [P: assn,Q: assn,R: assn] :
% 5.45/5.63 ( ( times_times_assn @ ( times_times_assn @ P @ Q ) @ R )
% 5.45/5.63 = ( times_times_assn @ P @ ( times_times_assn @ Q @ R ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % assn_times_assoc
% 5.45/5.63 thf(fact_90_assn__times__comm,axiom,
% 5.45/5.63 ( times_times_assn
% 5.45/5.63 = ( ^ [P4: assn,Q3: assn] : ( times_times_assn @ Q3 @ P4 ) ) ) ).
% 5.45/5.63
% 5.45/5.63 % assn_times_comm
% 5.45/5.63 thf(fact_91_Int__Un__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( sup_su6327502436637775413at_nat @ T @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(4)
% 5.45/5.63 thf(fact_92_Int__Un__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( sup_su718114333110466843at_nat @ T @ ( inf_in4302113700860409141at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(4)
% 5.45/5.63 thf(fact_93_Int__Un__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( sup_su3035147773818789531at_nat @ T @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(4)
% 5.45/5.63 thf(fact_94_Int__Un__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( sup_su5525570899277871387at_nat @ T @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(4)
% 5.45/5.63 thf(fact_95_Int__Un__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_nat,S: set_nat] :
% 5.45/5.63 ( ( sup_sup_set_nat @ T @ ( inf_inf_set_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(4)
% 5.45/5.63 thf(fact_96_Int__Un__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( sup_su6327502436637775413at_nat @ S @ ( inf_in2572325071724192079at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(3)
% 5.45/5.63 thf(fact_97_Int__Un__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( sup_su718114333110466843at_nat @ S @ ( inf_in4302113700860409141at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(3)
% 5.45/5.63 thf(fact_98_Int__Un__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( sup_su3035147773818789531at_nat @ S @ ( inf_in1697001100524423349at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(3)
% 5.45/5.63 thf(fact_99_Int__Un__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( sup_su5525570899277871387at_nat @ S @ ( inf_in7913087082777306421at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(3)
% 5.45/5.63 thf(fact_100_Int__Un__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_nat,T: set_nat] :
% 5.45/5.63 ( ( sup_sup_set_nat @ S @ ( inf_inf_set_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(3)
% 5.45/5.63 thf(fact_101_Int__Un__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(2)
% 5.45/5.63 thf(fact_102_Int__Un__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(2)
% 5.45/5.63 thf(fact_103_Int__Un__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(2)
% 5.45/5.63 thf(fact_104_Int__Un__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(2)
% 5.45/5.63 thf(fact_105_Int__Un__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_nat,T: set_nat] :
% 5.45/5.63 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(2)
% 5.45/5.63 thf(fact_106_Int__Un__eq_I1_J,axiom,
% 5.45/5.63 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ S @ T ) @ S )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(1)
% 5.45/5.63 thf(fact_107_Int__Un__eq_I1_J,axiom,
% 5.45/5.63 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ S @ T ) @ S )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(1)
% 5.45/5.63 thf(fact_108_Int__Un__eq_I1_J,axiom,
% 5.45/5.63 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ S @ T ) @ S )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(1)
% 5.45/5.63 thf(fact_109_Int__Un__eq_I1_J,axiom,
% 5.45/5.63 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ S @ T ) @ S )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(1)
% 5.45/5.63 thf(fact_110_Int__Un__eq_I1_J,axiom,
% 5.45/5.63 ! [S: set_nat,T: set_nat] :
% 5.45/5.63 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ S @ T ) @ S )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Int_Un_eq(1)
% 5.45/5.63 thf(fact_111_Un__Int__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( inf_in2572325071724192079at_nat @ T @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(4)
% 5.45/5.63 thf(fact_112_Un__Int__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( inf_in4302113700860409141at_nat @ T @ ( sup_su718114333110466843at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(4)
% 5.45/5.63 thf(fact_113_Un__Int__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( inf_in1697001100524423349at_nat @ T @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(4)
% 5.45/5.63 thf(fact_114_Un__Int__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( inf_in7913087082777306421at_nat @ T @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(4)
% 5.45/5.63 thf(fact_115_Un__Int__eq_I4_J,axiom,
% 5.45/5.63 ! [T: set_nat,S: set_nat] :
% 5.45/5.63 ( ( inf_inf_set_nat @ T @ ( sup_sup_set_nat @ S @ T ) )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(4)
% 5.45/5.63 thf(fact_116_Un__Int__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( inf_in2572325071724192079at_nat @ S @ ( sup_su6327502436637775413at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(3)
% 5.45/5.63 thf(fact_117_Un__Int__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( inf_in4302113700860409141at_nat @ S @ ( sup_su718114333110466843at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(3)
% 5.45/5.63 thf(fact_118_Un__Int__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.63 ( ( inf_in1697001100524423349at_nat @ S @ ( sup_su3035147773818789531at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(3)
% 5.45/5.63 thf(fact_119_Un__Int__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.63 ( ( inf_in7913087082777306421at_nat @ S @ ( sup_su5525570899277871387at_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(3)
% 5.45/5.63 thf(fact_120_Un__Int__eq_I3_J,axiom,
% 5.45/5.63 ! [S: set_nat,T: set_nat] :
% 5.45/5.63 ( ( inf_inf_set_nat @ S @ ( sup_sup_set_nat @ S @ T ) )
% 5.45/5.63 = S ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(3)
% 5.45/5.63 thf(fact_121_Un__Int__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.63 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ T )
% 5.45/5.63 = T ) ).
% 5.45/5.63
% 5.45/5.63 % Un_Int_eq(2)
% 5.45/5.63 thf(fact_122_Un__Int__eq_I2_J,axiom,
% 5.45/5.63 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.63 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ S @ T ) @ T )
% 5.45/5.64 = T ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(2)
% 5.45/5.64 thf(fact_123_Un__Int__eq_I2_J,axiom,
% 5.45/5.64 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ T )
% 5.45/5.64 = T ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(2)
% 5.45/5.64 thf(fact_124_Un__Int__eq_I2_J,axiom,
% 5.45/5.64 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ T )
% 5.45/5.64 = T ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(2)
% 5.45/5.64 thf(fact_125_Un__Int__eq_I2_J,axiom,
% 5.45/5.64 ! [S: set_nat,T: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ T )
% 5.45/5.64 = T ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(2)
% 5.45/5.64 thf(fact_126_Un__Int__eq_I1_J,axiom,
% 5.45/5.64 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) @ S )
% 5.45/5.64 = S ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(1)
% 5.45/5.64 thf(fact_127_Un__Int__eq_I1_J,axiom,
% 5.45/5.64 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ S @ T ) @ S )
% 5.45/5.64 = S ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(1)
% 5.45/5.64 thf(fact_128_Un__Int__eq_I1_J,axiom,
% 5.45/5.64 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) @ S )
% 5.45/5.64 = S ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(1)
% 5.45/5.64 thf(fact_129_Un__Int__eq_I1_J,axiom,
% 5.45/5.64 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) @ S )
% 5.45/5.64 = S ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(1)
% 5.45/5.64 thf(fact_130_Un__Int__eq_I1_J,axiom,
% 5.45/5.64 ! [S: set_nat,T: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ S @ T ) @ S )
% 5.45/5.64 = S ) ).
% 5.45/5.64
% 5.45/5.64 % Un_Int_eq(1)
% 5.45/5.64 thf(fact_131_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ( sup_su718114333110466843at_nat @ A3 @ B3 )
% 5.45/5.64 = bot_bo5327735625951526323at_nat )
% 5.45/5.64 = ( ( A3 = bot_bo5327735625951526323at_nat )
% 5.45/5.64 & ( B3 = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_132_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 5.45/5.64 = bot_bo8422036546324065075at_nat )
% 5.45/5.64 = ( ( A3 = bot_bo8422036546324065075at_nat )
% 5.45/5.64 & ( B3 = bot_bo8422036546324065075at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_133_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 5.45/5.64 = bot_bo228742789529271731at_nat )
% 5.45/5.64 = ( ( A3 = bot_bo228742789529271731at_nat )
% 5.45/5.64 & ( B3 = bot_bo228742789529271731at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_134_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ( sup_su6327502436637775413at_nat @ A3 @ B3 )
% 5.45/5.64 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 = ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 & ( B3 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_135_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( ( sup_sup_set_o @ A3 @ B3 )
% 5.45/5.64 = bot_bot_set_o )
% 5.45/5.64 = ( ( A3 = bot_bot_set_o )
% 5.45/5.64 & ( B3 = bot_bot_set_o ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_136_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( ( sup_sup_set_nat @ A3 @ B3 )
% 5.45/5.64 = bot_bot_set_nat )
% 5.45/5.64 = ( ( A3 = bot_bot_set_nat )
% 5.45/5.64 & ( B3 = bot_bot_set_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_137_Un__empty,axiom,
% 5.45/5.64 ! [A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( ( sup_sup_set_int @ A3 @ B3 )
% 5.45/5.64 = bot_bot_set_int )
% 5.45/5.64 = ( ( A3 = bot_bot_set_int )
% 5.45/5.64 & ( B3 = bot_bot_set_int ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_empty
% 5.45/5.64 thf(fact_138_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: assn,Y: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_139_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ ( sup_sup_Product_unit @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_140_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_141_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( inf_in4302113700860409141at_nat @ X @ ( sup_su718114333110466843at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_142_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_143_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_144_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_145_inf__sup__absorb,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_absorb
% 5.45/5.64 thf(fact_146_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: assn,Y: assn] :
% 5.45/5.64 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_147_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit] :
% 5.45/5.64 ( ( sup_sup_Product_unit @ X @ ( inf_inf_Product_unit @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_148_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_149_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ ( inf_in4302113700860409141at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_150_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_151_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_152_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_153_sup__inf__absorb,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_inf_absorb
% 5.45/5.64 thf(fact_154_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_155_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_156_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_157_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_158_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_o] :
% 5.45/5.64 ( ( sup_sup_set_o @ bot_bot_set_o @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_159_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ bot_bot_set_nat @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_160_sup__bot__left,axiom,
% 5.45/5.64 ! [X: set_int] :
% 5.45/5.64 ( ( sup_sup_set_int @ bot_bot_set_int @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_left
% 5.45/5.64 thf(fact_161_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: product_prod_int_int > $o] :
% 5.45/5.64 ( ( bot_bo1796632182523588997nt_int
% 5.45/5.64 = ( collec213857154873943460nt_int @ P ) )
% 5.45/5.64 = ( ! [X4: product_prod_int_int] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_162_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: list_nat > $o] :
% 5.45/5.64 ( ( bot_bot_set_list_nat
% 5.45/5.64 = ( collect_list_nat @ P ) )
% 5.45/5.64 = ( ! [X4: list_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_163_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: set_nat > $o] :
% 5.45/5.64 ( ( bot_bot_set_set_nat
% 5.45/5.64 = ( collect_set_nat @ P ) )
% 5.45/5.64 = ( ! [X4: set_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_164_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: product_prod_nat_nat > $o] :
% 5.45/5.64 ( ( bot_bo2099793752762293965at_nat
% 5.45/5.64 = ( collec3392354462482085612at_nat @ P ) )
% 5.45/5.64 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_165_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: $o > $o] :
% 5.45/5.64 ( ( bot_bot_set_o
% 5.45/5.64 = ( collect_o @ P ) )
% 5.45/5.64 = ( ! [X4: $o] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_166_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: nat > $o] :
% 5.45/5.64 ( ( bot_bot_set_nat
% 5.45/5.64 = ( collect_nat @ P ) )
% 5.45/5.64 = ( ! [X4: nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_167_empty__Collect__eq,axiom,
% 5.45/5.64 ! [P: int > $o] :
% 5.45/5.64 ( ( bot_bot_set_int
% 5.45/5.64 = ( collect_int @ P ) )
% 5.45/5.64 = ( ! [X4: int] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % empty_Collect_eq
% 5.45/5.64 thf(fact_168_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: product_prod_int_int > $o] :
% 5.45/5.64 ( ( ( collec213857154873943460nt_int @ P )
% 5.45/5.64 = bot_bo1796632182523588997nt_int )
% 5.45/5.64 = ( ! [X4: product_prod_int_int] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_169_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: list_nat > $o] :
% 5.45/5.64 ( ( ( collect_list_nat @ P )
% 5.45/5.64 = bot_bot_set_list_nat )
% 5.45/5.64 = ( ! [X4: list_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_170_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: set_nat > $o] :
% 5.45/5.64 ( ( ( collect_set_nat @ P )
% 5.45/5.64 = bot_bot_set_set_nat )
% 5.45/5.64 = ( ! [X4: set_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_171_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: product_prod_nat_nat > $o] :
% 5.45/5.64 ( ( ( collec3392354462482085612at_nat @ P )
% 5.45/5.64 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_172_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: $o > $o] :
% 5.45/5.64 ( ( ( collect_o @ P )
% 5.45/5.64 = bot_bot_set_o )
% 5.45/5.64 = ( ! [X4: $o] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_173_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: nat > $o] :
% 5.45/5.64 ( ( ( collect_nat @ P )
% 5.45/5.64 = bot_bot_set_nat )
% 5.45/5.64 = ( ! [X4: nat] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_174_Collect__empty__eq,axiom,
% 5.45/5.64 ! [P: int > $o] :
% 5.45/5.64 ( ( ( collect_int @ P )
% 5.45/5.64 = bot_bot_set_int )
% 5.45/5.64 = ( ! [X4: int] :
% 5.45/5.64 ~ ( P @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Collect_empty_eq
% 5.45/5.64 thf(fact_175_all__not__in__conv,axiom,
% 5.45/5.64 ! [A3: set_set_nat] :
% 5.45/5.64 ( ( ! [X4: set_nat] :
% 5.45/5.64 ~ ( member_set_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 = bot_bot_set_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % all_not_in_conv
% 5.45/5.64 thf(fact_176_all__not__in__conv,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ! [X4: product_prod_nat_nat] :
% 5.45/5.64 ~ ( member8440522571783428010at_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % all_not_in_conv
% 5.45/5.64 thf(fact_177_all__not__in__conv,axiom,
% 5.45/5.64 ! [A3: set_o] :
% 5.45/5.64 ( ( ! [X4: $o] :
% 5.45/5.64 ~ ( member_o @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % all_not_in_conv
% 5.45/5.64 thf(fact_178_all__not__in__conv,axiom,
% 5.45/5.64 ! [A3: set_nat] :
% 5.45/5.64 ( ( ! [X4: nat] :
% 5.45/5.64 ~ ( member_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % all_not_in_conv
% 5.45/5.64 thf(fact_179_all__not__in__conv,axiom,
% 5.45/5.64 ! [A3: set_int] :
% 5.45/5.64 ( ( ! [X4: int] :
% 5.45/5.64 ~ ( member_int @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.64
% 5.45/5.64 % all_not_in_conv
% 5.45/5.64 thf(fact_180_empty__iff,axiom,
% 5.45/5.64 ! [C: set_nat] :
% 5.45/5.64 ~ ( member_set_nat @ C @ bot_bot_set_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % empty_iff
% 5.45/5.64 thf(fact_181_empty__iff,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat] :
% 5.45/5.64 ~ ( member8440522571783428010at_nat @ C @ bot_bo2099793752762293965at_nat ) ).
% 5.45/5.64
% 5.45/5.64 % empty_iff
% 5.45/5.64 thf(fact_182_empty__iff,axiom,
% 5.45/5.64 ! [C: $o] :
% 5.45/5.64 ~ ( member_o @ C @ bot_bot_set_o ) ).
% 5.45/5.64
% 5.45/5.64 % empty_iff
% 5.45/5.64 thf(fact_183_empty__iff,axiom,
% 5.45/5.64 ! [C: nat] :
% 5.45/5.64 ~ ( member_nat @ C @ bot_bot_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % empty_iff
% 5.45/5.64 thf(fact_184_empty__iff,axiom,
% 5.45/5.64 ! [C: int] :
% 5.45/5.64 ~ ( member_int @ C @ bot_bot_set_int ) ).
% 5.45/5.64
% 5.45/5.64 % empty_iff
% 5.45/5.64 thf(fact_185_inf__right__idem,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y )
% 5.45/5.64 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_right_idem
% 5.45/5.64 thf(fact_186_inf__right__idem,axiom,
% 5.45/5.64 ! [X: assn,Y: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Y )
% 5.45/5.64 = ( inf_inf_assn @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_right_idem
% 5.45/5.64 thf(fact_187_inf__right__idem,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Y )
% 5.45/5.64 = ( inf_inf_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_right_idem
% 5.45/5.64 thf(fact_188_inf__right__idem,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Y )
% 5.45/5.64 = ( inf_inf_Product_unit @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_right_idem
% 5.45/5.64 thf(fact_189_inf__right__idem,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_right_idem
% 5.45/5.64 thf(fact_190_inf_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B )
% 5.45/5.64 = ( inf_inf_set_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.right_idem
% 5.45/5.64 thf(fact_191_inf_Oright__idem,axiom,
% 5.45/5.64 ! [A: assn,B: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ ( inf_inf_assn @ A @ B ) @ B )
% 5.45/5.64 = ( inf_inf_assn @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.right_idem
% 5.45/5.64 thf(fact_192_inf_Oright__idem,axiom,
% 5.45/5.64 ! [A: nat,B: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ B )
% 5.45/5.64 = ( inf_inf_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.right_idem
% 5.45/5.64 thf(fact_193_inf_Oright__idem,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ A @ B ) @ B )
% 5.45/5.64 = ( inf_inf_Product_unit @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.right_idem
% 5.45/5.64 thf(fact_194_inf_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.right_idem
% 5.45/5.64 thf(fact_195_inf__left__idem,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_idem
% 5.45/5.64 thf(fact_196_inf__left__idem,axiom,
% 5.45/5.64 ! [X: assn,Y: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_assn @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_idem
% 5.45/5.64 thf(fact_197_inf__left__idem,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_idem
% 5.45/5.64 thf(fact_198_inf__left__idem,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_idem
% 5.45/5.64 thf(fact_199_inf__left__idem,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_idem
% 5.45/5.64 thf(fact_200_inf_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ A @ B ) )
% 5.45/5.64 = ( inf_inf_set_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_idem
% 5.45/5.64 thf(fact_201_inf_Oleft__idem,axiom,
% 5.45/5.64 ! [A: assn,B: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ A @ ( inf_inf_assn @ A @ B ) )
% 5.45/5.64 = ( inf_inf_assn @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_idem
% 5.45/5.64 thf(fact_202_inf_Oleft__idem,axiom,
% 5.45/5.64 ! [A: nat,B: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ A @ ( inf_inf_nat @ A @ B ) )
% 5.45/5.64 = ( inf_inf_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_idem
% 5.45/5.64 thf(fact_203_inf_Oleft__idem,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ A @ B ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_idem
% 5.45/5.64 thf(fact_204_inf_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_idem
% 5.45/5.64 thf(fact_205_inf__idem,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_idem
% 5.45/5.64 thf(fact_206_inf__idem,axiom,
% 5.45/5.64 ! [X: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_idem
% 5.45/5.64 thf(fact_207_inf__idem,axiom,
% 5.45/5.64 ! [X: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_idem
% 5.45/5.64 thf(fact_208_inf__idem,axiom,
% 5.45/5.64 ! [X: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_idem
% 5.45/5.64 thf(fact_209_inf__idem,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % inf_idem
% 5.45/5.64 thf(fact_210_inf_Oidem,axiom,
% 5.45/5.64 ! [A: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.idem
% 5.45/5.64 thf(fact_211_inf_Oidem,axiom,
% 5.45/5.64 ! [A: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.idem
% 5.45/5.64 thf(fact_212_inf_Oidem,axiom,
% 5.45/5.64 ! [A: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.idem
% 5.45/5.64 thf(fact_213_inf_Oidem,axiom,
% 5.45/5.64 ! [A: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.idem
% 5.45/5.64 thf(fact_214_inf_Oidem,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.idem
% 5.45/5.64 thf(fact_215_sup_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ A @ B ) @ B )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.right_idem
% 5.45/5.64 thf(fact_216_sup_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ B )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.right_idem
% 5.45/5.64 thf(fact_217_sup_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ B )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.right_idem
% 5.45/5.64 thf(fact_218_sup_Oright__idem,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ B )
% 5.45/5.64 = ( sup_sup_set_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.right_idem
% 5.45/5.64 thf(fact_219_sup_Oright__idem,axiom,
% 5.45/5.64 ! [A: nat,B: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ B )
% 5.45/5.64 = ( sup_sup_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.right_idem
% 5.45/5.64 thf(fact_220_sup__left__idem,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_idem
% 5.45/5.64 thf(fact_221_sup__left__idem,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_idem
% 5.45/5.64 thf(fact_222_sup__left__idem,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_idem
% 5.45/5.64 thf(fact_223_sup__left__idem,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_idem
% 5.45/5.64 thf(fact_224_sup__left__idem,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_idem
% 5.45/5.64 thf(fact_225_sup_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A @ ( sup_su718114333110466843at_nat @ A @ B ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_idem
% 5.45/5.64 thf(fact_226_sup_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_idem
% 5.45/5.64 thf(fact_227_sup_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_idem
% 5.45/5.64 thf(fact_228_sup_Oleft__idem,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) )
% 5.45/5.64 = ( sup_sup_set_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_idem
% 5.45/5.64 thf(fact_229_sup_Oleft__idem,axiom,
% 5.45/5.64 ! [A: nat,B: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ A @ ( sup_sup_nat @ A @ B ) )
% 5.45/5.64 = ( sup_sup_nat @ A @ B ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_idem
% 5.45/5.64 thf(fact_230_sup__idem,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_idem
% 5.45/5.64 thf(fact_231_sup__idem,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_idem
% 5.45/5.64 thf(fact_232_sup__idem,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_idem
% 5.45/5.64 thf(fact_233_sup__idem,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_idem
% 5.45/5.64 thf(fact_234_sup__idem,axiom,
% 5.45/5.64 ! [X: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ X )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_idem
% 5.45/5.64 thf(fact_235_sup_Oidem,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup.idem
% 5.45/5.64 thf(fact_236_sup_Oidem,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup.idem
% 5.45/5.64 thf(fact_237_sup_Oidem,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup.idem
% 5.45/5.64 thf(fact_238_sup_Oidem,axiom,
% 5.45/5.64 ! [A: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup.idem
% 5.45/5.64 thf(fact_239_sup_Oidem,axiom,
% 5.45/5.64 ! [A: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ A @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup.idem
% 5.45/5.64 thf(fact_240_Int__iff,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_o @ C @ A3 )
% 5.45/5.64 & ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_iff
% 5.45/5.64 thf(fact_241_Int__iff,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_set_nat @ C @ A3 )
% 5.45/5.64 & ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_iff
% 5.45/5.64 thf(fact_242_Int__iff,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_int @ C @ A3 )
% 5.45/5.64 & ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_iff
% 5.45/5.64 thf(fact_243_Int__iff,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_nat @ C @ A3 )
% 5.45/5.64 & ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_iff
% 5.45/5.64 thf(fact_244_Int__iff,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 & ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_iff
% 5.45/5.64 thf(fact_245_IntI,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ A3 )
% 5.45/5.64 => ( ( member_o @ C @ B3 )
% 5.45/5.64 => ( member_o @ C @ ( inf_inf_set_o @ A3 @ B3 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntI
% 5.45/5.64 thf(fact_246_IntI,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ A3 )
% 5.45/5.64 => ( ( member_set_nat @ C @ B3 )
% 5.45/5.64 => ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntI
% 5.45/5.64 thf(fact_247_IntI,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ A3 )
% 5.45/5.64 => ( ( member_int @ C @ B3 )
% 5.45/5.64 => ( member_int @ C @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntI
% 5.45/5.64 thf(fact_248_IntI,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ A3 )
% 5.45/5.64 => ( ( member_nat @ C @ B3 )
% 5.45/5.64 => ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntI
% 5.45/5.64 thf(fact_249_IntI,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 => ( ( member8440522571783428010at_nat @ C @ B3 )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntI
% 5.45/5.64 thf(fact_250_Un__iff,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 | ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_251_Un__iff,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_o @ C @ A3 )
% 5.45/5.64 | ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_252_Un__iff,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_set_nat @ C @ A3 )
% 5.45/5.64 | ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_253_Un__iff,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_int @ C @ A3 )
% 5.45/5.64 | ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_254_Un__iff,axiom,
% 5.45/5.64 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member8206827879206165904at_nat @ C @ A3 )
% 5.45/5.64 | ( member8206827879206165904at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_255_Un__iff,axiom,
% 5.45/5.64 ! [C: produc4166570645942440679at_nat,A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member6689249552917799696at_nat @ C @ A3 )
% 5.45/5.64 | ( member6689249552917799696at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_256_Un__iff,axiom,
% 5.45/5.64 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member8757157785044589968at_nat @ C @ A3 )
% 5.45/5.64 | ( member8757157785044589968at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_257_Un__iff,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( ( member_nat @ C @ A3 )
% 5.45/5.64 | ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_iff
% 5.45/5.64 thf(fact_258_UnCI,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ~ ( member8440522571783428010at_nat @ C @ B3 )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ A3 ) )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_259_UnCI,axiom,
% 5.45/5.64 ! [C: $o,B3: set_o,A3: set_o] :
% 5.45/5.64 ( ( ~ ( member_o @ C @ B3 )
% 5.45/5.64 => ( member_o @ C @ A3 ) )
% 5.45/5.64 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_260_UnCI,axiom,
% 5.45/5.64 ! [C: set_nat,B3: set_set_nat,A3: set_set_nat] :
% 5.45/5.64 ( ( ~ ( member_set_nat @ C @ B3 )
% 5.45/5.64 => ( member_set_nat @ C @ A3 ) )
% 5.45/5.64 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_261_UnCI,axiom,
% 5.45/5.64 ! [C: int,B3: set_int,A3: set_int] :
% 5.45/5.64 ( ( ~ ( member_int @ C @ B3 )
% 5.45/5.64 => ( member_int @ C @ A3 ) )
% 5.45/5.64 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_262_UnCI,axiom,
% 5.45/5.64 ! [C: produc859450856879609959at_nat,B3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ~ ( member8206827879206165904at_nat @ C @ B3 )
% 5.45/5.64 => ( member8206827879206165904at_nat @ C @ A3 ) )
% 5.45/5.64 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_263_UnCI,axiom,
% 5.45/5.64 ! [C: produc4166570645942440679at_nat,B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ~ ( member6689249552917799696at_nat @ C @ B3 )
% 5.45/5.64 => ( member6689249552917799696at_nat @ C @ A3 ) )
% 5.45/5.64 => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_264_UnCI,axiom,
% 5.45/5.64 ! [C: produc3843707927480180839at_nat,B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ~ ( member8757157785044589968at_nat @ C @ B3 )
% 5.45/5.64 => ( member8757157785044589968at_nat @ C @ A3 ) )
% 5.45/5.64 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_265_UnCI,axiom,
% 5.45/5.64 ! [C: nat,B3: set_nat,A3: set_nat] :
% 5.45/5.64 ( ( ~ ( member_nat @ C @ B3 )
% 5.45/5.64 => ( member_nat @ C @ A3 ) )
% 5.45/5.64 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnCI
% 5.45/5.64 thf(fact_266_mod__or__dist,axiom,
% 5.45/5.64 ! [P: assn,Q: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.64 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ H )
% 5.45/5.64 = ( ( rep_assn @ P @ H )
% 5.45/5.64 | ( rep_assn @ Q @ H ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % mod_or_dist
% 5.45/5.64 thf(fact_267_star__false__left,axiom,
% 5.45/5.64 ! [P: assn] :
% 5.45/5.64 ( ( times_times_assn @ bot_bot_assn @ P )
% 5.45/5.64 = bot_bot_assn ) ).
% 5.45/5.64
% 5.45/5.64 % star_false_left
% 5.45/5.64 thf(fact_268_star__false__right,axiom,
% 5.45/5.64 ! [P: assn] :
% 5.45/5.64 ( ( times_times_assn @ P @ bot_bot_assn )
% 5.45/5.64 = bot_bot_assn ) ).
% 5.45/5.64
% 5.45/5.64 % star_false_right
% 5.45/5.64 thf(fact_269_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.64 & ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_270_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: assn,B: assn,C: assn] :
% 5.45/5.64 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.64 & ( ord_less_eq_assn @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_271_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit,C: product_unit] :
% 5.45/5.64 ( ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) )
% 5.45/5.64 = ( ( ord_le3221252021190050221t_unit @ A @ B )
% 5.45/5.64 & ( ord_le3221252021190050221t_unit @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_272_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 5.45/5.64 = ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.45/5.64 & ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_273_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.64 & ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_274_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: rat,B: rat,C: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.64 & ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_275_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: nat,B: nat,C: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.64 & ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_276_inf_Obounded__iff,axiom,
% 5.45/5.64 ! [A: int,B: int,C: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 5.45/5.64 = ( ( ord_less_eq_int @ A @ B )
% 5.45/5.64 & ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.bounded_iff
% 5.45/5.64 thf(fact_277_le__inf__iff,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_set_nat @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_set_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_278_le__inf__iff,axiom,
% 5.45/5.64 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.64 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_assn @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_279_le__inf__iff,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.64 ( ( ord_le3221252021190050221t_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 5.45/5.64 & ( ord_le3221252021190050221t_unit @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_280_le__inf__iff,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.45/5.64 & ( ord_le3146513528884898305at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_281_le__inf__iff,axiom,
% 5.45/5.64 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_282_le__inf__iff,axiom,
% 5.45/5.64 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_283_le__inf__iff,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_284_le__inf__iff,axiom,
% 5.45/5.64 ! [X: int,Y: int,Z: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) )
% 5.45/5.64 = ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.64 & ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_inf_iff
% 5.45/5.64 thf(fact_285_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_le3000389064537975527at_nat @ B @ A )
% 5.45/5.64 & ( ord_le3000389064537975527at_nat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_286_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_le8081472938463900775at_nat @ B @ A )
% 5.45/5.64 & ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_287_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_le1268244103169919719at_nat @ B @ A )
% 5.45/5.64 & ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_288_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: set_nat,C: set_nat,A: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.64 & ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_289_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: set_int,C: set_int,A: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.64 & ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_290_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: rat,C: rat,A: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.64 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_291_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: nat,C: nat,A: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.64 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_292_sup_Obounded__iff,axiom,
% 5.45/5.64 ! [B: int,C: int,A: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 5.45/5.64 = ( ( ord_less_eq_int @ B @ A )
% 5.45/5.64 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.bounded_iff
% 5.45/5.64 thf(fact_293_le__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_le3000389064537975527at_nat @ X @ Z )
% 5.45/5.64 & ( ord_le3000389064537975527at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_294_le__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_le8081472938463900775at_nat @ X @ Z )
% 5.45/5.64 & ( ord_le8081472938463900775at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_295_le__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_le1268244103169919719at_nat @ X @ Z )
% 5.45/5.64 & ( ord_le1268244103169919719at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_296_le__sup__iff,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_less_eq_set_nat @ X @ Z )
% 5.45/5.64 & ( ord_less_eq_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_297_le__sup__iff,axiom,
% 5.45/5.64 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_less_eq_set_int @ X @ Z )
% 5.45/5.64 & ( ord_less_eq_set_int @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_298_le__sup__iff,axiom,
% 5.45/5.64 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ ( sup_sup_rat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_less_eq_rat @ X @ Z )
% 5.45/5.64 & ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_299_le__sup__iff,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_less_eq_nat @ X @ Z )
% 5.45/5.64 & ( ord_less_eq_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_300_le__sup__iff,axiom,
% 5.45/5.64 ! [X: int,Y: int,Z: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ ( sup_sup_int @ X @ Y ) @ Z )
% 5.45/5.64 = ( ( ord_less_eq_int @ X @ Z )
% 5.45/5.64 & ( ord_less_eq_int @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % le_sup_iff
% 5.45/5.64 thf(fact_301_inf__bot__right,axiom,
% 5.45/5.64 ! [X: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 5.45/5.64 = bot_bot_assn ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_302_inf__bot__right,axiom,
% 5.45/5.64 ! [X: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ bot_bot_Product_unit )
% 5.45/5.64 = bot_bot_Product_unit ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_303_inf__bot__right,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 5.45/5.64 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_304_inf__bot__right,axiom,
% 5.45/5.64 ! [X: set_o] :
% 5.45/5.64 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 5.45/5.64 = bot_bot_set_o ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_305_inf__bot__right,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 5.45/5.64 = bot_bot_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_306_inf__bot__right,axiom,
% 5.45/5.64 ! [X: set_int] :
% 5.45/5.64 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 5.45/5.64 = bot_bot_set_int ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_right
% 5.45/5.64 thf(fact_307_inf__bot__left,axiom,
% 5.45/5.64 ! [X: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 5.45/5.64 = bot_bot_assn ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_308_inf__bot__left,axiom,
% 5.45/5.64 ! [X: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X )
% 5.45/5.64 = bot_bot_Product_unit ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_309_inf__bot__left,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 5.45/5.64 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_310_inf__bot__left,axiom,
% 5.45/5.64 ! [X: set_o] :
% 5.45/5.64 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 5.45/5.64 = bot_bot_set_o ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_311_inf__bot__left,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 5.45/5.64 = bot_bot_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_312_inf__bot__left,axiom,
% 5.45/5.64 ! [X: set_int] :
% 5.45/5.64 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 5.45/5.64 = bot_bot_set_int ) ).
% 5.45/5.64
% 5.45/5.64 % inf_bot_left
% 5.45/5.64 thf(fact_313_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A @ bot_bo5327735625951526323at_nat )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_314_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A @ bot_bo8422036546324065075at_nat )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_315_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A @ bot_bo228742789529271731at_nat )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_316_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( sup_su6327502436637775413at_nat @ A @ bot_bo2099793752762293965at_nat )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_317_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_o] :
% 5.45/5.64 ( ( sup_sup_set_o @ A @ bot_bot_set_o )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_318_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A @ bot_bot_set_nat )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_319_sup__bot_Oright__neutral,axiom,
% 5.45/5.64 ! [A: set_int] :
% 5.45/5.64 ( ( sup_sup_set_int @ A @ bot_bot_set_int )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.right_neutral
% 5.45/5.64 thf(fact_320_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( bot_bo5327735625951526323at_nat
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bo5327735625951526323at_nat )
% 5.45/5.64 & ( B = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_321_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( bot_bo8422036546324065075at_nat
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bo8422036546324065075at_nat )
% 5.45/5.64 & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_322_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( bot_bo228742789529271731at_nat
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bo228742789529271731at_nat )
% 5.45/5.64 & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_323_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( bot_bo2099793752762293965at_nat
% 5.45/5.64 = ( sup_su6327502436637775413at_nat @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bo2099793752762293965at_nat )
% 5.45/5.64 & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_324_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_o,B: set_o] :
% 5.45/5.64 ( ( bot_bot_set_o
% 5.45/5.64 = ( sup_sup_set_o @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bot_set_o )
% 5.45/5.64 & ( B = bot_bot_set_o ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_325_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( bot_bot_set_nat
% 5.45/5.64 = ( sup_sup_set_nat @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bot_set_nat )
% 5.45/5.64 & ( B = bot_bot_set_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_326_sup__bot_Oneutr__eq__iff,axiom,
% 5.45/5.64 ! [A: set_int,B: set_int] :
% 5.45/5.64 ( ( bot_bot_set_int
% 5.45/5.64 = ( sup_sup_set_int @ A @ B ) )
% 5.45/5.64 = ( ( A = bot_bot_set_int )
% 5.45/5.64 & ( B = bot_bot_set_int ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.neutr_eq_iff
% 5.45/5.64 thf(fact_327_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_328_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_329_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_330_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_331_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_o] :
% 5.45/5.64 ( ( sup_sup_set_o @ bot_bot_set_o @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_332_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ bot_bot_set_nat @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_333_sup__bot_Oleft__neutral,axiom,
% 5.45/5.64 ! [A: set_int] :
% 5.45/5.64 ( ( sup_sup_set_int @ bot_bot_set_int @ A )
% 5.45/5.64 = A ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.left_neutral
% 5.45/5.64 thf(fact_334_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ( sup_su718114333110466843at_nat @ A @ B )
% 5.45/5.64 = bot_bo5327735625951526323at_nat )
% 5.45/5.64 = ( ( A = bot_bo5327735625951526323at_nat )
% 5.45/5.64 & ( B = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_335_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ( sup_su3035147773818789531at_nat @ A @ B )
% 5.45/5.64 = bot_bo8422036546324065075at_nat )
% 5.45/5.64 = ( ( A = bot_bo8422036546324065075at_nat )
% 5.45/5.64 & ( B = bot_bo8422036546324065075at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_336_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ( sup_su5525570899277871387at_nat @ A @ B )
% 5.45/5.64 = bot_bo228742789529271731at_nat )
% 5.45/5.64 = ( ( A = bot_bo228742789529271731at_nat )
% 5.45/5.64 & ( B = bot_bo228742789529271731at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_337_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ( sup_su6327502436637775413at_nat @ A @ B )
% 5.45/5.64 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 = ( ( A = bot_bo2099793752762293965at_nat )
% 5.45/5.64 & ( B = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_338_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_o,B: set_o] :
% 5.45/5.64 ( ( ( sup_sup_set_o @ A @ B )
% 5.45/5.64 = bot_bot_set_o )
% 5.45/5.64 = ( ( A = bot_bot_set_o )
% 5.45/5.64 & ( B = bot_bot_set_o ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_339_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] :
% 5.45/5.64 ( ( ( sup_sup_set_nat @ A @ B )
% 5.45/5.64 = bot_bot_set_nat )
% 5.45/5.64 = ( ( A = bot_bot_set_nat )
% 5.45/5.64 & ( B = bot_bot_set_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_340_sup__bot_Oeq__neutr__iff,axiom,
% 5.45/5.64 ! [A: set_int,B: set_int] :
% 5.45/5.64 ( ( ( sup_sup_set_int @ A @ B )
% 5.45/5.64 = bot_bot_set_int )
% 5.45/5.64 = ( ( A = bot_bot_set_int )
% 5.45/5.64 & ( B = bot_bot_set_int ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot.eq_neutr_iff
% 5.45/5.64 thf(fact_341_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( ( sup_su718114333110466843at_nat @ X @ Y )
% 5.45/5.64 = bot_bo5327735625951526323at_nat )
% 5.45/5.64 = ( ( X = bot_bo5327735625951526323at_nat )
% 5.45/5.64 & ( Y = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_342_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 5.45/5.64 = bot_bo8422036546324065075at_nat )
% 5.45/5.64 = ( ( X = bot_bo8422036546324065075at_nat )
% 5.45/5.64 & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_343_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 5.45/5.64 = bot_bo228742789529271731at_nat )
% 5.45/5.64 = ( ( X = bot_bo228742789529271731at_nat )
% 5.45/5.64 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_344_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ( sup_su6327502436637775413at_nat @ X @ Y )
% 5.45/5.64 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 = ( ( X = bot_bo2099793752762293965at_nat )
% 5.45/5.64 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_345_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_o,Y: set_o] :
% 5.45/5.64 ( ( ( sup_sup_set_o @ X @ Y )
% 5.45/5.64 = bot_bot_set_o )
% 5.45/5.64 = ( ( X = bot_bot_set_o )
% 5.45/5.64 & ( Y = bot_bot_set_o ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_346_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( ( sup_sup_set_nat @ X @ Y )
% 5.45/5.64 = bot_bot_set_nat )
% 5.45/5.64 = ( ( X = bot_bot_set_nat )
% 5.45/5.64 & ( Y = bot_bot_set_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_347_sup__eq__bot__iff,axiom,
% 5.45/5.64 ! [X: set_int,Y: set_int] :
% 5.45/5.64 ( ( ( sup_sup_set_int @ X @ Y )
% 5.45/5.64 = bot_bot_set_int )
% 5.45/5.64 = ( ( X = bot_bot_set_int )
% 5.45/5.64 & ( Y = bot_bot_set_int ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_eq_bot_iff
% 5.45/5.64 thf(fact_348_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( bot_bo5327735625951526323at_nat
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bo5327735625951526323at_nat )
% 5.45/5.64 & ( Y = bot_bo5327735625951526323at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_349_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( bot_bo8422036546324065075at_nat
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bo8422036546324065075at_nat )
% 5.45/5.64 & ( Y = bot_bo8422036546324065075at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_350_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( bot_bo228742789529271731at_nat
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bo228742789529271731at_nat )
% 5.45/5.64 & ( Y = bot_bo228742789529271731at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_351_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( bot_bo2099793752762293965at_nat
% 5.45/5.64 = ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bo2099793752762293965at_nat )
% 5.45/5.64 & ( Y = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_352_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_o,Y: set_o] :
% 5.45/5.64 ( ( bot_bot_set_o
% 5.45/5.64 = ( sup_sup_set_o @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bot_set_o )
% 5.45/5.64 & ( Y = bot_bot_set_o ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_353_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( bot_bot_set_nat
% 5.45/5.64 = ( sup_sup_set_nat @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bot_set_nat )
% 5.45/5.64 & ( Y = bot_bot_set_nat ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_354_bot__eq__sup__iff,axiom,
% 5.45/5.64 ! [X: set_int,Y: set_int] :
% 5.45/5.64 ( ( bot_bot_set_int
% 5.45/5.64 = ( sup_sup_set_int @ X @ Y ) )
% 5.45/5.64 = ( ( X = bot_bot_set_int )
% 5.45/5.64 & ( Y = bot_bot_set_int ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_eq_sup_iff
% 5.45/5.64 thf(fact_355_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ bot_bo5327735625951526323at_nat )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_356_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_357_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_358_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_359_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_o] :
% 5.45/5.64 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_360_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_361_sup__bot__right,axiom,
% 5.45/5.64 ! [X: set_int] :
% 5.45/5.64 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 5.45/5.64 = X ) ).
% 5.45/5.64
% 5.45/5.64 % sup_bot_right
% 5.45/5.64 thf(fact_362_mod__h__bot__iff_I6_J,axiom,
% 5.45/5.64 ! [P: assn,Q: assn,H: heap_e7401611519738050253t_unit] :
% 5.45/5.64 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.64 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.64 & ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % mod_h_bot_iff(6)
% 5.45/5.64 thf(fact_363_mod__h__bot__iff_I7_J,axiom,
% 5.45/5.64 ! [P: assn,Q: assn,H: heap_e7401611519738050253t_unit] :
% 5.45/5.64 ( ( rep_assn @ ( sup_sup_assn @ P @ Q ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.64 = ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.64 | ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % mod_h_bot_iff(7)
% 5.45/5.64 thf(fact_364_bot__set__def,axiom,
% 5.45/5.64 ( bot_bo1796632182523588997nt_int
% 5.45/5.64 = ( collec213857154873943460nt_int @ bot_bo8147686125503663512_int_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_365_bot__set__def,axiom,
% 5.45/5.64 ( bot_bot_set_list_nat
% 5.45/5.64 = ( collect_list_nat @ bot_bot_list_nat_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_366_bot__set__def,axiom,
% 5.45/5.64 ( bot_bot_set_set_nat
% 5.45/5.64 = ( collect_set_nat @ bot_bot_set_nat_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_367_bot__set__def,axiom,
% 5.45/5.64 ( bot_bo2099793752762293965at_nat
% 5.45/5.64 = ( collec3392354462482085612at_nat @ bot_bo482883023278783056_nat_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_368_bot__set__def,axiom,
% 5.45/5.64 ( bot_bot_set_o
% 5.45/5.64 = ( collect_o @ bot_bot_o_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_369_bot__set__def,axiom,
% 5.45/5.64 ( bot_bot_set_nat
% 5.45/5.64 = ( collect_nat @ bot_bot_nat_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_370_bot__set__def,axiom,
% 5.45/5.64 ( bot_bot_set_int
% 5.45/5.64 = ( collect_int @ bot_bot_int_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % bot_set_def
% 5.45/5.64 thf(fact_371_mod__and__dist,axiom,
% 5.45/5.64 ! [P: assn,Q: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.64 ( ( rep_assn @ ( inf_inf_assn @ P @ Q ) @ H )
% 5.45/5.64 = ( ( rep_assn @ P @ H )
% 5.45/5.64 & ( rep_assn @ Q @ H ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % mod_and_dist
% 5.45/5.64 thf(fact_372_mod__false,axiom,
% 5.45/5.64 ! [H: produc3658429121746597890et_nat] :
% 5.45/5.64 ~ ( rep_assn @ bot_bot_assn @ H ) ).
% 5.45/5.64
% 5.45/5.64 % mod_false
% 5.45/5.64 thf(fact_373_star__or__dist1,axiom,
% 5.45/5.64 ! [A3: assn,B3: assn,C3: assn] :
% 5.45/5.64 ( ( times_times_assn @ ( sup_sup_assn @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( sup_sup_assn @ ( times_times_assn @ A3 @ C3 ) @ ( times_times_assn @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % star_or_dist1
% 5.45/5.64 thf(fact_374_star__or__dist2,axiom,
% 5.45/5.64 ! [C3: assn,A3: assn,B3: assn] :
% 5.45/5.64 ( ( times_times_assn @ C3 @ ( sup_sup_assn @ A3 @ B3 ) )
% 5.45/5.64 = ( sup_sup_assn @ ( times_times_assn @ C3 @ A3 ) @ ( times_times_assn @ C3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % star_or_dist2
% 5.45/5.64 thf(fact_375_ex__in__conv,axiom,
% 5.45/5.64 ! [A3: set_set_nat] :
% 5.45/5.64 ( ( ? [X4: set_nat] : ( member_set_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 != bot_bot_set_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % ex_in_conv
% 5.45/5.64 thf(fact_376_ex__in__conv,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ? [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 != bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % ex_in_conv
% 5.45/5.64 thf(fact_377_ex__in__conv,axiom,
% 5.45/5.64 ! [A3: set_o] :
% 5.45/5.64 ( ( ? [X4: $o] : ( member_o @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 != bot_bot_set_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % ex_in_conv
% 5.45/5.64 thf(fact_378_ex__in__conv,axiom,
% 5.45/5.64 ! [A3: set_nat] :
% 5.45/5.64 ( ( ? [X4: nat] : ( member_nat @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 != bot_bot_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % ex_in_conv
% 5.45/5.64 thf(fact_379_ex__in__conv,axiom,
% 5.45/5.64 ! [A3: set_int] :
% 5.45/5.64 ( ( ? [X4: int] : ( member_int @ X4 @ A3 ) )
% 5.45/5.64 = ( A3 != bot_bot_set_int ) ) ).
% 5.45/5.64
% 5.45/5.64 % ex_in_conv
% 5.45/5.64 thf(fact_380_equals0I,axiom,
% 5.45/5.64 ! [A3: set_set_nat] :
% 5.45/5.64 ( ! [Y3: set_nat] :
% 5.45/5.64 ~ ( member_set_nat @ Y3 @ A3 )
% 5.45/5.64 => ( A3 = bot_bot_set_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0I
% 5.45/5.64 thf(fact_381_equals0I,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ! [Y3: product_prod_nat_nat] :
% 5.45/5.64 ~ ( member8440522571783428010at_nat @ Y3 @ A3 )
% 5.45/5.64 => ( A3 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0I
% 5.45/5.64 thf(fact_382_equals0I,axiom,
% 5.45/5.64 ! [A3: set_o] :
% 5.45/5.64 ( ! [Y3: $o] :
% 5.45/5.64 ~ ( member_o @ Y3 @ A3 )
% 5.45/5.64 => ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0I
% 5.45/5.64 thf(fact_383_equals0I,axiom,
% 5.45/5.64 ! [A3: set_nat] :
% 5.45/5.64 ( ! [Y3: nat] :
% 5.45/5.64 ~ ( member_nat @ Y3 @ A3 )
% 5.45/5.64 => ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0I
% 5.45/5.64 thf(fact_384_equals0I,axiom,
% 5.45/5.64 ! [A3: set_int] :
% 5.45/5.64 ( ! [Y3: int] :
% 5.45/5.64 ~ ( member_int @ Y3 @ A3 )
% 5.45/5.64 => ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0I
% 5.45/5.64 thf(fact_385_equals0D,axiom,
% 5.45/5.64 ! [A3: set_set_nat,A: set_nat] :
% 5.45/5.64 ( ( A3 = bot_bot_set_set_nat )
% 5.45/5.64 => ~ ( member_set_nat @ A @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0D
% 5.45/5.64 thf(fact_386_equals0D,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat,A: product_prod_nat_nat] :
% 5.45/5.64 ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.45/5.64 => ~ ( member8440522571783428010at_nat @ A @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0D
% 5.45/5.64 thf(fact_387_equals0D,axiom,
% 5.45/5.64 ! [A3: set_o,A: $o] :
% 5.45/5.64 ( ( A3 = bot_bot_set_o )
% 5.45/5.64 => ~ ( member_o @ A @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0D
% 5.45/5.64 thf(fact_388_equals0D,axiom,
% 5.45/5.64 ! [A3: set_nat,A: nat] :
% 5.45/5.64 ( ( A3 = bot_bot_set_nat )
% 5.45/5.64 => ~ ( member_nat @ A @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0D
% 5.45/5.64 thf(fact_389_equals0D,axiom,
% 5.45/5.64 ! [A3: set_int,A: int] :
% 5.45/5.64 ( ( A3 = bot_bot_set_int )
% 5.45/5.64 => ~ ( member_int @ A @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % equals0D
% 5.45/5.64 thf(fact_390_emptyE,axiom,
% 5.45/5.64 ! [A: set_nat] :
% 5.45/5.64 ~ ( member_set_nat @ A @ bot_bot_set_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % emptyE
% 5.45/5.64 thf(fact_391_emptyE,axiom,
% 5.45/5.64 ! [A: product_prod_nat_nat] :
% 5.45/5.64 ~ ( member8440522571783428010at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 5.45/5.64
% 5.45/5.64 % emptyE
% 5.45/5.64 thf(fact_392_emptyE,axiom,
% 5.45/5.64 ! [A: $o] :
% 5.45/5.64 ~ ( member_o @ A @ bot_bot_set_o ) ).
% 5.45/5.64
% 5.45/5.64 % emptyE
% 5.45/5.64 thf(fact_393_emptyE,axiom,
% 5.45/5.64 ! [A: nat] :
% 5.45/5.64 ~ ( member_nat @ A @ bot_bot_set_nat ) ).
% 5.45/5.64
% 5.45/5.64 % emptyE
% 5.45/5.64 thf(fact_394_emptyE,axiom,
% 5.45/5.64 ! [A: int] :
% 5.45/5.64 ~ ( member_int @ A @ bot_bot_set_int ) ).
% 5.45/5.64
% 5.45/5.64 % emptyE
% 5.45/5.64 thf(fact_395_inf__left__commute,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_commute
% 5.45/5.64 thf(fact_396_inf__left__commute,axiom,
% 5.45/5.64 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_commute
% 5.45/5.64 thf(fact_397_inf__left__commute,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_commute
% 5.45/5.64 thf(fact_398_inf__left__commute,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ Y @ ( inf_inf_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_commute
% 5.45/5.64 thf(fact_399_inf__left__commute,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_left_commute
% 5.45/5.64 thf(fact_400_inf_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ B @ ( inf_inf_set_nat @ A @ C ) )
% 5.45/5.64 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_commute
% 5.45/5.64 thf(fact_401_inf_Oleft__commute,axiom,
% 5.45/5.64 ! [B: assn,A: assn,C: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ B @ ( inf_inf_assn @ A @ C ) )
% 5.45/5.64 = ( inf_inf_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_commute
% 5.45/5.64 thf(fact_402_inf_Oleft__commute,axiom,
% 5.45/5.64 ! [B: nat,A: nat,C: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ B @ ( inf_inf_nat @ A @ C ) )
% 5.45/5.64 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_commute
% 5.45/5.64 thf(fact_403_inf_Oleft__commute,axiom,
% 5.45/5.64 ! [B: product_unit,A: product_unit,C: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ B @ ( inf_inf_Product_unit @ A @ C ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_commute
% 5.45/5.64 thf(fact_404_inf_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ B @ ( inf_in2572325071724192079at_nat @ A @ C ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.left_commute
% 5.45/5.64 thf(fact_405_inf__commute,axiom,
% 5.45/5.64 ( inf_inf_set_nat
% 5.45/5.64 = ( ^ [X4: set_nat,Y4: set_nat] : ( inf_inf_set_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_commute
% 5.45/5.64 thf(fact_406_inf__commute,axiom,
% 5.45/5.64 ( inf_inf_assn
% 5.45/5.64 = ( ^ [X4: assn,Y4: assn] : ( inf_inf_assn @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_commute
% 5.45/5.64 thf(fact_407_inf__commute,axiom,
% 5.45/5.64 ( inf_inf_nat
% 5.45/5.64 = ( ^ [X4: nat,Y4: nat] : ( inf_inf_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_commute
% 5.45/5.64 thf(fact_408_inf__commute,axiom,
% 5.45/5.64 ( inf_inf_Product_unit
% 5.45/5.64 = ( ^ [X4: product_unit,Y4: product_unit] : ( inf_inf_Product_unit @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_commute
% 5.45/5.64 thf(fact_409_inf__commute,axiom,
% 5.45/5.64 ( inf_in2572325071724192079at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_commute
% 5.45/5.64 thf(fact_410_inf_Ocommute,axiom,
% 5.45/5.64 ( inf_inf_set_nat
% 5.45/5.64 = ( ^ [A5: set_nat,B5: set_nat] : ( inf_inf_set_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.commute
% 5.45/5.64 thf(fact_411_inf_Ocommute,axiom,
% 5.45/5.64 ( inf_inf_assn
% 5.45/5.64 = ( ^ [A5: assn,B5: assn] : ( inf_inf_assn @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.commute
% 5.45/5.64 thf(fact_412_inf_Ocommute,axiom,
% 5.45/5.64 ( inf_inf_nat
% 5.45/5.64 = ( ^ [A5: nat,B5: nat] : ( inf_inf_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.commute
% 5.45/5.64 thf(fact_413_inf_Ocommute,axiom,
% 5.45/5.64 ( inf_inf_Product_unit
% 5.45/5.64 = ( ^ [A5: product_unit,B5: product_unit] : ( inf_inf_Product_unit @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.commute
% 5.45/5.64 thf(fact_414_inf_Ocommute,axiom,
% 5.45/5.64 ( inf_in2572325071724192079at_nat
% 5.45/5.64 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.commute
% 5.45/5.64 thf(fact_415_inf__assoc,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_assoc
% 5.45/5.64 thf(fact_416_inf__assoc,axiom,
% 5.45/5.64 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_assoc
% 5.45/5.64 thf(fact_417_inf__assoc,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_assoc
% 5.45/5.64 thf(fact_418_inf__assoc,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_assoc
% 5.45/5.64 thf(fact_419_inf__assoc,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_assoc
% 5.45/5.64 thf(fact_420_inf_Oassoc,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C )
% 5.45/5.64 = ( inf_inf_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.assoc
% 5.45/5.64 thf(fact_421_inf_Oassoc,axiom,
% 5.45/5.64 ! [A: assn,B: assn,C: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ ( inf_inf_assn @ A @ B ) @ C )
% 5.45/5.64 = ( inf_inf_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.assoc
% 5.45/5.64 thf(fact_422_inf_Oassoc,axiom,
% 5.45/5.64 ! [A: nat,B: nat,C: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ ( inf_inf_nat @ A @ B ) @ C )
% 5.45/5.64 = ( inf_inf_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.assoc
% 5.45/5.64 thf(fact_423_inf_Oassoc,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit,C: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ A @ B ) @ C )
% 5.45/5.64 = ( inf_inf_Product_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.assoc
% 5.45/5.64 thf(fact_424_inf_Oassoc,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.assoc
% 5.45/5.64 thf(fact_425_inf__sup__aci_I1_J,axiom,
% 5.45/5.64 ( inf_inf_set_nat
% 5.45/5.64 = ( ^ [X4: set_nat,Y4: set_nat] : ( inf_inf_set_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(1)
% 5.45/5.64 thf(fact_426_inf__sup__aci_I1_J,axiom,
% 5.45/5.64 ( inf_inf_assn
% 5.45/5.64 = ( ^ [X4: assn,Y4: assn] : ( inf_inf_assn @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(1)
% 5.45/5.64 thf(fact_427_inf__sup__aci_I1_J,axiom,
% 5.45/5.64 ( inf_inf_nat
% 5.45/5.64 = ( ^ [X4: nat,Y4: nat] : ( inf_inf_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(1)
% 5.45/5.64 thf(fact_428_inf__sup__aci_I1_J,axiom,
% 5.45/5.64 ( inf_inf_Product_unit
% 5.45/5.64 = ( ^ [X4: product_unit,Y4: product_unit] : ( inf_inf_Product_unit @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(1)
% 5.45/5.64 thf(fact_429_inf__sup__aci_I1_J,axiom,
% 5.45/5.64 ( inf_in2572325071724192079at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(1)
% 5.45/5.64 thf(fact_430_inf__sup__aci_I2_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(2)
% 5.45/5.64 thf(fact_431_inf__sup__aci_I2_J,axiom,
% 5.45/5.64 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(2)
% 5.45/5.64 thf(fact_432_inf__sup__aci_I2_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ ( inf_inf_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(2)
% 5.45/5.64 thf(fact_433_inf__sup__aci_I2_J,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(2)
% 5.45/5.64 thf(fact_434_inf__sup__aci_I2_J,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(2)
% 5.45/5.64 thf(fact_435_inf__sup__aci_I3_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_set_nat @ Y @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(3)
% 5.45/5.64 thf(fact_436_inf__sup__aci_I3_J,axiom,
% 5.45/5.64 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_assn @ Y @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(3)
% 5.45/5.64 thf(fact_437_inf__sup__aci_I3_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_nat @ Y @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(3)
% 5.45/5.64 thf(fact_438_inf__sup__aci_I3_J,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ Y @ ( inf_inf_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(3)
% 5.45/5.64 thf(fact_439_inf__sup__aci_I3_J,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ Y @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(3)
% 5.45/5.64 thf(fact_440_inf__sup__aci_I4_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_set_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(4)
% 5.45/5.64 thf(fact_441_inf__sup__aci_I4_J,axiom,
% 5.45/5.64 ! [X: assn,Y: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_assn @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(4)
% 5.45/5.64 thf(fact_442_inf__sup__aci_I4_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ X @ ( inf_inf_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(4)
% 5.45/5.64 thf(fact_443_inf__sup__aci_I4_J,axiom,
% 5.45/5.64 ! [X: product_unit,Y: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ X @ Y ) )
% 5.45/5.64 = ( inf_inf_Product_unit @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(4)
% 5.45/5.64 thf(fact_444_inf__sup__aci_I4_J,axiom,
% 5.45/5.64 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(4)
% 5.45/5.64 thf(fact_445_sup__left__commute,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ Y @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_commute
% 5.45/5.64 thf(fact_446_sup__left__commute,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_commute
% 5.45/5.64 thf(fact_447_sup__left__commute,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_commute
% 5.45/5.64 thf(fact_448_sup__left__commute,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_commute
% 5.45/5.64 thf(fact_449_sup__left__commute,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_left_commute
% 5.45/5.64 thf(fact_450_sup_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ B @ ( sup_su718114333110466843at_nat @ A @ C ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A @ ( sup_su718114333110466843at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_commute
% 5.45/5.64 thf(fact_451_sup_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ C ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_commute
% 5.45/5.64 thf(fact_452_sup_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ C ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_commute
% 5.45/5.64 thf(fact_453_sup_Oleft__commute,axiom,
% 5.45/5.64 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ B @ ( sup_sup_set_nat @ A @ C ) )
% 5.45/5.64 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_commute
% 5.45/5.64 thf(fact_454_sup_Oleft__commute,axiom,
% 5.45/5.64 ! [B: nat,A: nat,C: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ B @ ( sup_sup_nat @ A @ C ) )
% 5.45/5.64 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.left_commute
% 5.45/5.64 thf(fact_455_sup__commute,axiom,
% 5.45/5.64 ( sup_su718114333110466843at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_commute
% 5.45/5.64 thf(fact_456_sup__commute,axiom,
% 5.45/5.64 ( sup_su3035147773818789531at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_commute
% 5.45/5.64 thf(fact_457_sup__commute,axiom,
% 5.45/5.64 ( sup_su5525570899277871387at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_commute
% 5.45/5.64 thf(fact_458_sup__commute,axiom,
% 5.45/5.64 ( sup_sup_set_nat
% 5.45/5.64 = ( ^ [X4: set_nat,Y4: set_nat] : ( sup_sup_set_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_commute
% 5.45/5.64 thf(fact_459_sup__commute,axiom,
% 5.45/5.64 ( sup_sup_nat
% 5.45/5.64 = ( ^ [X4: nat,Y4: nat] : ( sup_sup_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_commute
% 5.45/5.64 thf(fact_460_sup_Ocommute,axiom,
% 5.45/5.64 ( sup_su718114333110466843at_nat
% 5.45/5.64 = ( ^ [A5: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.commute
% 5.45/5.64 thf(fact_461_sup_Ocommute,axiom,
% 5.45/5.64 ( sup_su3035147773818789531at_nat
% 5.45/5.64 = ( ^ [A5: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.commute
% 5.45/5.64 thf(fact_462_sup_Ocommute,axiom,
% 5.45/5.64 ( sup_su5525570899277871387at_nat
% 5.45/5.64 = ( ^ [A5: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.commute
% 5.45/5.64 thf(fact_463_sup_Ocommute,axiom,
% 5.45/5.64 ( sup_sup_set_nat
% 5.45/5.64 = ( ^ [A5: set_nat,B5: set_nat] : ( sup_sup_set_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.commute
% 5.45/5.64 thf(fact_464_sup_Ocommute,axiom,
% 5.45/5.64 ( sup_sup_nat
% 5.45/5.64 = ( ^ [A5: nat,B5: nat] : ( sup_sup_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.commute
% 5.45/5.64 thf(fact_465_sup__assoc,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_assoc
% 5.45/5.64 thf(fact_466_sup__assoc,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_assoc
% 5.45/5.64 thf(fact_467_sup__assoc,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_assoc
% 5.45/5.64 thf(fact_468_sup__assoc,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_assoc
% 5.45/5.64 thf(fact_469_sup__assoc,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup_assoc
% 5.45/5.64 thf(fact_470_sup_Oassoc,axiom,
% 5.45/5.64 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ A @ B ) @ C )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A @ ( sup_su718114333110466843at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.assoc
% 5.45/5.64 thf(fact_471_sup_Oassoc,axiom,
% 5.45/5.64 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ C )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A @ ( sup_su3035147773818789531at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.assoc
% 5.45/5.64 thf(fact_472_sup_Oassoc,axiom,
% 5.45/5.64 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ C )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A @ ( sup_su5525570899277871387at_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.assoc
% 5.45/5.64 thf(fact_473_sup_Oassoc,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A @ B ) @ C )
% 5.45/5.64 = ( sup_sup_set_nat @ A @ ( sup_sup_set_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.assoc
% 5.45/5.64 thf(fact_474_sup_Oassoc,axiom,
% 5.45/5.64 ! [A: nat,B: nat,C: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ ( sup_sup_nat @ A @ B ) @ C )
% 5.45/5.64 = ( sup_sup_nat @ A @ ( sup_sup_nat @ B @ C ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % sup.assoc
% 5.45/5.64 thf(fact_475_inf__sup__aci_I5_J,axiom,
% 5.45/5.64 ( sup_su718114333110466843at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(5)
% 5.45/5.64 thf(fact_476_inf__sup__aci_I5_J,axiom,
% 5.45/5.64 ( sup_su3035147773818789531at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(5)
% 5.45/5.64 thf(fact_477_inf__sup__aci_I5_J,axiom,
% 5.45/5.64 ( sup_su5525570899277871387at_nat
% 5.45/5.64 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(5)
% 5.45/5.64 thf(fact_478_inf__sup__aci_I5_J,axiom,
% 5.45/5.64 ( sup_sup_set_nat
% 5.45/5.64 = ( ^ [X4: set_nat,Y4: set_nat] : ( sup_sup_set_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(5)
% 5.45/5.64 thf(fact_479_inf__sup__aci_I5_J,axiom,
% 5.45/5.64 ( sup_sup_nat
% 5.45/5.64 = ( ^ [X4: nat,Y4: nat] : ( sup_sup_nat @ Y4 @ X4 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(5)
% 5.45/5.64 thf(fact_480_inf__sup__aci_I6_J,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(6)
% 5.45/5.64 thf(fact_481_inf__sup__aci_I6_J,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(6)
% 5.45/5.64 thf(fact_482_inf__sup__aci_I6_J,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(6)
% 5.45/5.64 thf(fact_483_inf__sup__aci_I6_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(6)
% 5.45/5.64 thf(fact_484_inf__sup__aci_I6_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ ( sup_sup_nat @ X @ Y ) @ Z )
% 5.45/5.64 = ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(6)
% 5.45/5.64 thf(fact_485_inf__sup__aci_I7_J,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ Y @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(7)
% 5.45/5.64 thf(fact_486_inf__sup__aci_I7_J,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(7)
% 5.45/5.64 thf(fact_487_inf__sup__aci_I7_J,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(7)
% 5.45/5.64 thf(fact_488_inf__sup__aci_I7_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_sup_set_nat @ Y @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(7)
% 5.45/5.64 thf(fact_489_inf__sup__aci_I7_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 5.45/5.64 = ( sup_sup_nat @ Y @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(7)
% 5.45/5.64 thf(fact_490_inf__sup__aci_I8_J,axiom,
% 5.45/5.64 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ X @ ( sup_su718114333110466843at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(8)
% 5.45/5.64 thf(fact_491_inf__sup__aci_I8_J,axiom,
% 5.45/5.64 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(8)
% 5.45/5.64 thf(fact_492_inf__sup__aci_I8_J,axiom,
% 5.45/5.64 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(8)
% 5.45/5.64 thf(fact_493_inf__sup__aci_I8_J,axiom,
% 5.45/5.64 ! [X: set_nat,Y: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(8)
% 5.45/5.64 thf(fact_494_inf__sup__aci_I8_J,axiom,
% 5.45/5.64 ! [X: nat,Y: nat] :
% 5.45/5.64 ( ( sup_sup_nat @ X @ ( sup_sup_nat @ X @ Y ) )
% 5.45/5.64 = ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf_sup_aci(8)
% 5.45/5.64 thf(fact_495_Int__left__commute,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( inf_inf_set_nat @ B3 @ ( inf_inf_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_left_commute
% 5.45/5.64 thf(fact_496_Int__left__commute,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ B3 @ ( inf_in2572325071724192079at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_left_commute
% 5.45/5.64 thf(fact_497_Int__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_left_absorb
% 5.45/5.64 thf(fact_498_Int__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_left_absorb
% 5.45/5.64 thf(fact_499_Int__commute,axiom,
% 5.45/5.64 ( inf_inf_set_nat
% 5.45/5.64 = ( ^ [A6: set_nat,B6: set_nat] : ( inf_inf_set_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_commute
% 5.45/5.64 thf(fact_500_Int__commute,axiom,
% 5.45/5.64 ( inf_in2572325071724192079at_nat
% 5.45/5.64 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_commute
% 5.45/5.64 thf(fact_501_Int__absorb,axiom,
% 5.45/5.64 ! [A3: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Int_absorb
% 5.45/5.64 thf(fact_502_Int__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Int_absorb
% 5.45/5.64 thf(fact_503_Int__assoc,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( inf_inf_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_assoc
% 5.45/5.64 thf(fact_504_Int__assoc,axiom,
% 5.45/5.64 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( inf_in2572325071724192079at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Int_assoc
% 5.45/5.64 thf(fact_505_IntD2,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.64 => ( member_o @ C @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD2
% 5.45/5.64 thf(fact_506_IntD2,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member_set_nat @ C @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD2
% 5.45/5.64 thf(fact_507_IntD2,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.64 => ( member_int @ C @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD2
% 5.45/5.64 thf(fact_508_IntD2,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member_nat @ C @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD2
% 5.45/5.64 thf(fact_509_IntD2,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD2
% 5.45/5.64 thf(fact_510_IntD1,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.64 => ( member_o @ C @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD1
% 5.45/5.64 thf(fact_511_IntD1,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member_set_nat @ C @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD1
% 5.45/5.64 thf(fact_512_IntD1,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.64 => ( member_int @ C @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD1
% 5.45/5.64 thf(fact_513_IntD1,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member_nat @ C @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD1
% 5.45/5.64 thf(fact_514_IntD1,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ A3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntD1
% 5.45/5.64 thf(fact_515_IntE,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.64 => ~ ( ( member_o @ C @ A3 )
% 5.45/5.64 => ~ ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntE
% 5.45/5.64 thf(fact_516_IntE,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( inf_inf_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ~ ( ( member_set_nat @ C @ A3 )
% 5.45/5.64 => ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntE
% 5.45/5.64 thf(fact_517_IntE,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.64 => ~ ( ( member_int @ C @ A3 )
% 5.45/5.64 => ~ ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntE
% 5.45/5.64 thf(fact_518_IntE,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ~ ( ( member_nat @ C @ A3 )
% 5.45/5.64 => ~ ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntE
% 5.45/5.64 thf(fact_519_IntE,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ~ ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 => ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % IntE
% 5.45/5.64 thf(fact_520_Un__left__commute,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ B3 @ ( sup_su718114333110466843at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_commute
% 5.45/5.64 thf(fact_521_Un__left__commute,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ B3 @ ( sup_su3035147773818789531at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_commute
% 5.45/5.64 thf(fact_522_Un__left__commute,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ B3 @ ( sup_su5525570899277871387at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_commute
% 5.45/5.64 thf(fact_523_Un__left__commute,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) )
% 5.45/5.64 = ( sup_sup_set_nat @ B3 @ ( sup_sup_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_commute
% 5.45/5.64 thf(fact_524_Un__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_absorb
% 5.45/5.64 thf(fact_525_Un__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_absorb
% 5.45/5.64 thf(fact_526_Un__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_absorb
% 5.45/5.64 thf(fact_527_Un__left__absorb,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.64 = ( sup_sup_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_left_absorb
% 5.45/5.64 thf(fact_528_Un__commute,axiom,
% 5.45/5.64 ( sup_su718114333110466843at_nat
% 5.45/5.64 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] : ( sup_su718114333110466843at_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_commute
% 5.45/5.64 thf(fact_529_Un__commute,axiom,
% 5.45/5.64 ( sup_su3035147773818789531at_nat
% 5.45/5.64 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] : ( sup_su3035147773818789531at_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_commute
% 5.45/5.64 thf(fact_530_Un__commute,axiom,
% 5.45/5.64 ( sup_su5525570899277871387at_nat
% 5.45/5.64 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] : ( sup_su5525570899277871387at_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_commute
% 5.45/5.64 thf(fact_531_Un__commute,axiom,
% 5.45/5.64 ( sup_sup_set_nat
% 5.45/5.64 = ( ^ [A6: set_nat,B6: set_nat] : ( sup_sup_set_nat @ B6 @ A6 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_commute
% 5.45/5.64 thf(fact_532_Un__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Un_absorb
% 5.45/5.64 thf(fact_533_Un__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Un_absorb
% 5.45/5.64 thf(fact_534_Un__absorb,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Un_absorb
% 5.45/5.64 thf(fact_535_Un__absorb,axiom,
% 5.45/5.64 ! [A3: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ A3 @ A3 )
% 5.45/5.64 = A3 ) ).
% 5.45/5.64
% 5.45/5.64 % Un_absorb
% 5.45/5.64 thf(fact_536_Un__assoc,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( sup_su718114333110466843at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_assoc
% 5.45/5.64 thf(fact_537_Un__assoc,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( sup_su3035147773818789531at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_assoc
% 5.45/5.64 thf(fact_538_Un__assoc,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( sup_su5525570899277871387at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_assoc
% 5.45/5.64 thf(fact_539_Un__assoc,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.64 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.64 = ( sup_sup_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % Un_assoc
% 5.45/5.64 thf(fact_540_ball__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,P: produc859450856879609959at_nat > $o] :
% 5.45/5.64 ( ( ! [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( P @ X4 ) ) )
% 5.45/5.64 = ( ! [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ A3 )
% 5.45/5.64 => ( P @ X4 ) )
% 5.45/5.64 & ! [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ B3 )
% 5.45/5.64 => ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % ball_Un
% 5.45/5.64 thf(fact_541_ball__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 5.45/5.64 ( ( ! [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( P @ X4 ) ) )
% 5.45/5.64 = ( ! [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ A3 )
% 5.45/5.64 => ( P @ X4 ) )
% 5.45/5.64 & ! [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ B3 )
% 5.45/5.64 => ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % ball_Un
% 5.45/5.64 thf(fact_542_ball__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 5.45/5.64 ( ( ! [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( P @ X4 ) ) )
% 5.45/5.64 = ( ! [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ A3 )
% 5.45/5.64 => ( P @ X4 ) )
% 5.45/5.64 & ! [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ B3 )
% 5.45/5.64 => ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % ball_Un
% 5.45/5.64 thf(fact_543_ball__Un,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,P: nat > $o] :
% 5.45/5.64 ( ( ! [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( P @ X4 ) ) )
% 5.45/5.64 = ( ! [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ A3 )
% 5.45/5.64 => ( P @ X4 ) )
% 5.45/5.64 & ! [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ B3 )
% 5.45/5.64 => ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % ball_Un
% 5.45/5.64 thf(fact_544_bex__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,P: produc859450856879609959at_nat > $o] :
% 5.45/5.64 ( ( ? [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.64 & ( P @ X4 ) ) )
% 5.45/5.64 = ( ? [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ A3 )
% 5.45/5.64 & ( P @ X4 ) )
% 5.45/5.64 | ? [X4: produc859450856879609959at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ X4 @ B3 )
% 5.45/5.64 & ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bex_Un
% 5.45/5.64 thf(fact_545_bex__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,P: produc4166570645942440679at_nat > $o] :
% 5.45/5.64 ( ( ? [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.64 & ( P @ X4 ) ) )
% 5.45/5.64 = ( ? [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ A3 )
% 5.45/5.64 & ( P @ X4 ) )
% 5.45/5.64 | ? [X4: produc4166570645942440679at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ X4 @ B3 )
% 5.45/5.64 & ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bex_Un
% 5.45/5.64 thf(fact_546_bex__Un,axiom,
% 5.45/5.64 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,P: produc3843707927480180839at_nat > $o] :
% 5.45/5.64 ( ( ? [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.64 & ( P @ X4 ) ) )
% 5.45/5.64 = ( ? [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ A3 )
% 5.45/5.64 & ( P @ X4 ) )
% 5.45/5.64 | ? [X4: produc3843707927480180839at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ X4 @ B3 )
% 5.45/5.64 & ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bex_Un
% 5.45/5.64 thf(fact_547_bex__Un,axiom,
% 5.45/5.64 ! [A3: set_nat,B3: set_nat,P: nat > $o] :
% 5.45/5.64 ( ( ? [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.64 & ( P @ X4 ) ) )
% 5.45/5.64 = ( ? [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ A3 )
% 5.45/5.64 & ( P @ X4 ) )
% 5.45/5.64 | ? [X4: nat] :
% 5.45/5.64 ( ( member_nat @ X4 @ B3 )
% 5.45/5.64 & ( P @ X4 ) ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % bex_Un
% 5.45/5.64 thf(fact_548_UnI2,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ B3 )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_549_UnI2,axiom,
% 5.45/5.64 ! [C: $o,B3: set_o,A3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ B3 )
% 5.45/5.64 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_550_UnI2,axiom,
% 5.45/5.64 ! [C: set_nat,B3: set_set_nat,A3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ B3 )
% 5.45/5.64 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_551_UnI2,axiom,
% 5.45/5.64 ! [C: int,B3: set_int,A3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ B3 )
% 5.45/5.64 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_552_UnI2,axiom,
% 5.45/5.64 ! [C: produc859450856879609959at_nat,B3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ C @ B3 )
% 5.45/5.64 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_553_UnI2,axiom,
% 5.45/5.64 ! [C: produc4166570645942440679at_nat,B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ C @ B3 )
% 5.45/5.64 => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_554_UnI2,axiom,
% 5.45/5.64 ! [C: produc3843707927480180839at_nat,B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ C @ B3 )
% 5.45/5.64 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_555_UnI2,axiom,
% 5.45/5.64 ! [C: nat,B3: set_nat,A3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ B3 )
% 5.45/5.64 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI2
% 5.45/5.64 thf(fact_556_UnI1,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_557_UnI1,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ A3 )
% 5.45/5.64 => ( member_o @ C @ ( sup_sup_set_o @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_558_UnI1,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ A3 )
% 5.45/5.64 => ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_559_UnI1,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ A3 )
% 5.45/5.64 => ( member_int @ C @ ( sup_sup_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_560_UnI1,axiom,
% 5.45/5.64 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ C @ A3 )
% 5.45/5.64 => ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_561_UnI1,axiom,
% 5.45/5.64 ! [C: produc4166570645942440679at_nat,A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ C @ A3 )
% 5.45/5.64 => ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_562_UnI1,axiom,
% 5.45/5.64 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ C @ A3 )
% 5.45/5.64 => ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_563_UnI1,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ A3 )
% 5.45/5.64 => ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnI1
% 5.45/5.64 thf(fact_564_UnE,axiom,
% 5.45/5.64 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( member8440522571783428010at_nat @ C @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.64 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_565_UnE,axiom,
% 5.45/5.64 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.64 ( ( member_o @ C @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member_o @ C @ A3 )
% 5.45/5.64 => ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_566_UnE,axiom,
% 5.45/5.64 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.64 ( ( member_set_nat @ C @ ( sup_sup_set_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member_set_nat @ C @ A3 )
% 5.45/5.64 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_567_UnE,axiom,
% 5.45/5.64 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.64 ( ( member_int @ C @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member_int @ C @ A3 )
% 5.45/5.64 => ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_568_UnE,axiom,
% 5.45/5.64 ! [C: produc859450856879609959at_nat,A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.64 ( ( member8206827879206165904at_nat @ C @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member8206827879206165904at_nat @ C @ A3 )
% 5.45/5.64 => ( member8206827879206165904at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_569_UnE,axiom,
% 5.45/5.64 ! [C: produc4166570645942440679at_nat,A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.64 ( ( member6689249552917799696at_nat @ C @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member6689249552917799696at_nat @ C @ A3 )
% 5.45/5.64 => ( member6689249552917799696at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_570_UnE,axiom,
% 5.45/5.64 ! [C: produc3843707927480180839at_nat,A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.64 ( ( member8757157785044589968at_nat @ C @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member8757157785044589968at_nat @ C @ A3 )
% 5.45/5.64 => ( member8757157785044589968at_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_571_UnE,axiom,
% 5.45/5.64 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.64 ( ( member_nat @ C @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.64 => ( ~ ( member_nat @ C @ A3 )
% 5.45/5.64 => ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % UnE
% 5.45/5.64 thf(fact_572_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: set_nat,C: set_nat,A: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ B @ C )
% 5.45/5.64 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_573_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: assn,C: assn,A: assn] :
% 5.45/5.64 ( ( ord_less_eq_assn @ B @ C )
% 5.45/5.64 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_574_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: product_unit,C: product_unit,A: product_unit] :
% 5.45/5.64 ( ( ord_le3221252021190050221t_unit @ B @ C )
% 5.45/5.64 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_575_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ord_le3146513528884898305at_nat @ B @ C )
% 5.45/5.64 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_576_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: set_int,C: set_int,A: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ B @ C )
% 5.45/5.64 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_577_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: rat,C: rat,A: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.64 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_578_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: nat,C: nat,A: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.64 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_579_inf_OcoboundedI2,axiom,
% 5.45/5.64 ! [B: int,C: int,A: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ B @ C )
% 5.45/5.64 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI2
% 5.45/5.64 thf(fact_580_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: set_nat,C: set_nat,B: set_nat] :
% 5.45/5.64 ( ( ord_less_eq_set_nat @ A @ C )
% 5.45/5.64 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_581_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: assn,C: assn,B: assn] :
% 5.45/5.64 ( ( ord_less_eq_assn @ A @ C )
% 5.45/5.64 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_582_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: product_unit,C: product_unit,B: product_unit] :
% 5.45/5.64 ( ( ord_le3221252021190050221t_unit @ A @ C )
% 5.45/5.64 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_583_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( ord_le3146513528884898305at_nat @ A @ C )
% 5.45/5.64 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_584_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: set_int,C: set_int,B: set_int] :
% 5.45/5.64 ( ( ord_less_eq_set_int @ A @ C )
% 5.45/5.64 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_585_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: rat,C: rat,B: rat] :
% 5.45/5.64 ( ( ord_less_eq_rat @ A @ C )
% 5.45/5.64 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_586_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: nat,C: nat,B: nat] :
% 5.45/5.64 ( ( ord_less_eq_nat @ A @ C )
% 5.45/5.64 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_587_inf_OcoboundedI1,axiom,
% 5.45/5.64 ! [A: int,C: int,B: int] :
% 5.45/5.64 ( ( ord_less_eq_int @ A @ C )
% 5.45/5.64 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.coboundedI1
% 5.45/5.64 thf(fact_588_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_set_nat
% 5.45/5.64 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_589_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_assn
% 5.45/5.64 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_590_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_le3221252021190050221t_unit
% 5.45/5.64 = ( ^ [B5: product_unit,A5: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_591_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_le3146513528884898305at_nat
% 5.45/5.64 = ( ^ [B5: set_Pr1261947904930325089at_nat,A5: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_592_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_set_int
% 5.45/5.64 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.64 ( ( inf_inf_set_int @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_593_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_rat
% 5.45/5.64 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.64 ( ( inf_inf_rat @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_594_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_nat
% 5.45/5.64 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_595_inf_Oabsorb__iff2,axiom,
% 5.45/5.64 ( ord_less_eq_int
% 5.45/5.64 = ( ^ [B5: int,A5: int] :
% 5.45/5.64 ( ( inf_inf_int @ A5 @ B5 )
% 5.45/5.64 = B5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff2
% 5.45/5.64 thf(fact_596_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_set_nat
% 5.45/5.64 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.45/5.64 ( ( inf_inf_set_nat @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_597_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_assn
% 5.45/5.64 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.64 ( ( inf_inf_assn @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_598_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_le3221252021190050221t_unit
% 5.45/5.64 = ( ^ [A5: product_unit,B5: product_unit] :
% 5.45/5.64 ( ( inf_inf_Product_unit @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_599_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_le3146513528884898305at_nat
% 5.45/5.64 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.45/5.64 ( ( inf_in2572325071724192079at_nat @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_600_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_set_int
% 5.45/5.64 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.64 ( ( inf_inf_set_int @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_601_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_rat
% 5.45/5.64 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.64 ( ( inf_inf_rat @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_602_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_nat
% 5.45/5.64 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.64 ( ( inf_inf_nat @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_603_inf_Oabsorb__iff1,axiom,
% 5.45/5.64 ( ord_less_eq_int
% 5.45/5.64 = ( ^ [A5: int,B5: int] :
% 5.45/5.64 ( ( inf_inf_int @ A5 @ B5 )
% 5.45/5.64 = A5 ) ) ) ).
% 5.45/5.64
% 5.45/5.64 % inf.absorb_iff1
% 5.45/5.64 thf(fact_604_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_605_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_606_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_607_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_608_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_609_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_610_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_611_inf_Ocobounded2,axiom,
% 5.45/5.64 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ B ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded2
% 5.45/5.64 thf(fact_612_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_613_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: assn,B: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_614_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: product_unit,B: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_615_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_616_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_617_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ A ) ).
% 5.45/5.64
% 5.45/5.64 % inf.cobounded1
% 5.45/5.64 thf(fact_618_inf_Ocobounded1,axiom,
% 5.45/5.64 ! [A: nat,B: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ A ) ).
% 5.45/5.65
% 5.45/5.65 % inf.cobounded1
% 5.45/5.65 thf(fact_619_inf_Ocobounded1,axiom,
% 5.45/5.65 ! [A: int,B: int] : ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ A ) ).
% 5.45/5.65
% 5.45/5.65 % inf.cobounded1
% 5.45/5.65 thf(fact_620_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_set_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_621_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_assn
% 5.45/5.65 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_assn @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_622_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_le3221252021190050221t_unit
% 5.45/5.65 = ( ^ [A5: product_unit,B5: product_unit] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_Product_unit @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_623_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_le3146513528884898305at_nat
% 5.45/5.65 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_624_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_set_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_625_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_rat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_626_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_627_inf_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [A5: int,B5: int] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( inf_inf_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.order_iff
% 5.45/5.65 thf(fact_628_inf__greatest,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_629_inf__greatest,axiom,
% 5.45/5.65 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_assn @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_630_inf__greatest,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 5.45/5.65 => ( ( ord_le3221252021190050221t_unit @ X @ Z )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_631_inf__greatest,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.45/5.65 => ( ( ord_le3146513528884898305at_nat @ X @ Z )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_632_inf__greatest,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_633_inf__greatest,axiom,
% 5.45/5.65 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_rat @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_634_inf__greatest,axiom,
% 5.45/5.65 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_nat @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_635_inf__greatest,axiom,
% 5.45/5.65 ! [X: int,Y: int,Z: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.65 => ( ( ord_less_eq_int @ X @ Z )
% 5.45/5.65 => ( ord_less_eq_int @ X @ ( inf_inf_int @ Y @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_greatest
% 5.45/5.65 thf(fact_636_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ A @ C )
% 5.45/5.65 => ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_637_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: assn,B: assn,C: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_assn @ A @ C )
% 5.45/5.65 => ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_638_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: product_unit,B: product_unit,C: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ B )
% 5.45/5.65 => ( ( ord_le3221252021190050221t_unit @ A @ C )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_639_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.45/5.65 => ( ( ord_le3146513528884898305at_nat @ A @ C )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_640_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ A @ C )
% 5.45/5.65 => ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_641_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: rat,B: rat,C: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_rat @ A @ C )
% 5.45/5.65 => ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_642_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: nat,B: nat,C: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_nat @ A @ C )
% 5.45/5.65 => ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_643_inf_OboundedI,axiom,
% 5.45/5.65 ! [A: int,B: int,C: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.65 => ( ( ord_less_eq_int @ A @ C )
% 5.45/5.65 => ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedI
% 5.45/5.65 thf(fact_644_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_set_nat @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_645_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: assn,B: assn,C: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_assn @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_646_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: product_unit,B: product_unit,C: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_le3221252021190050221t_unit @ A @ B )
% 5.45/5.65 => ~ ( ord_le3221252021190050221t_unit @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_647_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.45/5.65 => ~ ( ord_le3146513528884898305at_nat @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_648_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ ( inf_inf_set_int @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_649_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: rat,B: rat,C: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_650_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: nat,B: nat,C: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_651_inf_OboundedE,axiom,
% 5.45/5.65 ! [A: int,B: int,C: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ ( inf_inf_int @ B @ C ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_int @ A @ B )
% 5.45/5.65 => ~ ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.boundedE
% 5.45/5.65 thf(fact_652_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: set_nat,X: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_set_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_653_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: assn,X: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_assn @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_654_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: product_unit,X: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_655_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ Y @ X )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_656_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: set_int,X: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_set_int @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_657_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: rat,X: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_rat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_658_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: nat,X: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_659_inf__absorb2,axiom,
% 5.45/5.65 ! [Y: int,X: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.65 => ( ( inf_inf_int @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb2
% 5.45/5.65 thf(fact_660_inf__absorb1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_set_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_661_inf__absorb1,axiom,
% 5.45/5.65 ! [X: assn,Y: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_assn @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_662_inf__absorb1,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_663_inf__absorb1,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ X @ Y )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_664_inf__absorb1,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_set_int @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_665_inf__absorb1,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_rat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_666_inf__absorb1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_667_inf__absorb1,axiom,
% 5.45/5.65 ! [X: int,Y: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.65 => ( ( inf_inf_int @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_absorb1
% 5.45/5.65 thf(fact_668_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.65 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_669_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: assn,A: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ B @ A )
% 5.45/5.65 => ( ( inf_inf_assn @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_670_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: product_unit,A: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ B @ A )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_671_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ B @ A )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_672_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.65 => ( ( inf_inf_set_int @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_673_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.65 => ( ( inf_inf_rat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_674_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.65 => ( ( inf_inf_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_675_inf_Oabsorb2,axiom,
% 5.45/5.65 ! [B: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.65 => ( ( inf_inf_int @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb2
% 5.45/5.65 thf(fact_676_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.65 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_677_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: assn,B: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.65 => ( ( inf_inf_assn @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_678_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: product_unit,B: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ B )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_679_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_680_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.65 => ( ( inf_inf_set_int @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_681_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.65 => ( ( inf_inf_rat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_682_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.65 => ( ( inf_inf_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_683_inf_Oabsorb1,axiom,
% 5.45/5.65 ! [A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.65 => ( ( inf_inf_int @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.absorb1
% 5.45/5.65 thf(fact_684_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_685_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_assn
% 5.45/5.65 = ( ^ [X4: assn,Y4: assn] :
% 5.45/5.65 ( ( inf_inf_assn @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_686_le__iff__inf,axiom,
% 5.45/5.65 ( ord_le3221252021190050221t_unit
% 5.45/5.65 = ( ^ [X4: product_unit,Y4: product_unit] :
% 5.45/5.65 ( ( inf_inf_Product_unit @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_687_le__iff__inf,axiom,
% 5.45/5.65 ( ord_le3146513528884898305at_nat
% 5.45/5.65 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_688_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.65 ( ( inf_inf_set_int @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_689_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.65 ( ( inf_inf_rat @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_690_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.65 ( ( inf_inf_nat @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_691_le__iff__inf,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [X4: int,Y4: int] :
% 5.45/5.65 ( ( inf_inf_int @ X4 @ Y4 )
% 5.45/5.65 = X4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_inf
% 5.45/5.65 thf(fact_692_inf__unique,axiom,
% 5.45/5.65 ! [F: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 5.45/5.65 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_set_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_set_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_693_inf__unique,axiom,
% 5.45/5.65 ! [F: assn > assn > assn,X: assn,Y: assn] :
% 5.45/5.65 ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: assn,Y3: assn] : ( ord_less_eq_assn @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: assn,Y3: assn,Z2: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_assn @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_assn @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_assn @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_694_inf__unique,axiom,
% 5.45/5.65 ! [F: product_unit > product_unit > product_unit,X: product_unit,Y: product_unit] :
% 5.45/5.65 ( ! [X3: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: product_unit,Y3: product_unit] : ( ord_le3221252021190050221t_unit @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: product_unit,Y3: product_unit,Z2: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_le3221252021190050221t_unit @ X3 @ Z2 )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_695_inf__unique,axiom,
% 5.45/5.65 ! [F: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_le3146513528884898305at_nat @ X3 @ Z2 )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_696_inf__unique,axiom,
% 5.45/5.65 ! [F: set_int > set_int > set_int,X: set_int,Y: set_int] :
% 5.45/5.65 ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: set_int,Y3: set_int,Z2: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_set_int @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_set_int @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_697_inf__unique,axiom,
% 5.45/5.65 ! [F: rat > rat > rat,X: rat,Y: rat] :
% 5.45/5.65 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_rat @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_rat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_rat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_698_inf__unique,axiom,
% 5.45/5.65 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 5.45/5.65 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_nat @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_nat @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_699_inf__unique,axiom,
% 5.45/5.65 ! [F: int > int > int,X: int,Y: int] :
% 5.45/5.65 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F @ X3 @ Y3 ) @ X3 )
% 5.45/5.65 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ ( F @ X3 @ Y3 ) @ Y3 )
% 5.45/5.65 => ( ! [X3: int,Y3: int,Z2: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.45/5.65 => ( ( ord_less_eq_int @ X3 @ Z2 )
% 5.45/5.65 => ( ord_less_eq_int @ X3 @ ( F @ Y3 @ Z2 ) ) ) )
% 5.45/5.65 => ( ( inf_inf_int @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_unique
% 5.45/5.65 thf(fact_700_inf_OorderI,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_set_nat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_set_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_701_inf_OorderI,axiom,
% 5.45/5.65 ! [A: assn,B: assn] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_assn @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_assn @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_702_inf_OorderI,axiom,
% 5.45/5.65 ! [A: product_unit,B: product_unit] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_Product_unit @ A @ B ) )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_703_inf_OorderI,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ A @ B ) )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_704_inf_OorderI,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_set_int @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_705_inf_OorderI,axiom,
% 5.45/5.65 ! [A: rat,B: rat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_rat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_706_inf_OorderI,axiom,
% 5.45/5.65 ! [A: nat,B: nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_nat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_707_inf_OorderI,axiom,
% 5.45/5.65 ! [A: int,B: int] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( inf_inf_int @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderI
% 5.45/5.65 thf(fact_708_inf_OorderE,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_709_inf_OorderE,axiom,
% 5.45/5.65 ! [A: assn,B: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_assn @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_710_inf_OorderE,axiom,
% 5.45/5.65 ! [A: product_unit,B: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_Product_unit @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_711_inf_OorderE,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_712_inf_OorderE,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_713_inf_OorderE,axiom,
% 5.45/5.65 ! [A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_714_inf_OorderE,axiom,
% 5.45/5.65 ! [A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_715_inf_OorderE,axiom,
% 5.45/5.65 ! [A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( inf_inf_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf.orderE
% 5.45/5.65 thf(fact_716_le__infI2,axiom,
% 5.45/5.65 ! [B: set_nat,X: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_717_le__infI2,axiom,
% 5.45/5.65 ! [B: assn,X: assn,A: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ B @ X )
% 5.45/5.65 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_718_le__infI2,axiom,
% 5.45/5.65 ! [B: product_unit,X: product_unit,A: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ B @ X )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_719_le__infI2,axiom,
% 5.45/5.65 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ B @ X )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_720_le__infI2,axiom,
% 5.45/5.65 ! [B: set_int,X: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ B @ X )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_721_le__infI2,axiom,
% 5.45/5.65 ! [B: rat,X: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_722_le__infI2,axiom,
% 5.45/5.65 ! [B: nat,X: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_723_le__infI2,axiom,
% 5.45/5.65 ! [B: int,X: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ B @ X )
% 5.45/5.65 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI2
% 5.45/5.65 thf(fact_724_le__infI1,axiom,
% 5.45/5.65 ! [A: set_nat,X: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ X )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_725_le__infI1,axiom,
% 5.45/5.65 ! [A: assn,X: assn,B: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ X )
% 5.45/5.65 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_726_le__infI1,axiom,
% 5.45/5.65 ! [A: product_unit,X: product_unit,B: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ X )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_727_le__infI1,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ X )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_728_le__infI1,axiom,
% 5.45/5.65 ! [A: set_int,X: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ X )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_729_le__infI1,axiom,
% 5.45/5.65 ! [A: rat,X: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ X )
% 5.45/5.65 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_730_le__infI1,axiom,
% 5.45/5.65 ! [A: nat,X: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ X )
% 5.45/5.65 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_731_le__infI1,axiom,
% 5.45/5.65 ! [A: int,X: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ X )
% 5.45/5.65 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI1
% 5.45/5.65 thf(fact_732_inf__mono,axiom,
% 5.45/5.65 ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A @ B ) @ ( inf_inf_set_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_733_inf__mono,axiom,
% 5.45/5.65 ! [A: assn,C: assn,B: assn,D2: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_assn @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_assn @ ( inf_inf_assn @ A @ B ) @ ( inf_inf_assn @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_734_inf__mono,axiom,
% 5.45/5.65 ! [A: product_unit,C: product_unit,B: product_unit,D2: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ A @ C )
% 5.45/5.65 => ( ( ord_le3221252021190050221t_unit @ B @ D2 )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ A @ B ) @ ( inf_inf_Product_unit @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_735_inf__mono,axiom,
% 5.45/5.65 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,D2: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ A @ C )
% 5.45/5.65 => ( ( ord_le3146513528884898305at_nat @ B @ D2 )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ ( inf_in2572325071724192079at_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_736_inf__mono,axiom,
% 5.45/5.65 ! [A: set_int,C: set_int,B: set_int,D2: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A @ B ) @ ( inf_inf_set_int @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_737_inf__mono,axiom,
% 5.45/5.65 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_rat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_rat @ ( inf_inf_rat @ A @ B ) @ ( inf_inf_rat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_738_inf__mono,axiom,
% 5.45/5.65 ! [A: nat,C: nat,B: nat,D2: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_nat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_nat @ ( inf_inf_nat @ A @ B ) @ ( inf_inf_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_739_inf__mono,axiom,
% 5.45/5.65 ! [A: int,C: int,B: int,D2: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_int @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_int @ ( inf_inf_int @ A @ B ) @ ( inf_inf_int @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_mono
% 5.45/5.65 thf(fact_740_le__infI,axiom,
% 5.45/5.65 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_741_le__infI,axiom,
% 5.45/5.65 ! [X: assn,A: assn,B: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_assn @ X @ B )
% 5.45/5.65 => ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_742_le__infI,axiom,
% 5.45/5.65 ! [X: product_unit,A: product_unit,B: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ X @ A )
% 5.45/5.65 => ( ( ord_le3221252021190050221t_unit @ X @ B )
% 5.45/5.65 => ( ord_le3221252021190050221t_unit @ X @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_743_le__infI,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ X @ A )
% 5.45/5.65 => ( ( ord_le3146513528884898305at_nat @ X @ B )
% 5.45/5.65 => ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_744_le__infI,axiom,
% 5.45/5.65 ! [X: set_int,A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ X @ B )
% 5.45/5.65 => ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_745_le__infI,axiom,
% 5.45/5.65 ! [X: rat,A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_rat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_746_le__infI,axiom,
% 5.45/5.65 ! [X: nat,A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_nat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_747_le__infI,axiom,
% 5.45/5.65 ! [X: int,A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ A )
% 5.45/5.65 => ( ( ord_less_eq_int @ X @ B )
% 5.45/5.65 => ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infI
% 5.45/5.65 thf(fact_748_le__infE,axiom,
% 5.45/5.65 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ ( inf_inf_set_nat @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_nat @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_set_nat @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_749_le__infE,axiom,
% 5.45/5.65 ! [X: assn,A: assn,B: assn] :
% 5.45/5.65 ( ( ord_less_eq_assn @ X @ ( inf_inf_assn @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_assn @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_assn @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_750_le__infE,axiom,
% 5.45/5.65 ! [X: product_unit,A: product_unit,B: product_unit] :
% 5.45/5.65 ( ( ord_le3221252021190050221t_unit @ X @ ( inf_inf_Product_unit @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_le3221252021190050221t_unit @ X @ A )
% 5.45/5.65 => ~ ( ord_le3221252021190050221t_unit @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_751_le__infE,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ord_le3146513528884898305at_nat @ X @ ( inf_in2572325071724192079at_nat @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_le3146513528884898305at_nat @ X @ A )
% 5.45/5.65 => ~ ( ord_le3146513528884898305at_nat @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_752_le__infE,axiom,
% 5.45/5.65 ! [X: set_int,A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ ( inf_inf_set_int @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_int @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_set_int @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_753_le__infE,axiom,
% 5.45/5.65 ! [X: rat,A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ ( inf_inf_rat @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_rat @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_rat @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_754_le__infE,axiom,
% 5.45/5.65 ! [X: nat,A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ ( inf_inf_nat @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_nat @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_nat @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_755_le__infE,axiom,
% 5.45/5.65 ! [X: int,A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ ( inf_inf_int @ A @ B ) )
% 5.45/5.65 => ~ ( ( ord_less_eq_int @ X @ A )
% 5.45/5.65 => ~ ( ord_less_eq_int @ X @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_infE
% 5.45/5.65 thf(fact_756_inf__le2,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_757_inf__le2,axiom,
% 5.45/5.65 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_758_inf__le2,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_759_inf__le2,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_760_inf__le2,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_761_inf__le2,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_762_inf__le2,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_763_inf__le2,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le2
% 5.45/5.65 thf(fact_764_inf__le1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_765_inf__le1,axiom,
% 5.45/5.65 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_766_inf__le1,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_767_inf__le1,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_768_inf__le1,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_769_inf__le1,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_770_inf__le1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_771_inf__le1,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_le1
% 5.45/5.65 thf(fact_772_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_773_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_774_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_775_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_776_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_777_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_778_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_779_inf__sup__ord_I1_J,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ X ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(1)
% 5.45/5.65 thf(fact_780_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_781_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: assn,Y: assn] : ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_782_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit] : ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_783_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_784_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_785_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( inf_inf_rat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_786_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ ( inf_inf_nat @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_787_inf__sup__ord_I2_J,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ ( inf_inf_int @ X @ Y ) @ Y ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(2)
% 5.45/5.65 thf(fact_788_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ C @ B )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ C @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_789_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ C @ B )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_790_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ C @ B )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_791_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ C @ B )
% 5.45/5.65 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_792_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: set_int,B: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ C @ B )
% 5.45/5.65 => ( ord_less_eq_set_int @ C @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_793_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: rat,B: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ C @ B )
% 5.45/5.65 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_794_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: nat,B: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ C @ B )
% 5.45/5.65 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_795_sup_OcoboundedI2,axiom,
% 5.45/5.65 ! [C: int,B: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ C @ B )
% 5.45/5.65 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI2
% 5.45/5.65 thf(fact_796_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ C @ A )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ C @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_797_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ C @ A )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_798_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ C @ A )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_799_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_800_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: set_int,A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.65 => ( ord_less_eq_set_int @ C @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_801_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: rat,A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_802_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: nat,A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_803_sup_OcoboundedI1,axiom,
% 5.45/5.65 ! [C: int,A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ C @ A )
% 5.45/5.65 => ( ord_less_eq_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.coboundedI1
% 5.45/5.65 thf(fact_804_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_le3000389064537975527at_nat
% 5.45/5.65 = ( ^ [A5: set_Pr8693737435421807431at_nat,B5: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_805_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_le8081472938463900775at_nat
% 5.45/5.65 = ( ^ [A5: set_Pr8551490117392284871at_nat,B5: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_806_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_le1268244103169919719at_nat
% 5.45/5.65 = ( ^ [A5: set_Pr4329608150637261639at_nat,B5: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_807_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_808_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.65 ( ( sup_sup_set_int @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_809_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.65 ( ( sup_sup_rat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_810_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_811_sup_Oabsorb__iff2,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [A5: int,B5: int] :
% 5.45/5.65 ( ( sup_sup_int @ A5 @ B5 )
% 5.45/5.65 = B5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff2
% 5.45/5.65 thf(fact_812_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_le3000389064537975527at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr8693737435421807431at_nat,A5: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_813_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_le8081472938463900775at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_814_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_le1268244103169919719at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_815_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_816_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.65 ( ( sup_sup_set_int @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_817_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.65 ( ( sup_sup_rat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_818_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_819_sup_Oabsorb__iff1,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [B5: int,A5: int] :
% 5.45/5.65 ( ( sup_sup_int @ A5 @ B5 )
% 5.45/5.65 = A5 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb_iff1
% 5.45/5.65 thf(fact_820_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ B @ ( sup_su718114333110466843at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_821_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_822_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_823_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: set_nat,A: set_nat] : ( ord_less_eq_set_nat @ B @ ( sup_sup_set_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_824_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: set_int,A: set_int] : ( ord_less_eq_set_int @ B @ ( sup_sup_set_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_825_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( sup_sup_rat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_826_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( sup_sup_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_827_sup_Ocobounded2,axiom,
% 5.45/5.65 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( sup_sup_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded2
% 5.45/5.65 thf(fact_828_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ A @ ( sup_su718114333110466843at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_829_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_830_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_831_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] : ( ord_less_eq_set_nat @ A @ ( sup_sup_set_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_832_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] : ( ord_less_eq_set_int @ A @ ( sup_sup_set_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_833_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( sup_sup_rat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_834_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( sup_sup_nat @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_835_sup_Ocobounded1,axiom,
% 5.45/5.65 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( sup_sup_int @ A @ B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.cobounded1
% 5.45/5.65 thf(fact_836_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_le3000389064537975527at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr8693737435421807431at_nat,A5: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_837_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_le8081472938463900775at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_838_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_le1268244103169919719at_nat
% 5.45/5.65 = ( ^ [B5: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_839_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_sup_set_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_840_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_sup_set_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_841_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_sup_rat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_842_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_sup_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_843_sup_Oorder__iff,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [B5: int,A5: int] :
% 5.45/5.65 ( A5
% 5.45/5.65 = ( sup_sup_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.order_iff
% 5.45/5.65 thf(fact_844_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ B @ A )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ C @ A )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_845_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ C @ A )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_846_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ C @ A )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_847_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: set_nat,A: set_nat,C: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_848_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: set_int,A: set_int,C: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_849_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: rat,A: rat,C: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.65 => ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_850_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: nat,A: nat,C: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.65 => ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.65 => ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_851_sup_OboundedI,axiom,
% 5.45/5.65 ! [B: int,A: int,C: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.65 => ( ( ord_less_eq_int @ C @ A )
% 5.45/5.65 => ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedI
% 5.45/5.65 thf(fact_852_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_le3000389064537975527at_nat @ B @ A )
% 5.45/5.65 => ~ ( ord_le3000389064537975527at_nat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_853_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_le8081472938463900775at_nat @ B @ A )
% 5.45/5.65 => ~ ( ord_le8081472938463900775at_nat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_854_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_le1268244103169919719at_nat @ B @ A )
% 5.45/5.65 => ~ ( ord_le1268244103169919719at_nat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_855_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: set_nat,C: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.65 => ~ ( ord_less_eq_set_nat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_856_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: set_int,C: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.65 => ~ ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_857_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: rat,C: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.65 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_858_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: nat,C: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.65 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_859_sup_OboundedE,axiom,
% 5.45/5.65 ! [B: int,C: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ ( sup_sup_int @ B @ C ) @ A )
% 5.45/5.65 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.45/5.65 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.boundedE
% 5.45/5.65 thf(fact_860_sup__absorb2,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ X @ Y )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_861_sup__absorb2,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ X @ Y )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_862_sup__absorb2,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ X @ Y )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_863_sup__absorb2,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ Y )
% 5.45/5.65 => ( ( sup_sup_set_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_864_sup__absorb2,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.65 => ( ( sup_sup_set_int @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_865_sup__absorb2,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.65 => ( ( sup_sup_rat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_866_sup__absorb2,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.65 => ( ( sup_sup_nat @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_867_sup__absorb2,axiom,
% 5.45/5.65 ! [X: int,Y: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.65 => ( ( sup_sup_int @ X @ Y )
% 5.45/5.65 = Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb2
% 5.45/5.65 thf(fact_868_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ Y @ X )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_869_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_870_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_871_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: set_nat,X: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.45/5.65 => ( ( sup_sup_set_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_872_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: set_int,X: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.65 => ( ( sup_sup_set_int @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_873_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: rat,X: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.65 => ( ( sup_sup_rat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_874_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: nat,X: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.65 => ( ( sup_sup_nat @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_875_sup__absorb1,axiom,
% 5.45/5.65 ! [Y: int,X: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.65 => ( ( sup_sup_int @ X @ Y )
% 5.45/5.65 = X ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_absorb1
% 5.45/5.65 thf(fact_876_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ A @ B )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_877_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ A @ B )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_878_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ A @ B )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_879_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ B )
% 5.45/5.65 => ( ( sup_sup_set_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_880_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.65 => ( ( sup_sup_set_int @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_881_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.65 => ( ( sup_sup_rat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_882_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.65 => ( ( sup_sup_nat @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_883_sup_Oabsorb2,axiom,
% 5.45/5.65 ! [A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.65 => ( ( sup_sup_int @ A @ B )
% 5.45/5.65 = B ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb2
% 5.45/5.65 thf(fact_884_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ B @ A )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_885_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_886_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_887_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.65 => ( ( sup_sup_set_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_888_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.65 => ( ( sup_sup_set_int @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_889_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.65 => ( ( sup_sup_rat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_890_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.65 => ( ( sup_sup_nat @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_891_sup_Oabsorb1,axiom,
% 5.45/5.65 ! [B: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.65 => ( ( sup_sup_int @ A @ B )
% 5.45/5.65 = A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.absorb1
% 5.45/5.65 thf(fact_892_sup__unique,axiom,
% 5.45/5.65 ! [F: set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat > set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z2: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_893_sup__unique,axiom,
% 5.45/5.65 ! [F: set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat > set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_894_sup__unique,axiom,
% 5.45/5.65 ! [F: set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat > set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_895_sup__unique,axiom,
% 5.45/5.65 ! [F: set_nat > set_nat > set_nat,X: set_nat,Y: set_nat] :
% 5.45/5.65 ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_nat,Y3: set_nat] : ( ord_less_eq_set_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_sup_set_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_896_sup__unique,axiom,
% 5.45/5.65 ! [F: set_int > set_int > set_int,X: set_int,Y: set_int] :
% 5.45/5.65 ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_int,Y3: set_int] : ( ord_less_eq_set_int @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: set_int,Y3: set_int,Z2: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ Z2 @ X3 )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_sup_set_int @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_897_sup__unique,axiom,
% 5.45/5.65 ! [F: rat > rat > rat,X: rat,Y: rat] :
% 5.45/5.65 ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: rat,Y3: rat] : ( ord_less_eq_rat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: rat,Y3: rat,Z2: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_less_eq_rat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_less_eq_rat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_sup_rat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_898_sup__unique,axiom,
% 5.45/5.65 ! [F: nat > nat > nat,X: nat,Y: nat] :
% 5.45/5.65 ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_less_eq_nat @ Z2 @ X3 )
% 5.45/5.65 => ( ord_less_eq_nat @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_sup_nat @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_899_sup__unique,axiom,
% 5.45/5.65 ! [F: int > int > int,X: int,Y: int] :
% 5.45/5.65 ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ X3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: int,Y3: int] : ( ord_less_eq_int @ Y3 @ ( F @ X3 @ Y3 ) )
% 5.45/5.65 => ( ! [X3: int,Y3: int,Z2: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ Y3 @ X3 )
% 5.45/5.65 => ( ( ord_less_eq_int @ Z2 @ X3 )
% 5.45/5.65 => ( ord_less_eq_int @ ( F @ Y3 @ Z2 ) @ X3 ) ) )
% 5.45/5.65 => ( ( sup_sup_int @ X @ Y )
% 5.45/5.65 = ( F @ X @ Y ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_unique
% 5.45/5.65 thf(fact_900_sup_OorderI,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ A @ B ) )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_901_sup_OorderI,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ A @ B ) )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_902_sup_OorderI,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ A @ B ) )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_903_sup_OorderI,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_sup_set_nat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_set_nat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_904_sup_OorderI,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_sup_set_int @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_905_sup_OorderI,axiom,
% 5.45/5.65 ! [A: rat,B: rat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_sup_rat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_906_sup_OorderI,axiom,
% 5.45/5.65 ! [A: nat,B: nat] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_sup_nat @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_907_sup_OorderI,axiom,
% 5.45/5.65 ! [A: int,B: int] :
% 5.45/5.65 ( ( A
% 5.45/5.65 = ( sup_sup_int @ A @ B ) )
% 5.45/5.65 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderI
% 5.45/5.65 thf(fact_908_sup_OorderE,axiom,
% 5.45/5.65 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_909_sup_OorderE,axiom,
% 5.45/5.65 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_910_sup_OorderE,axiom,
% 5.45/5.65 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_911_sup_OorderE,axiom,
% 5.45/5.65 ! [B: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_912_sup_OorderE,axiom,
% 5.45/5.65 ! [B: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_sup_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_913_sup_OorderE,axiom,
% 5.45/5.65 ! [B: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_914_sup_OorderE,axiom,
% 5.45/5.65 ! [B: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_915_sup_OorderE,axiom,
% 5.45/5.65 ! [B: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.65 => ( A
% 5.45/5.65 = ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.orderE
% 5.45/5.65 thf(fact_916_le__iff__sup,axiom,
% 5.45/5.65 ( ord_le3000389064537975527at_nat
% 5.45/5.65 = ( ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_917_le__iff__sup,axiom,
% 5.45/5.65 ( ord_le8081472938463900775at_nat
% 5.45/5.65 = ( ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_918_le__iff__sup,axiom,
% 5.45/5.65 ( ord_le1268244103169919719at_nat
% 5.45/5.65 = ( ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_919_le__iff__sup,axiom,
% 5.45/5.65 ( ord_less_eq_set_nat
% 5.45/5.65 = ( ^ [X4: set_nat,Y4: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_920_le__iff__sup,axiom,
% 5.45/5.65 ( ord_less_eq_set_int
% 5.45/5.65 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.65 ( ( sup_sup_set_int @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_921_le__iff__sup,axiom,
% 5.45/5.65 ( ord_less_eq_rat
% 5.45/5.65 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.65 ( ( sup_sup_rat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_922_le__iff__sup,axiom,
% 5.45/5.65 ( ord_less_eq_nat
% 5.45/5.65 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_923_le__iff__sup,axiom,
% 5.45/5.65 ( ord_less_eq_int
% 5.45/5.65 = ( ^ [X4: int,Y4: int] :
% 5.45/5.65 ( ( sup_sup_int @ X4 @ Y4 )
% 5.45/5.65 = Y4 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_iff_sup
% 5.45/5.65 thf(fact_924_sup__least,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ Y @ X )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ Z @ X )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_925_sup__least,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ Y @ X )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ Z @ X )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_926_sup__least,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ Y @ X )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ Z @ X )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_927_sup__least,axiom,
% 5.45/5.65 ! [Y: set_nat,X: set_nat,Z: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ Y @ X )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ Z @ X )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_928_sup__least,axiom,
% 5.45/5.65 ! [Y: set_int,X: set_int,Z: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ Z @ X )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_929_sup__least,axiom,
% 5.45/5.65 ! [Y: rat,X: rat,Z: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.65 => ( ( ord_less_eq_rat @ Z @ X )
% 5.45/5.65 => ( ord_less_eq_rat @ ( sup_sup_rat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_930_sup__least,axiom,
% 5.45/5.65 ! [Y: nat,X: nat,Z: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.65 => ( ( ord_less_eq_nat @ Z @ X )
% 5.45/5.65 => ( ord_less_eq_nat @ ( sup_sup_nat @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_931_sup__least,axiom,
% 5.45/5.65 ! [Y: int,X: int,Z: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.65 => ( ( ord_less_eq_int @ Z @ X )
% 5.45/5.65 => ( ord_less_eq_int @ ( sup_sup_int @ Y @ Z ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_least
% 5.45/5.65 thf(fact_932_sup__mono,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,D2: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ A @ C )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ B @ D2 )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A @ B ) @ ( sup_su718114333110466843at_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_933_sup__mono,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ A @ C )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ B @ D2 )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ ( sup_su3035147773818789531at_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_934_sup__mono,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ A @ C )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ B @ D2 )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ ( sup_su5525570899277871387at_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_935_sup__mono,axiom,
% 5.45/5.65 ! [A: set_nat,C: set_nat,B: set_nat,D2: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ ( sup_sup_set_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_936_sup__mono,axiom,
% 5.45/5.65 ! [A: set_int,C: set_int,B: set_int,D2: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ ( sup_sup_set_int @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_937_sup__mono,axiom,
% 5.45/5.65 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_rat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ ( sup_sup_rat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_938_sup__mono,axiom,
% 5.45/5.65 ! [A: nat,C: nat,B: nat,D2: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_nat @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ ( sup_sup_nat @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_939_sup__mono,axiom,
% 5.45/5.65 ! [A: int,C: int,B: int,D2: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ C )
% 5.45/5.65 => ( ( ord_less_eq_int @ B @ D2 )
% 5.45/5.65 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ ( sup_sup_int @ C @ D2 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_mono
% 5.45/5.65 thf(fact_940_sup_Omono,axiom,
% 5.45/5.65 ! [C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,D2: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ C @ A )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ D2 @ B )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ C @ D2 ) @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_941_sup_Omono,axiom,
% 5.45/5.65 ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,D2: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ C @ A )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ D2 @ B )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ C @ D2 ) @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_942_sup_Omono,axiom,
% 5.45/5.65 ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,D2: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ C @ A )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ D2 @ B )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ C @ D2 ) @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_943_sup_Omono,axiom,
% 5.45/5.65 ! [C: set_nat,A: set_nat,D2: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ C @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ D2 @ B )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ C @ D2 ) @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_944_sup_Omono,axiom,
% 5.45/5.65 ! [C: set_int,A: set_int,D2: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ D2 @ B )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ C @ D2 ) @ ( sup_sup_set_int @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_945_sup_Omono,axiom,
% 5.45/5.65 ! [C: rat,A: rat,D2: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.65 => ( ( ord_less_eq_rat @ D2 @ B )
% 5.45/5.65 => ( ord_less_eq_rat @ ( sup_sup_rat @ C @ D2 ) @ ( sup_sup_rat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_946_sup_Omono,axiom,
% 5.45/5.65 ! [C: nat,A: nat,D2: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.65 => ( ( ord_less_eq_nat @ D2 @ B )
% 5.45/5.65 => ( ord_less_eq_nat @ ( sup_sup_nat @ C @ D2 ) @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_947_sup_Omono,axiom,
% 5.45/5.65 ! [C: int,A: int,D2: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ C @ A )
% 5.45/5.65 => ( ( ord_less_eq_int @ D2 @ B )
% 5.45/5.65 => ( ord_less_eq_int @ ( sup_sup_int @ C @ D2 ) @ ( sup_sup_int @ A @ B ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup.mono
% 5.45/5.65 thf(fact_948_le__supI2,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ X @ B )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_949_le__supI2,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ X @ B )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_950_le__supI2,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ X @ B )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_951_le__supI2,axiom,
% 5.45/5.65 ! [X: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_952_le__supI2,axiom,
% 5.45/5.65 ! [X: set_int,B: set_int,A: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ B )
% 5.45/5.65 => ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_953_le__supI2,axiom,
% 5.45/5.65 ! [X: rat,B: rat,A: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_954_le__supI2,axiom,
% 5.45/5.65 ! [X: nat,B: nat,A: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ B )
% 5.45/5.65 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_955_le__supI2,axiom,
% 5.45/5.65 ! [X: int,B: int,A: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ B )
% 5.45/5.65 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI2
% 5.45/5.65 thf(fact_956_le__supI1,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ X @ A )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_957_le__supI1,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ X @ A )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_958_le__supI1,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ X @ A )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_959_le__supI1,axiom,
% 5.45/5.65 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ X @ A )
% 5.45/5.65 => ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_960_le__supI1,axiom,
% 5.45/5.65 ! [X: set_int,A: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ X @ A )
% 5.45/5.65 => ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_961_le__supI1,axiom,
% 5.45/5.65 ! [X: rat,A: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ X @ A )
% 5.45/5.65 => ( ord_less_eq_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_962_le__supI1,axiom,
% 5.45/5.65 ! [X: nat,A: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ X @ A )
% 5.45/5.65 => ( ord_less_eq_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_963_le__supI1,axiom,
% 5.45/5.65 ! [X: int,A: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ X @ A )
% 5.45/5.65 => ( ord_less_eq_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI1
% 5.45/5.65 thf(fact_964_sup__ge2,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y @ ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_965_sup__ge2,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_966_sup__ge2,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_967_sup__ge2,axiom,
% 5.45/5.65 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_968_sup__ge2,axiom,
% 5.45/5.65 ! [Y: set_int,X: set_int] : ( ord_less_eq_set_int @ Y @ ( sup_sup_set_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_969_sup__ge2,axiom,
% 5.45/5.65 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_970_sup__ge2,axiom,
% 5.45/5.65 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_971_sup__ge2,axiom,
% 5.45/5.65 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge2
% 5.45/5.65 thf(fact_972_sup__ge1,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_973_sup__ge1,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_974_sup__ge1,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_975_sup__ge1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_976_sup__ge1,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_977_sup__ge1,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_978_sup__ge1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_979_sup__ge1,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_ge1
% 5.45/5.65 thf(fact_980_le__supI,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ A @ X )
% 5.45/5.65 => ( ( ord_le3000389064537975527at_nat @ B @ X )
% 5.45/5.65 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_981_le__supI,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ A @ X )
% 5.45/5.65 => ( ( ord_le8081472938463900775at_nat @ B @ X )
% 5.45/5.65 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_982_le__supI,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ A @ X )
% 5.45/5.65 => ( ( ord_le1268244103169919719at_nat @ B @ X )
% 5.45/5.65 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_983_le__supI,axiom,
% 5.45/5.65 ! [A: set_nat,X: set_nat,B: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ A @ X )
% 5.45/5.65 => ( ( ord_less_eq_set_nat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_984_le__supI,axiom,
% 5.45/5.65 ! [A: set_int,X: set_int,B: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ A @ X )
% 5.45/5.65 => ( ( ord_less_eq_set_int @ B @ X )
% 5.45/5.65 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_985_le__supI,axiom,
% 5.45/5.65 ! [A: rat,X: rat,B: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ A @ X )
% 5.45/5.65 => ( ( ord_less_eq_rat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_986_le__supI,axiom,
% 5.45/5.65 ! [A: nat,X: nat,B: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ A @ X )
% 5.45/5.65 => ( ( ord_less_eq_nat @ B @ X )
% 5.45/5.65 => ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_987_le__supI,axiom,
% 5.45/5.65 ! [A: int,X: int,B: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ A @ X )
% 5.45/5.65 => ( ( ord_less_eq_int @ B @ X )
% 5.45/5.65 => ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supI
% 5.45/5.65 thf(fact_988_le__supE,axiom,
% 5.45/5.65 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_le3000389064537975527at_nat @ A @ X )
% 5.45/5.65 => ~ ( ord_le3000389064537975527at_nat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_989_le__supE,axiom,
% 5.45/5.65 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_le8081472938463900775at_nat @ A @ X )
% 5.45/5.65 => ~ ( ord_le8081472938463900775at_nat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_990_le__supE,axiom,
% 5.45/5.65 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_le1268244103169919719at_nat @ A @ X )
% 5.45/5.65 => ~ ( ord_le1268244103169919719at_nat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_991_le__supE,axiom,
% 5.45/5.65 ! [A: set_nat,B: set_nat,X: set_nat] :
% 5.45/5.65 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_nat @ A @ X )
% 5.45/5.65 => ~ ( ord_less_eq_set_nat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_992_le__supE,axiom,
% 5.45/5.65 ! [A: set_int,B: set_int,X: set_int] :
% 5.45/5.65 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_less_eq_set_int @ A @ X )
% 5.45/5.65 => ~ ( ord_less_eq_set_int @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_993_le__supE,axiom,
% 5.45/5.65 ! [A: rat,B: rat,X: rat] :
% 5.45/5.65 ( ( ord_less_eq_rat @ ( sup_sup_rat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_less_eq_rat @ A @ X )
% 5.45/5.65 => ~ ( ord_less_eq_rat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_994_le__supE,axiom,
% 5.45/5.65 ! [A: nat,B: nat,X: nat] :
% 5.45/5.65 ( ( ord_less_eq_nat @ ( sup_sup_nat @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_less_eq_nat @ A @ X )
% 5.45/5.65 => ~ ( ord_less_eq_nat @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_995_le__supE,axiom,
% 5.45/5.65 ! [A: int,B: int,X: int] :
% 5.45/5.65 ( ( ord_less_eq_int @ ( sup_sup_int @ A @ B ) @ X )
% 5.45/5.65 => ~ ( ( ord_less_eq_int @ A @ X )
% 5.45/5.65 => ~ ( ord_less_eq_int @ B @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % le_supE
% 5.45/5.65 thf(fact_996_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_997_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_998_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_999_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat] : ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_1000_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: set_int,Y: set_int] : ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_1001_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ X @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_1002_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: nat,Y: nat] : ( ord_less_eq_nat @ X @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_1003_inf__sup__ord_I3_J,axiom,
% 5.45/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ X @ ( sup_sup_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(3)
% 5.45/5.65 thf(fact_1004_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y @ ( sup_su718114333110466843at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1005_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1006_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1007_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: set_nat,X: set_nat] : ( ord_less_eq_set_nat @ Y @ ( sup_sup_set_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1008_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: set_int,X: set_int] : ( ord_less_eq_set_int @ Y @ ( sup_sup_set_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1009_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: rat,X: rat] : ( ord_less_eq_rat @ Y @ ( sup_sup_rat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1010_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: nat,X: nat] : ( ord_less_eq_nat @ Y @ ( sup_sup_nat @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1011_inf__sup__ord_I4_J,axiom,
% 5.45/5.65 ! [Y: int,X: int] : ( ord_less_eq_int @ Y @ ( sup_sup_int @ X @ Y ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_ord(4)
% 5.45/5.65 thf(fact_1012_disjoint__iff__not__equal,axiom,
% 5.45/5.65 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bo2099793752762293965at_nat )
% 5.45/5.65 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.65 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.65 => ! [Y4: product_prod_nat_nat] :
% 5.45/5.65 ( ( member8440522571783428010at_nat @ Y4 @ B3 )
% 5.45/5.65 => ( X4 != Y4 ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff_not_equal
% 5.45/5.65 thf(fact_1013_disjoint__iff__not__equal,axiom,
% 5.45/5.65 ! [A3: set_o,B3: set_o] :
% 5.45/5.65 ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_o )
% 5.45/5.65 = ( ! [X4: $o] :
% 5.45/5.65 ( ( member_o @ X4 @ A3 )
% 5.45/5.65 => ! [Y4: $o] :
% 5.45/5.65 ( ( member_o @ Y4 @ B3 )
% 5.45/5.65 => ( X4 = ~ Y4 ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff_not_equal
% 5.45/5.65 thf(fact_1014_disjoint__iff__not__equal,axiom,
% 5.45/5.65 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.65 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_nat )
% 5.45/5.65 = ( ! [X4: nat] :
% 5.45/5.65 ( ( member_nat @ X4 @ A3 )
% 5.45/5.65 => ! [Y4: nat] :
% 5.45/5.65 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.65 => ( X4 != Y4 ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff_not_equal
% 5.45/5.65 thf(fact_1015_disjoint__iff__not__equal,axiom,
% 5.45/5.65 ! [A3: set_int,B3: set_int] :
% 5.45/5.65 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_int )
% 5.45/5.65 = ( ! [X4: int] :
% 5.45/5.65 ( ( member_int @ X4 @ A3 )
% 5.45/5.65 => ! [Y4: int] :
% 5.45/5.65 ( ( member_int @ Y4 @ B3 )
% 5.45/5.65 => ( X4 != Y4 ) ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff_not_equal
% 5.45/5.65 thf(fact_1016_Int__empty__right,axiom,
% 5.45/5.65 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 5.45/5.65 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_right
% 5.45/5.65 thf(fact_1017_Int__empty__right,axiom,
% 5.45/5.65 ! [A3: set_o] :
% 5.45/5.65 ( ( inf_inf_set_o @ A3 @ bot_bot_set_o )
% 5.45/5.65 = bot_bot_set_o ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_right
% 5.45/5.65 thf(fact_1018_Int__empty__right,axiom,
% 5.45/5.65 ! [A3: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ A3 @ bot_bot_set_nat )
% 5.45/5.65 = bot_bot_set_nat ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_right
% 5.45/5.65 thf(fact_1019_Int__empty__right,axiom,
% 5.45/5.65 ! [A3: set_int] :
% 5.45/5.65 ( ( inf_inf_set_int @ A3 @ bot_bot_set_int )
% 5.45/5.65 = bot_bot_set_int ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_right
% 5.45/5.65 thf(fact_1020_Int__empty__left,axiom,
% 5.45/5.65 ! [B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ B3 )
% 5.45/5.65 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_left
% 5.45/5.65 thf(fact_1021_Int__empty__left,axiom,
% 5.45/5.65 ! [B3: set_o] :
% 5.45/5.65 ( ( inf_inf_set_o @ bot_bot_set_o @ B3 )
% 5.45/5.65 = bot_bot_set_o ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_left
% 5.45/5.65 thf(fact_1022_Int__empty__left,axiom,
% 5.45/5.65 ! [B3: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ bot_bot_set_nat @ B3 )
% 5.45/5.65 = bot_bot_set_nat ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_left
% 5.45/5.65 thf(fact_1023_Int__empty__left,axiom,
% 5.45/5.65 ! [B3: set_int] :
% 5.45/5.65 ( ( inf_inf_set_int @ bot_bot_set_int @ B3 )
% 5.45/5.65 = bot_bot_set_int ) ).
% 5.45/5.65
% 5.45/5.65 % Int_empty_left
% 5.45/5.65 thf(fact_1024_disjoint__iff,axiom,
% 5.45/5.65 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.65 ( ( ( inf_inf_set_set_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_set_nat )
% 5.45/5.65 = ( ! [X4: set_nat] :
% 5.45/5.65 ( ( member_set_nat @ X4 @ A3 )
% 5.45/5.65 => ~ ( member_set_nat @ X4 @ B3 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff
% 5.45/5.65 thf(fact_1025_disjoint__iff,axiom,
% 5.45/5.65 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bo2099793752762293965at_nat )
% 5.45/5.65 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.65 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.65 => ~ ( member8440522571783428010at_nat @ X4 @ B3 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff
% 5.45/5.65 thf(fact_1026_disjoint__iff,axiom,
% 5.45/5.65 ! [A3: set_o,B3: set_o] :
% 5.45/5.65 ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_o )
% 5.45/5.65 = ( ! [X4: $o] :
% 5.45/5.65 ( ( member_o @ X4 @ A3 )
% 5.45/5.65 => ~ ( member_o @ X4 @ B3 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff
% 5.45/5.65 thf(fact_1027_disjoint__iff,axiom,
% 5.45/5.65 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.65 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_nat )
% 5.45/5.65 = ( ! [X4: nat] :
% 5.45/5.65 ( ( member_nat @ X4 @ A3 )
% 5.45/5.65 => ~ ( member_nat @ X4 @ B3 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff
% 5.45/5.65 thf(fact_1028_disjoint__iff,axiom,
% 5.45/5.65 ! [A3: set_int,B3: set_int] :
% 5.45/5.65 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_int )
% 5.45/5.65 = ( ! [X4: int] :
% 5.45/5.65 ( ( member_int @ X4 @ A3 )
% 5.45/5.65 => ~ ( member_int @ X4 @ B3 ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % disjoint_iff
% 5.45/5.65 thf(fact_1029_Int__emptyI,axiom,
% 5.45/5.65 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.65 ( ! [X3: set_nat] :
% 5.45/5.65 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.65 => ~ ( member_set_nat @ X3 @ B3 ) )
% 5.45/5.65 => ( ( inf_inf_set_set_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_set_nat ) ) ).
% 5.45/5.65
% 5.45/5.65 % Int_emptyI
% 5.45/5.65 thf(fact_1030_Int__emptyI,axiom,
% 5.45/5.65 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ! [X3: product_prod_nat_nat] :
% 5.45/5.65 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.65 => ~ ( member8440522571783428010at_nat @ X3 @ B3 ) )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.65
% 5.45/5.65 % Int_emptyI
% 5.45/5.65 thf(fact_1031_Int__emptyI,axiom,
% 5.45/5.65 ! [A3: set_o,B3: set_o] :
% 5.45/5.65 ( ! [X3: $o] :
% 5.45/5.65 ( ( member_o @ X3 @ A3 )
% 5.45/5.65 => ~ ( member_o @ X3 @ B3 ) )
% 5.45/5.65 => ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_o ) ) ).
% 5.45/5.65
% 5.45/5.65 % Int_emptyI
% 5.45/5.65 thf(fact_1032_Int__emptyI,axiom,
% 5.45/5.65 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.65 ( ! [X3: nat] :
% 5.45/5.65 ( ( member_nat @ X3 @ A3 )
% 5.45/5.65 => ~ ( member_nat @ X3 @ B3 ) )
% 5.45/5.65 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_nat ) ) ).
% 5.45/5.65
% 5.45/5.65 % Int_emptyI
% 5.45/5.65 thf(fact_1033_Int__emptyI,axiom,
% 5.45/5.65 ! [A3: set_int,B3: set_int] :
% 5.45/5.65 ( ! [X3: int] :
% 5.45/5.65 ( ( member_int @ X3 @ A3 )
% 5.45/5.65 => ~ ( member_int @ X3 @ B3 ) )
% 5.45/5.65 => ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.65 = bot_bot_set_int ) ) ).
% 5.45/5.65
% 5.45/5.65 % Int_emptyI
% 5.45/5.65 thf(fact_1034_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: assn,Z: assn,X: assn] :
% 5.45/5.65 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1035_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: product_unit,Z: product_unit,X: product_unit] :
% 5.45/5.65 ( ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ X ) @ ( sup_sup_Product_unit @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1036_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1037_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ Y @ X ) @ ( sup_su718114333110466843at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1038_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1039_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1040_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1041_sup__inf__distrib2,axiom,
% 5.45/5.65 ! [Y: nat,Z: nat,X: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ ( inf_inf_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( inf_inf_nat @ ( sup_sup_nat @ Y @ X ) @ ( sup_sup_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib2
% 5.45/5.65 thf(fact_1042_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.65 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1043_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.65 ( ( sup_sup_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) @ ( sup_sup_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1044_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1045_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ X @ ( inf_in4302113700860409141at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1046_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1047_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1048_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1049_sup__inf__distrib1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % sup_inf_distrib1
% 5.45/5.65 thf(fact_1050_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: assn,Z: assn,X: assn] :
% 5.45/5.65 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1051_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: product_unit,Z: product_unit,X: product_unit] :
% 5.45/5.65 ( ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ X ) @ ( inf_inf_Product_unit @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1052_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1053_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ Y @ X ) @ ( inf_in4302113700860409141at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1054_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1055_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1056_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1057_inf__sup__distrib2,axiom,
% 5.45/5.65 ! [Y: nat,Z: nat,X: nat] :
% 5.45/5.65 ( ( inf_inf_nat @ ( sup_sup_nat @ Y @ Z ) @ X )
% 5.45/5.65 = ( sup_sup_nat @ ( inf_inf_nat @ Y @ X ) @ ( inf_inf_nat @ Z @ X ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib2
% 5.45/5.65 thf(fact_1058_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.65 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1059_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.65 ( ( inf_inf_Product_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ ( inf_inf_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1060_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1061_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( inf_in4302113700860409141at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) @ ( inf_in4302113700860409141at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1062_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1063_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1064_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1065_inf__sup__distrib1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.65 ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % inf_sup_distrib1
% 5.45/5.65 thf(fact_1066_distrib__imp2,axiom,
% 5.45/5.65 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.65 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 5.45/5.65 ( ( sup_sup_assn @ X3 @ ( inf_inf_assn @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_inf_assn @ ( sup_sup_assn @ X3 @ Y3 ) @ ( sup_sup_assn @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1067_distrib__imp2,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.65 ( ! [X3: product_unit,Y3: product_unit,Z2: product_unit] :
% 5.45/5.65 ( ( sup_sup_Product_unit @ X3 @ ( inf_inf_Product_unit @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X3 @ Y3 ) @ ( sup_sup_Product_unit @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_inf_Product_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ ( inf_inf_Product_unit @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1068_distrib__imp2,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X3 @ Y3 ) @ ( sup_su6327502436637775413at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1069_distrib__imp2,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z2: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ X3 @ ( inf_in4302113700860409141at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X3 @ Y3 ) @ ( sup_su718114333110466843at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_in4302113700860409141at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) @ ( inf_in4302113700860409141at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1070_distrib__imp2,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ X3 @ ( inf_in1697001100524423349at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X3 @ Y3 ) @ ( sup_su3035147773818789531at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1071_distrib__imp2,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ X3 @ ( inf_in7913087082777306421at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X3 @ Y3 ) @ ( sup_su5525570899277871387at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1072_distrib__imp2,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.65 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ X3 @ ( inf_inf_set_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X3 @ Y3 ) @ ( sup_sup_set_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1073_distrib__imp2,axiom,
% 5.45/5.65 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.65 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.65 ( ( sup_sup_nat @ X3 @ ( inf_inf_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( inf_inf_nat @ ( sup_sup_nat @ X3 @ Y3 ) @ ( sup_sup_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) )
% 5.45/5.65 = ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp2
% 5.45/5.65 thf(fact_1074_distrib__imp1,axiom,
% 5.45/5.65 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.65 ( ! [X3: assn,Y3: assn,Z2: assn] :
% 5.45/5.65 ( ( inf_inf_assn @ X3 @ ( sup_sup_assn @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_sup_assn @ ( inf_inf_assn @ X3 @ Y3 ) @ ( inf_inf_assn @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1075_distrib__imp1,axiom,
% 5.45/5.65 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.65 ( ! [X3: product_unit,Y3: product_unit,Z2: product_unit] :
% 5.45/5.65 ( ( inf_inf_Product_unit @ X3 @ ( sup_sup_Product_unit @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X3 @ Y3 ) @ ( inf_inf_Product_unit @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_sup_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) @ ( sup_sup_Product_unit @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1076_distrib__imp1,axiom,
% 5.45/5.65 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr1261947904930325089at_nat,Y3: set_Pr1261947904930325089at_nat,Z2: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( inf_in2572325071724192079at_nat @ X3 @ ( sup_su6327502436637775413at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X3 @ Y3 ) @ ( inf_in2572325071724192079at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1077_distrib__imp1,axiom,
% 5.45/5.65 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8693737435421807431at_nat,Y3: set_Pr8693737435421807431at_nat,Z2: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( inf_in4302113700860409141at_nat @ X3 @ ( sup_su718114333110466843at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X3 @ Y3 ) @ ( inf_in4302113700860409141at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_su718114333110466843at_nat @ X @ ( inf_in4302113700860409141at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1078_distrib__imp1,axiom,
% 5.45/5.65 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr8551490117392284871at_nat,Y3: set_Pr8551490117392284871at_nat,Z2: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( inf_in1697001100524423349at_nat @ X3 @ ( sup_su3035147773818789531at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X3 @ Y3 ) @ ( inf_in1697001100524423349at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1079_distrib__imp1,axiom,
% 5.45/5.65 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ! [X3: set_Pr4329608150637261639at_nat,Y3: set_Pr4329608150637261639at_nat,Z2: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( inf_in7913087082777306421at_nat @ X3 @ ( sup_su5525570899277871387at_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X3 @ Y3 ) @ ( inf_in7913087082777306421at_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1080_distrib__imp1,axiom,
% 5.45/5.65 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.65 ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 5.45/5.65 ( ( inf_inf_set_nat @ X3 @ ( sup_sup_set_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X3 @ Y3 ) @ ( inf_inf_set_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1081_distrib__imp1,axiom,
% 5.45/5.65 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.65 ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.65 ( ( inf_inf_nat @ X3 @ ( sup_sup_nat @ Y3 @ Z2 ) )
% 5.45/5.65 = ( sup_sup_nat @ ( inf_inf_nat @ X3 @ Y3 ) @ ( inf_inf_nat @ X3 @ Z2 ) ) )
% 5.45/5.65 => ( ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) )
% 5.45/5.65 = ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % distrib_imp1
% 5.45/5.65 thf(fact_1082_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ A3 @ bot_bo5327735625951526323at_nat )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1083_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ A3 @ bot_bo8422036546324065075at_nat )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1084_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ A3 @ bot_bo228742789529271731at_nat )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1085_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1086_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_o] :
% 5.45/5.65 ( ( sup_sup_set_o @ A3 @ bot_bot_set_o )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1087_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ A3 @ bot_bot_set_nat )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1088_Un__empty__right,axiom,
% 5.45/5.65 ! [A3: set_int] :
% 5.45/5.65 ( ( sup_sup_set_int @ A3 @ bot_bot_set_int )
% 5.45/5.65 = A3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_right
% 5.45/5.65 thf(fact_1089_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1090_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.65 ( ( sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1091_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.65 ( ( sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1092_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1093_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_o] :
% 5.45/5.65 ( ( sup_sup_set_o @ bot_bot_set_o @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1094_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_nat] :
% 5.45/5.65 ( ( sup_sup_set_nat @ bot_bot_set_nat @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1095_Un__empty__left,axiom,
% 5.45/5.65 ! [B3: set_int] :
% 5.45/5.65 ( ( sup_sup_set_int @ bot_bot_set_int @ B3 )
% 5.45/5.65 = B3 ) ).
% 5.45/5.65
% 5.45/5.65 % Un_empty_left
% 5.45/5.65 thf(fact_1096_Un__Int__distrib2,axiom,
% 5.45/5.65 ! [B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.65 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.65 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B3 @ A3 ) @ ( sup_su6327502436637775413at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.65
% 5.45/5.65 % Un_Int_distrib2
% 5.45/5.65 thf(fact_1097_Un__Int__distrib2,axiom,
% 5.45/5.65 ! [B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.65 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.65 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ B3 @ A3 ) @ ( sup_su718114333110466843at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib2
% 5.45/5.66 thf(fact_1098_Un__Int__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B3 @ A3 ) @ ( sup_su3035147773818789531at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib2
% 5.45/5.66 thf(fact_1099_Un__Int__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ A3 ) @ ( sup_su5525570899277871387at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib2
% 5.45/5.66 thf(fact_1100_Un__Int__distrib2,axiom,
% 5.45/5.66 ! [B3: set_nat,C3: set_nat,A3: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ B3 @ A3 ) @ ( sup_sup_set_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib2
% 5.45/5.66 thf(fact_1101_Int__Un__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ B3 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib2
% 5.45/5.66 thf(fact_1102_Int__Un__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ B3 @ A3 ) @ ( inf_in4302113700860409141at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib2
% 5.45/5.66 thf(fact_1103_Int__Un__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ B3 @ A3 ) @ ( inf_in1697001100524423349at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib2
% 5.45/5.66 thf(fact_1104_Int__Un__distrib2,axiom,
% 5.45/5.66 ! [B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ B3 @ A3 ) @ ( inf_in7913087082777306421at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib2
% 5.45/5.66 thf(fact_1105_Int__Un__distrib2,axiom,
% 5.45/5.66 ! [B3: set_nat,C3: set_nat,A3: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ B3 @ C3 ) @ A3 )
% 5.45/5.66 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ B3 @ A3 ) @ ( inf_inf_set_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib2
% 5.45/5.66 thf(fact_1106_Un__Int__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( sup_su6327502436637775413at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) @ ( sup_su6327502436637775413at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib
% 5.45/5.66 thf(fact_1107_Un__Int__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ A3 @ ( inf_in4302113700860409141at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ ( sup_su718114333110466843at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib
% 5.45/5.66 thf(fact_1108_Un__Int__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ A3 @ ( inf_in1697001100524423349at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ ( sup_su3035147773818789531at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib
% 5.45/5.66 thf(fact_1109_Un__Int__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ A3 @ ( inf_in7913087082777306421at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ ( sup_su5525570899277871387at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib
% 5.45/5.66 thf(fact_1110_Un__Int__distrib,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ ( sup_sup_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_distrib
% 5.45/5.66 thf(fact_1111_Int__Un__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib
% 5.45/5.66 thf(fact_1112_Int__Un__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( inf_in4302113700860409141at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) @ ( inf_in4302113700860409141at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib
% 5.45/5.66 thf(fact_1113_Int__Un__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( inf_in1697001100524423349at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) @ ( inf_in1697001100524423349at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib
% 5.45/5.66 thf(fact_1114_Int__Un__distrib,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( inf_in7913087082777306421at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) @ ( inf_in7913087082777306421at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib
% 5.45/5.66 thf(fact_1115_Int__Un__distrib,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) )
% 5.45/5.66 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Un_distrib
% 5.45/5.66 thf(fact_1116_Un__Int__crazy,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( sup_su6327502436637775413at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) ) @ ( inf_in2572325071724192079at_nat @ C3 @ A3 ) )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) @ ( sup_su6327502436637775413at_nat @ B3 @ C3 ) ) @ ( sup_su6327502436637775413at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_crazy
% 5.45/5.66 thf(fact_1117_Un__Int__crazy,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) @ ( inf_in4302113700860409141at_nat @ B3 @ C3 ) ) @ ( inf_in4302113700860409141at_nat @ C3 @ A3 ) )
% 5.45/5.66 = ( inf_in4302113700860409141at_nat @ ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) ) @ ( sup_su718114333110466843at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_crazy
% 5.45/5.66 thf(fact_1118_Un__Int__crazy,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) @ ( inf_in1697001100524423349at_nat @ B3 @ C3 ) ) @ ( inf_in1697001100524423349at_nat @ C3 @ A3 ) )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) ) @ ( sup_su3035147773818789531at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_crazy
% 5.45/5.66 thf(fact_1119_Un__Int__crazy,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) @ ( inf_in7913087082777306421at_nat @ B3 @ C3 ) ) @ ( inf_in7913087082777306421at_nat @ C3 @ A3 ) )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) ) @ ( sup_su5525570899277871387at_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_crazy
% 5.45/5.66 thf(fact_1120_Un__Int__crazy,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ B3 @ C3 ) ) @ ( inf_inf_set_nat @ C3 @ A3 ) )
% 5.45/5.66 = ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ ( sup_sup_set_nat @ B3 @ C3 ) ) @ ( sup_sup_set_nat @ C3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_crazy
% 5.45/5.66 thf(fact_1121_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) ) @ ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1122_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: product_unit,Y: product_unit,Z: product_unit] : ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) ) @ ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) @ ( sup_sup_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1123_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ X @ ( inf_inf_rat @ Y @ Z ) ) @ ( inf_inf_rat @ ( sup_sup_rat @ X @ Y ) @ ( sup_sup_rat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1124_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ X @ ( inf_inf_nat @ Y @ Z ) ) @ ( inf_inf_nat @ ( sup_sup_nat @ X @ Y ) @ ( sup_sup_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1125_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ X @ ( inf_inf_int @ Y @ Z ) ) @ ( inf_inf_int @ ( sup_sup_int @ X @ Y ) @ ( sup_sup_int @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1126_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) ) @ ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1127_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int,Z: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ X @ ( inf_inf_set_int @ Y @ Z ) ) @ ( inf_inf_set_int @ ( sup_sup_set_int @ X @ Y ) @ ( sup_sup_set_int @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1128_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) ) @ ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1129_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ X @ ( inf_in4302113700860409141at_nat @ Y @ Z ) ) @ ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1130_distrib__sup__le,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) ) @ ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_sup_le
% 5.45/5.66 thf(fact_1131_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: assn,Y: assn,Z: assn] : ( ord_less_eq_assn @ ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) @ ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1132_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: product_unit,Y: product_unit,Z: product_unit] : ( ord_le3221252021190050221t_unit @ ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ ( inf_inf_Product_unit @ X @ Z ) ) @ ( inf_inf_Product_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1133_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: rat,Y: rat,Z: rat] : ( ord_less_eq_rat @ ( sup_sup_rat @ ( inf_inf_rat @ X @ Y ) @ ( inf_inf_rat @ X @ Z ) ) @ ( inf_inf_rat @ X @ ( sup_sup_rat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1134_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: nat,Y: nat,Z: nat] : ( ord_less_eq_nat @ ( sup_sup_nat @ ( inf_inf_nat @ X @ Y ) @ ( inf_inf_nat @ X @ Z ) ) @ ( inf_inf_nat @ X @ ( sup_sup_nat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1135_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: int,Y: int,Z: int] : ( ord_less_eq_int @ ( sup_sup_int @ ( inf_inf_int @ X @ Y ) @ ( inf_inf_int @ X @ Z ) ) @ ( inf_inf_int @ X @ ( sup_sup_int @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1136_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat,Z: set_nat] : ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) @ ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1137_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int,Z: set_int] : ( ord_less_eq_set_int @ ( sup_sup_set_int @ ( inf_inf_set_int @ X @ Y ) @ ( inf_inf_set_int @ X @ Z ) ) @ ( inf_inf_set_int @ X @ ( sup_sup_set_int @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1138_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) @ ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1139_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) @ ( inf_in4302113700860409141at_nat @ X @ Z ) ) @ ( inf_in4302113700860409141at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1140_distrib__inf__le,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) @ ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % distrib_inf_le
% 5.45/5.66 thf(fact_1141_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: assn] :
% 5.45/5.66 ( ( inf_inf_assn @ X @ bot_bot_assn )
% 5.45/5.66 = bot_bot_assn ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1142_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: product_unit] :
% 5.45/5.66 ( ( inf_inf_Product_unit @ X @ bot_bot_Product_unit )
% 5.45/5.66 = bot_bot_Product_unit ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1143_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ X @ bot_bo2099793752762293965at_nat )
% 5.45/5.66 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1144_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: set_o] :
% 5.45/5.66 ( ( inf_inf_set_o @ X @ bot_bot_set_o )
% 5.45/5.66 = bot_bot_set_o ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1145_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ X @ bot_bot_set_nat )
% 5.45/5.66 = bot_bot_set_nat ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1146_boolean__algebra_Oconj__zero__right,axiom,
% 5.45/5.66 ! [X: set_int] :
% 5.45/5.66 ( ( inf_inf_set_int @ X @ bot_bot_set_int )
% 5.45/5.66 = bot_bot_set_int ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_right
% 5.45/5.66 thf(fact_1147_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: assn] :
% 5.45/5.66 ( ( inf_inf_assn @ bot_bot_assn @ X )
% 5.45/5.66 = bot_bot_assn ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1148_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: product_unit] :
% 5.45/5.66 ( ( inf_inf_Product_unit @ bot_bot_Product_unit @ X )
% 5.45/5.66 = bot_bot_Product_unit ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1149_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ bot_bo2099793752762293965at_nat @ X )
% 5.45/5.66 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1150_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: set_o] :
% 5.45/5.66 ( ( inf_inf_set_o @ bot_bot_set_o @ X )
% 5.45/5.66 = bot_bot_set_o ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1151_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ bot_bot_set_nat @ X )
% 5.45/5.66 = bot_bot_set_nat ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1152_boolean__algebra_Oconj__zero__left,axiom,
% 5.45/5.66 ! [X: set_int] :
% 5.45/5.66 ( ( inf_inf_set_int @ bot_bot_set_int @ X )
% 5.45/5.66 = bot_bot_set_int ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_zero_left
% 5.45/5.66 thf(fact_1153_EX,axiom,
% 5.45/5.66 ( ( heap_Time_execute_a @ c @ h2 )
% 5.45/5.66 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ r2 @ ( produc584006145561248582it_nat @ h @ t ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % EX
% 5.45/5.66 thf(fact_1154_times__assn__raw_Oelims_I3_J,axiom,
% 5.45/5.66 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.66 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.66 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.66 ( ( Xb
% 5.45/5.66 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.66 => ? [As13: set_nat,As23: set_nat] :
% 5.45/5.66 ( ( As4
% 5.45/5.66 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 5.45/5.66 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As13 ) )
% 5.45/5.66 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As23 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % times_assn_raw.elims(3)
% 5.45/5.66 thf(fact_1155_times__assn__raw_Oelims_I2_J,axiom,
% 5.45/5.66 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.66 ( ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.66 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.66 ( ( Xb
% 5.45/5.66 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.66 => ~ ? [As1: set_nat,As2: set_nat] :
% 5.45/5.66 ( ( As4
% 5.45/5.66 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 5.45/5.66 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As1 ) )
% 5.45/5.66 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % times_assn_raw.elims(2)
% 5.45/5.66 thf(fact_1156_times__assn__raw_Oelims_I1_J,axiom,
% 5.45/5.66 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.66 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.66 = Y )
% 5.45/5.66 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.66 ( ( Xb
% 5.45/5.66 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.66 => ( Y
% 5.45/5.66 = ( ~ ? [As12: set_nat,As22: set_nat] :
% 5.45/5.66 ( ( As4
% 5.45/5.66 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 5.45/5.66 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As12 ) )
% 5.45/5.66 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As22 ) ) ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % times_assn_raw.elims(1)
% 5.45/5.66 thf(fact_1157_times__assn__raw_Osimps,axiom,
% 5.45/5.66 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.66 ( ( times_assn_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.66 = ( ? [As12: set_nat,As22: set_nat] :
% 5.45/5.66 ( ( As
% 5.45/5.66 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 5.45/5.66 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 & ( P @ ( produc7507926704131184380et_nat @ H @ As12 ) )
% 5.45/5.66 & ( Q @ ( produc7507926704131184380et_nat @ H @ As22 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % times_assn_raw.simps
% 5.45/5.66 thf(fact_1158_dual__order_Orefl,axiom,
% 5.45/5.66 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.refl
% 5.45/5.66 thf(fact_1159_dual__order_Orefl,axiom,
% 5.45/5.66 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.refl
% 5.45/5.66 thf(fact_1160_dual__order_Orefl,axiom,
% 5.45/5.66 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.refl
% 5.45/5.66 thf(fact_1161_dual__order_Orefl,axiom,
% 5.45/5.66 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.refl
% 5.45/5.66 thf(fact_1162_dual__order_Orefl,axiom,
% 5.45/5.66 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.refl
% 5.45/5.66 thf(fact_1163_order__refl,axiom,
% 5.45/5.66 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 5.45/5.66
% 5.45/5.66 % order_refl
% 5.45/5.66 thf(fact_1164_order__refl,axiom,
% 5.45/5.66 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.45/5.66
% 5.45/5.66 % order_refl
% 5.45/5.66 thf(fact_1165_order__refl,axiom,
% 5.45/5.66 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.45/5.66
% 5.45/5.66 % order_refl
% 5.45/5.66 thf(fact_1166_order__refl,axiom,
% 5.45/5.66 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.45/5.66
% 5.45/5.66 % order_refl
% 5.45/5.66 thf(fact_1167_order__refl,axiom,
% 5.45/5.66 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.45/5.66
% 5.45/5.66 % order_refl
% 5.45/5.66 thf(fact_1168_subset__empty,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 5.45/5.66 = ( A3 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_empty
% 5.45/5.66 thf(fact_1169_subset__empty,axiom,
% 5.45/5.66 ! [A3: set_o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A3 @ bot_bot_set_o )
% 5.45/5.66 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_empty
% 5.45/5.66 thf(fact_1170_subset__empty,axiom,
% 5.45/5.66 ! [A3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat )
% 5.45/5.66 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_empty
% 5.45/5.66 thf(fact_1171_subset__empty,axiom,
% 5.45/5.66 ! [A3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ bot_bot_set_int )
% 5.45/5.66 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_empty
% 5.45/5.66 thf(fact_1172_empty__subsetI,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % empty_subsetI
% 5.45/5.66 thf(fact_1173_empty__subsetI,axiom,
% 5.45/5.66 ! [A3: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % empty_subsetI
% 5.45/5.66 thf(fact_1174_empty__subsetI,axiom,
% 5.45/5.66 ! [A3: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % empty_subsetI
% 5.45/5.66 thf(fact_1175_empty__subsetI,axiom,
% 5.45/5.66 ! [A3: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % empty_subsetI
% 5.45/5.66 thf(fact_1176_Int__subset__iff,axiom,
% 5.45/5.66 ! [C3: set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ C3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.66 = ( ( ord_less_eq_set_nat @ C3 @ A3 )
% 5.45/5.66 & ( ord_less_eq_set_nat @ C3 @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_subset_iff
% 5.45/5.66 thf(fact_1177_Int__subset__iff,axiom,
% 5.45/5.66 ! [C3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ C3 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.66 = ( ( ord_le3146513528884898305at_nat @ C3 @ A3 )
% 5.45/5.66 & ( ord_le3146513528884898305at_nat @ C3 @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_subset_iff
% 5.45/5.66 thf(fact_1178_Int__subset__iff,axiom,
% 5.45/5.66 ! [C3: set_int,A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ C3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.66 = ( ( ord_less_eq_set_int @ C3 @ A3 )
% 5.45/5.66 & ( ord_less_eq_set_int @ C3 @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_subset_iff
% 5.45/5.66 thf(fact_1179_Un__subset__iff,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( ( ord_le3000389064537975527at_nat @ A3 @ C3 )
% 5.45/5.66 & ( ord_le3000389064537975527at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_subset_iff
% 5.45/5.66 thf(fact_1180_Un__subset__iff,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( ( ord_le8081472938463900775at_nat @ A3 @ C3 )
% 5.45/5.66 & ( ord_le8081472938463900775at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_subset_iff
% 5.45/5.66 thf(fact_1181_Un__subset__iff,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( ( ord_le1268244103169919719at_nat @ A3 @ C3 )
% 5.45/5.66 & ( ord_le1268244103169919719at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_subset_iff
% 5.45/5.66 thf(fact_1182_Un__subset__iff,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.66 & ( ord_less_eq_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_subset_iff
% 5.45/5.66 thf(fact_1183_Un__subset__iff,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( ( ord_less_eq_set_int @ A3 @ C3 )
% 5.45/5.66 & ( ord_less_eq_set_int @ B3 @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_subset_iff
% 5.45/5.66 thf(fact_1184_less__eq__assn__def,axiom,
% 5.45/5.66 ( ord_less_eq_assn
% 5.45/5.66 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.66 ( A5
% 5.45/5.66 = ( inf_inf_assn @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_assn_def
% 5.45/5.66 thf(fact_1185_Int__mono,axiom,
% 5.45/5.66 ! [A3: set_nat,C3: set_nat,B3: set_nat,D3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_mono
% 5.45/5.66 thf(fact_1186_Int__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,D3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le3146513528884898305at_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_mono
% 5.45/5.66 thf(fact_1187_Int__mono,axiom,
% 5.45/5.66 ! [A3: set_int,C3: set_int,B3: set_int,D3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B3 @ D3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ ( inf_inf_set_int @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_mono
% 5.45/5.66 thf(fact_1188_Int__lower1,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower1
% 5.45/5.66 thf(fact_1189_Int__lower1,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower1
% 5.45/5.66 thf(fact_1190_Int__lower1,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower1
% 5.45/5.66 thf(fact_1191_Int__lower2,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ B3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower2
% 5.45/5.66 thf(fact_1192_Int__lower2,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ B3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower2
% 5.45/5.66 thf(fact_1193_Int__lower2,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ B3 ) ).
% 5.45/5.66
% 5.45/5.66 % Int_lower2
% 5.45/5.66 thf(fact_1194_Int__absorb1,axiom,
% 5.45/5.66 ! [B3: set_nat,A3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb1
% 5.45/5.66 thf(fact_1195_Int__absorb1,axiom,
% 5.45/5.66 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb1
% 5.45/5.66 thf(fact_1196_Int__absorb1,axiom,
% 5.45/5.66 ! [B3: set_int,A3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.66 => ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb1
% 5.45/5.66 thf(fact_1197_Int__absorb2,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb2
% 5.45/5.66 thf(fact_1198_Int__absorb2,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb2
% 5.45/5.66 thf(fact_1199_Int__absorb2,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_absorb2
% 5.45/5.66 thf(fact_1200_Int__greatest,axiom,
% 5.45/5.66 ! [C3: set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ C3 @ A3 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ C3 @ B3 )
% 5.45/5.66 => ( ord_less_eq_set_nat @ C3 @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_greatest
% 5.45/5.66 thf(fact_1201_Int__greatest,axiom,
% 5.45/5.66 ! [C3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ C3 @ A3 )
% 5.45/5.66 => ( ( ord_le3146513528884898305at_nat @ C3 @ B3 )
% 5.45/5.66 => ( ord_le3146513528884898305at_nat @ C3 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_greatest
% 5.45/5.66 thf(fact_1202_Int__greatest,axiom,
% 5.45/5.66 ! [C3: set_int,A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ C3 @ A3 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ C3 @ B3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ C3 @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_greatest
% 5.45/5.66 thf(fact_1203_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_o,B3: set_o,P: $o > $o,Q: $o > $o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: $o] :
% 5.45/5.66 ( ( member_o @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_less_eq_set_o @ ( inf_inf_set_o @ A3 @ ( collect_o @ P ) ) @ ( inf_inf_set_o @ B3 @ ( collect_o @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1204_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr958786334691620121nt_int,B3: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.66 ( ( ord_le2843351958646193337nt_int @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: product_prod_int_int] :
% 5.45/5.66 ( ( member5262025264175285858nt_int @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_le2843351958646193337nt_int @ ( inf_in2269163501485487111nt_int @ A3 @ ( collec213857154873943460nt_int @ P ) ) @ ( inf_in2269163501485487111nt_int @ B3 @ ( collec213857154873943460nt_int @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1205_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_list_nat,B3: set_list_nat,P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.66 ( ( ord_le6045566169113846134st_nat @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: list_nat] :
% 5.45/5.66 ( ( member_list_nat @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_le6045566169113846134st_nat @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P ) ) @ ( inf_inf_set_list_nat @ B3 @ ( collect_list_nat @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1206_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_set_nat,B3: set_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.66 ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: set_nat] :
% 5.45/5.66 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_le6893508408891458716et_nat @ ( inf_inf_set_set_nat @ A3 @ ( collect_set_nat @ P ) ) @ ( inf_inf_set_set_nat @ B3 @ ( collect_set_nat @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1207_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,P: nat > $o,Q: nat > $o] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: nat] :
% 5.45/5.66 ( ( member_nat @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) @ ( inf_inf_set_nat @ B3 @ ( collect_nat @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1208_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.66 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ ( collec3392354462482085612at_nat @ P ) ) @ ( inf_in2572325071724192079at_nat @ B3 @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1209_Int__Collect__mono,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ! [X3: int] :
% 5.45/5.66 ( ( member_int @ X3 @ A3 )
% 5.45/5.66 => ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) ) )
% 5.45/5.66 => ( ord_less_eq_set_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) @ ( inf_inf_set_int @ B3 @ ( collect_int @ Q ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Int_Collect_mono
% 5.45/5.66 thf(fact_1210_Un__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,D3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le3000389064537975527at_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ ( sup_su718114333110466843at_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_mono
% 5.45/5.66 thf(fact_1211_Un__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,D3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le8081472938463900775at_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ ( sup_su3035147773818789531at_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_mono
% 5.45/5.66 thf(fact_1212_Un__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,D3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le1268244103169919719at_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ ( sup_su5525570899277871387at_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_mono
% 5.45/5.66 thf(fact_1213_Un__mono,axiom,
% 5.45/5.66 ! [A3: set_nat,C3: set_nat,B3: set_nat,D3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ B3 @ D3 )
% 5.45/5.66 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ ( sup_sup_set_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_mono
% 5.45/5.66 thf(fact_1214_Un__mono,axiom,
% 5.45/5.66 ! [A3: set_int,C3: set_int,B3: set_int,D3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B3 @ D3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B3 ) @ ( sup_sup_set_int @ C3 @ D3 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_mono
% 5.45/5.66 thf(fact_1215_Un__least,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le3000389064537975527at_nat @ B3 @ C3 )
% 5.45/5.66 => ( ord_le3000389064537975527at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_least
% 5.45/5.66 thf(fact_1216_Un__least,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le8081472938463900775at_nat @ B3 @ C3 )
% 5.45/5.66 => ( ord_le8081472938463900775at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_least
% 5.45/5.66 thf(fact_1217_Un__least,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_le1268244103169919719at_nat @ B3 @ C3 )
% 5.45/5.66 => ( ord_le1268244103169919719at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_least
% 5.45/5.66 thf(fact_1218_Un__least,axiom,
% 5.45/5.66 ! [A3: set_nat,C3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.66 => ( ord_less_eq_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_least
% 5.45/5.66 thf(fact_1219_Un__least,axiom,
% 5.45/5.66 ! [A3: set_int,C3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ C3 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B3 @ C3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ ( sup_sup_set_int @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_least
% 5.45/5.66 thf(fact_1220_Un__upper1,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ A3 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper1
% 5.45/5.66 thf(fact_1221_Un__upper1,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper1
% 5.45/5.66 thf(fact_1222_Un__upper1,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper1
% 5.45/5.66 thf(fact_1223_Un__upper1,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ A3 @ ( sup_sup_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper1
% 5.45/5.66 thf(fact_1224_Un__upper1,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ A3 @ ( sup_sup_set_int @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper1
% 5.45/5.66 thf(fact_1225_Un__upper2,axiom,
% 5.45/5.66 ! [B3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ B3 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper2
% 5.45/5.66 thf(fact_1226_Un__upper2,axiom,
% 5.45/5.66 ! [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ B3 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper2
% 5.45/5.66 thf(fact_1227_Un__upper2,axiom,
% 5.45/5.66 ! [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ B3 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper2
% 5.45/5.66 thf(fact_1228_Un__upper2,axiom,
% 5.45/5.66 ! [B3: set_nat,A3: set_nat] : ( ord_less_eq_set_nat @ B3 @ ( sup_sup_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper2
% 5.45/5.66 thf(fact_1229_Un__upper2,axiom,
% 5.45/5.66 ! [B3: set_int,A3: set_int] : ( ord_less_eq_set_int @ B3 @ ( sup_sup_set_int @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_upper2
% 5.45/5.66 thf(fact_1230_Un__absorb1,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( sup_su718114333110466843at_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb1
% 5.45/5.66 thf(fact_1231_Un__absorb1,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb1
% 5.45/5.66 thf(fact_1232_Un__absorb1,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb1
% 5.45/5.66 thf(fact_1233_Un__absorb1,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( sup_sup_set_nat @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb1
% 5.45/5.66 thf(fact_1234_Un__absorb1,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ( sup_sup_set_int @ A3 @ B3 )
% 5.45/5.66 = B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb1
% 5.45/5.66 thf(fact_1235_Un__absorb2,axiom,
% 5.45/5.66 ! [B3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( sup_su718114333110466843at_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb2
% 5.45/5.66 thf(fact_1236_Un__absorb2,axiom,
% 5.45/5.66 ! [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( sup_su3035147773818789531at_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb2
% 5.45/5.66 thf(fact_1237_Un__absorb2,axiom,
% 5.45/5.66 ! [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( sup_su5525570899277871387at_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb2
% 5.45/5.66 thf(fact_1238_Un__absorb2,axiom,
% 5.45/5.66 ! [B3: set_nat,A3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.66 => ( ( sup_sup_set_nat @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb2
% 5.45/5.66 thf(fact_1239_Un__absorb2,axiom,
% 5.45/5.66 ! [B3: set_int,A3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.66 => ( ( sup_sup_set_int @ A3 @ B3 )
% 5.45/5.66 = A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_absorb2
% 5.45/5.66 thf(fact_1240_subset__UnE,axiom,
% 5.45/5.66 ! [C3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ C3 @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.66 => ~ ! [A7: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ A7 @ A3 )
% 5.45/5.66 => ! [B7: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ord_le3000389064537975527at_nat @ B7 @ B3 )
% 5.45/5.66 => ( C3
% 5.45/5.66 != ( sup_su718114333110466843at_nat @ A7 @ B7 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_UnE
% 5.45/5.66 thf(fact_1241_subset__UnE,axiom,
% 5.45/5.66 ! [C3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ C3 @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.66 => ~ ! [A7: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ A7 @ A3 )
% 5.45/5.66 => ! [B7: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ord_le8081472938463900775at_nat @ B7 @ B3 )
% 5.45/5.66 => ( C3
% 5.45/5.66 != ( sup_su3035147773818789531at_nat @ A7 @ B7 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_UnE
% 5.45/5.66 thf(fact_1242_subset__UnE,axiom,
% 5.45/5.66 ! [C3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ C3 @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.66 => ~ ! [A7: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ A7 @ A3 )
% 5.45/5.66 => ! [B7: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ord_le1268244103169919719at_nat @ B7 @ B3 )
% 5.45/5.66 => ( C3
% 5.45/5.66 != ( sup_su5525570899277871387at_nat @ A7 @ B7 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_UnE
% 5.45/5.66 thf(fact_1243_subset__UnE,axiom,
% 5.45/5.66 ! [C3: set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ C3 @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.66 => ~ ! [A7: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A7 @ A3 )
% 5.45/5.66 => ! [B7: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ B7 @ B3 )
% 5.45/5.66 => ( C3
% 5.45/5.66 != ( sup_sup_set_nat @ A7 @ B7 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_UnE
% 5.45/5.66 thf(fact_1244_subset__UnE,axiom,
% 5.45/5.66 ! [C3: set_int,A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ C3 @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.66 => ~ ! [A7: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A7 @ A3 )
% 5.45/5.66 => ! [B7: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B7 @ B3 )
% 5.45/5.66 => ( C3
% 5.45/5.66 != ( sup_sup_set_int @ A7 @ B7 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_UnE
% 5.45/5.66 thf(fact_1245_subset__Un__eq,axiom,
% 5.45/5.66 ( ord_le3000389064537975527at_nat
% 5.45/5.66 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ A6 @ B6 )
% 5.45/5.66 = B6 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_Un_eq
% 5.45/5.66 thf(fact_1246_subset__Un__eq,axiom,
% 5.45/5.66 ( ord_le8081472938463900775at_nat
% 5.45/5.66 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ A6 @ B6 )
% 5.45/5.66 = B6 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_Un_eq
% 5.45/5.66 thf(fact_1247_subset__Un__eq,axiom,
% 5.45/5.66 ( ord_le1268244103169919719at_nat
% 5.45/5.66 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ A6 @ B6 )
% 5.45/5.66 = B6 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_Un_eq
% 5.45/5.66 thf(fact_1248_subset__Un__eq,axiom,
% 5.45/5.66 ( ord_less_eq_set_nat
% 5.45/5.66 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ A6 @ B6 )
% 5.45/5.66 = B6 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_Un_eq
% 5.45/5.66 thf(fact_1249_subset__Un__eq,axiom,
% 5.45/5.66 ( ord_less_eq_set_int
% 5.45/5.66 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.66 ( ( sup_sup_set_int @ A6 @ B6 )
% 5.45/5.66 = B6 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_Un_eq
% 5.45/5.66 thf(fact_1250_relH__subset,axiom,
% 5.45/5.66 ! [Bs: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.66 ( ( relH @ Bs @ H @ H3 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ As @ Bs )
% 5.45/5.66 => ( relH @ As @ H @ H3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % relH_subset
% 5.45/5.66 thf(fact_1251_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_le3146513528884898305at_nat @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1252_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_in4302113700860409141at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_le3000389064537975527at_nat @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1253_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_le8081472938463900775at_nat @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1254_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_le1268244103169919719at_nat @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1255_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.66 ( ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_inf_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_less_eq_set_nat @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1256_Un__Int__assoc__eq,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.66 ( ( ( sup_sup_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ C3 )
% 5.45/5.66 = ( inf_inf_set_int @ A3 @ ( sup_sup_set_int @ B3 @ C3 ) ) )
% 5.45/5.66 = ( ord_less_eq_set_int @ C3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % Un_Int_assoc_eq
% 5.45/5.66 thf(fact_1257_nle__le,axiom,
% 5.45/5.66 ! [A: rat,B: rat] :
% 5.45/5.66 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.66 = ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.66 & ( B != A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % nle_le
% 5.45/5.66 thf(fact_1258_nle__le,axiom,
% 5.45/5.66 ! [A: num,B: num] :
% 5.45/5.66 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.45/5.66 = ( ( ord_less_eq_num @ B @ A )
% 5.45/5.66 & ( B != A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % nle_le
% 5.45/5.66 thf(fact_1259_nle__le,axiom,
% 5.45/5.66 ! [A: nat,B: nat] :
% 5.45/5.66 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.45/5.66 = ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.66 & ( B != A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % nle_le
% 5.45/5.66 thf(fact_1260_nle__le,axiom,
% 5.45/5.66 ! [A: int,B: int] :
% 5.45/5.66 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.45/5.66 = ( ( ord_less_eq_int @ B @ A )
% 5.45/5.66 & ( B != A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % nle_le
% 5.45/5.66 thf(fact_1261_le__cases3,axiom,
% 5.45/5.66 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.66 ( ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_rat @ X @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.45/5.66 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 5.45/5.66 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 5.45/5.66 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_cases3
% 5.45/5.66 thf(fact_1262_le__cases3,axiom,
% 5.45/5.66 ! [X: num,Y: num,Z: num] :
% 5.45/5.66 ( ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_num @ Y @ X )
% 5.45/5.66 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.45/5.66 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_num @ Y @ X ) )
% 5.45/5.66 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.45/5.66 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.45/5.66 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_cases3
% 5.45/5.66 thf(fact_1263_le__cases3,axiom,
% 5.45/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.66 ( ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.45/5.66 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 5.45/5.66 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.45/5.66 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_cases3
% 5.45/5.66 thf(fact_1264_le__cases3,axiom,
% 5.45/5.66 ! [X: int,Y: int,Z: int] :
% 5.45/5.66 ( ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.66 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.45/5.66 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.45/5.66 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.45/5.66 => ~ ( ord_less_eq_int @ Y @ X ) )
% 5.45/5.66 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.45/5.66 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.45/5.66 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.45/5.66 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_cases3
% 5.45/5.66 thf(fact_1265_order__class_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 5.45/5.66 & ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_class.order_eq_iff
% 5.45/5.66 thf(fact_1266_order__class_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.45/5.66 & ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_class.order_eq_iff
% 5.45/5.66 thf(fact_1267_order__class_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [X4: num,Y4: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.45/5.66 & ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_class.order_eq_iff
% 5.45/5.66 thf(fact_1268_order__class_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.45/5.66 & ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_class.order_eq_iff
% 5.45/5.66 thf(fact_1269_order__class_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [X4: int,Y4: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.45/5.66 & ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_class.order_eq_iff
% 5.45/5.66 thf(fact_1270_ord__eq__le__trans,axiom,
% 5.45/5.66 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.66 ( ( A = B )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B @ C )
% 5.45/5.66 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_trans
% 5.45/5.66 thf(fact_1271_ord__eq__le__trans,axiom,
% 5.45/5.66 ! [A: rat,B: rat,C: rat] :
% 5.45/5.66 ( ( A = B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_trans
% 5.45/5.66 thf(fact_1272_ord__eq__le__trans,axiom,
% 5.45/5.66 ! [A: num,B: num,C: num] :
% 5.45/5.66 ( ( A = B )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_trans
% 5.45/5.66 thf(fact_1273_ord__eq__le__trans,axiom,
% 5.45/5.66 ! [A: nat,B: nat,C: nat] :
% 5.45/5.66 ( ( A = B )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_trans
% 5.45/5.66 thf(fact_1274_ord__eq__le__trans,axiom,
% 5.45/5.66 ! [A: int,B: int,C: int] :
% 5.45/5.66 ( ( A = B )
% 5.45/5.66 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.66 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_trans
% 5.45/5.66 thf(fact_1275_ord__le__eq__trans,axiom,
% 5.45/5.66 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.66 => ( ( B = C )
% 5.45/5.66 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_trans
% 5.45/5.66 thf(fact_1276_ord__le__eq__trans,axiom,
% 5.45/5.66 ! [A: rat,B: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( B = C )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_trans
% 5.45/5.66 thf(fact_1277_ord__le__eq__trans,axiom,
% 5.45/5.66 ! [A: num,B: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( B = C )
% 5.45/5.66 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_trans
% 5.45/5.66 thf(fact_1278_ord__le__eq__trans,axiom,
% 5.45/5.66 ! [A: nat,B: nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( B = C )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_trans
% 5.45/5.66 thf(fact_1279_ord__le__eq__trans,axiom,
% 5.45/5.66 ! [A: int,B: int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.66 => ( ( B = C )
% 5.45/5.66 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_trans
% 5.45/5.66 thf(fact_1280_order__antisym,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.66 => ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym
% 5.45/5.66 thf(fact_1281_order__antisym,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.66 => ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym
% 5.45/5.66 thf(fact_1282_order__antisym,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_num @ Y @ X )
% 5.45/5.66 => ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym
% 5.45/5.66 thf(fact_1283_order__antisym,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.66 => ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym
% 5.45/5.66 thf(fact_1284_order__antisym,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.66 => ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym
% 5.45/5.66 thf(fact_1285_order_Otrans,axiom,
% 5.45/5.66 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B @ C )
% 5.45/5.66 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order.trans
% 5.45/5.66 thf(fact_1286_order_Otrans,axiom,
% 5.45/5.66 ! [A: rat,B: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order.trans
% 5.45/5.66 thf(fact_1287_order_Otrans,axiom,
% 5.45/5.66 ! [A: num,B: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order.trans
% 5.45/5.66 thf(fact_1288_order_Otrans,axiom,
% 5.45/5.66 ! [A: nat,B: nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order.trans
% 5.45/5.66 thf(fact_1289_order_Otrans,axiom,
% 5.45/5.66 ! [A: int,B: int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.66 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order.trans
% 5.45/5.66 thf(fact_1290_order__trans,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.45/5.66 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_trans
% 5.45/5.66 thf(fact_1291_order__trans,axiom,
% 5.45/5.66 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.45/5.66 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_trans
% 5.45/5.66 thf(fact_1292_order__trans,axiom,
% 5.45/5.66 ! [X: num,Y: num,Z: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_num @ Y @ Z )
% 5.45/5.66 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_trans
% 5.45/5.66 thf(fact_1293_order__trans,axiom,
% 5.45/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.45/5.66 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_trans
% 5.45/5.66 thf(fact_1294_order__trans,axiom,
% 5.45/5.66 ! [X: int,Y: int,Z: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 => ( ( ord_less_eq_int @ Y @ Z )
% 5.45/5.66 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_trans
% 5.45/5.66 thf(fact_1295_linorder__wlog,axiom,
% 5.45/5.66 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.45/5.66 ( ! [A4: rat,B4: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A4 @ B4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( ! [A4: rat,B4: rat] :
% 5.45/5.66 ( ( P @ B4 @ A4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( P @ A @ B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_wlog
% 5.45/5.66 thf(fact_1296_linorder__wlog,axiom,
% 5.45/5.66 ! [P: num > num > $o,A: num,B: num] :
% 5.45/5.66 ( ! [A4: num,B4: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A4 @ B4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( ! [A4: num,B4: num] :
% 5.45/5.66 ( ( P @ B4 @ A4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( P @ A @ B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_wlog
% 5.45/5.66 thf(fact_1297_linorder__wlog,axiom,
% 5.45/5.66 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.45/5.66 ( ! [A4: nat,B4: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A4 @ B4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( ! [A4: nat,B4: nat] :
% 5.45/5.66 ( ( P @ B4 @ A4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( P @ A @ B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_wlog
% 5.45/5.66 thf(fact_1298_linorder__wlog,axiom,
% 5.45/5.66 ! [P: int > int > $o,A: int,B: int] :
% 5.45/5.66 ( ! [A4: int,B4: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ A4 @ B4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( ! [A4: int,B4: int] :
% 5.45/5.66 ( ( P @ B4 @ A4 )
% 5.45/5.66 => ( P @ A4 @ B4 ) )
% 5.45/5.66 => ( P @ A @ B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_wlog
% 5.45/5.66 thf(fact_1299_dual__order_Oeq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B5 @ A5 )
% 5.45/5.66 & ( ord_less_eq_set_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.eq_iff
% 5.45/5.66 thf(fact_1300_dual__order_Oeq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.45/5.66 & ( ord_less_eq_rat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.eq_iff
% 5.45/5.66 thf(fact_1301_dual__order_Oeq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: num,B5: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.45/5.66 & ( ord_less_eq_num @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.eq_iff
% 5.45/5.66 thf(fact_1302_dual__order_Oeq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.45/5.66 & ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.eq_iff
% 5.45/5.66 thf(fact_1303_dual__order_Oeq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: int,B5: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.45/5.66 & ( ord_less_eq_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.eq_iff
% 5.45/5.66 thf(fact_1304_dual__order_Oantisym,axiom,
% 5.45/5.66 ! [B: set_int,A: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.antisym
% 5.45/5.66 thf(fact_1305_dual__order_Oantisym,axiom,
% 5.45/5.66 ! [B: rat,A: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.antisym
% 5.45/5.66 thf(fact_1306_dual__order_Oantisym,axiom,
% 5.45/5.66 ! [B: num,A: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.antisym
% 5.45/5.66 thf(fact_1307_dual__order_Oantisym,axiom,
% 5.45/5.66 ! [B: nat,A: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.antisym
% 5.45/5.66 thf(fact_1308_dual__order_Oantisym,axiom,
% 5.45/5.66 ! [B: int,A: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_int @ A @ B )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.antisym
% 5.45/5.66 thf(fact_1309_dual__order_Otrans,axiom,
% 5.45/5.66 ! [B: set_int,A: set_int,C: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ C @ B )
% 5.45/5.66 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.trans
% 5.45/5.66 thf(fact_1310_dual__order_Otrans,axiom,
% 5.45/5.66 ! [B: rat,A: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_rat @ C @ B )
% 5.45/5.66 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.trans
% 5.45/5.66 thf(fact_1311_dual__order_Otrans,axiom,
% 5.45/5.66 ! [B: num,A: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_num @ C @ B )
% 5.45/5.66 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.trans
% 5.45/5.66 thf(fact_1312_dual__order_Otrans,axiom,
% 5.45/5.66 ! [B: nat,A: nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_nat @ C @ B )
% 5.45/5.66 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.trans
% 5.45/5.66 thf(fact_1313_dual__order_Otrans,axiom,
% 5.45/5.66 ! [B: int,A: int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.66 => ( ( ord_less_eq_int @ C @ B )
% 5.45/5.66 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % dual_order.trans
% 5.45/5.66 thf(fact_1314_antisym,axiom,
% 5.45/5.66 ! [A: set_int,B: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % antisym
% 5.45/5.66 thf(fact_1315_antisym,axiom,
% 5.45/5.66 ! [A: rat,B: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % antisym
% 5.45/5.66 thf(fact_1316_antisym,axiom,
% 5.45/5.66 ! [A: num,B: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ A )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % antisym
% 5.45/5.66 thf(fact_1317_antisym,axiom,
% 5.45/5.66 ! [A: nat,B: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % antisym
% 5.45/5.66 thf(fact_1318_antisym,axiom,
% 5.45/5.66 ! [A: int,B: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_int @ B @ A )
% 5.45/5.66 => ( A = B ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % antisym
% 5.45/5.66 thf(fact_1319_Orderings_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.45/5.66 & ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Orderings.order_eq_iff
% 5.45/5.66 thf(fact_1320_Orderings_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: rat,Z3: rat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.45/5.66 & ( ord_less_eq_rat @ B5 @ A5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Orderings.order_eq_iff
% 5.45/5.66 thf(fact_1321_Orderings_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: num,B5: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.45/5.66 & ( ord_less_eq_num @ B5 @ A5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Orderings.order_eq_iff
% 5.45/5.66 thf(fact_1322_Orderings_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.45/5.66 & ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Orderings.order_eq_iff
% 5.45/5.66 thf(fact_1323_Orderings_Oorder__eq__iff,axiom,
% 5.45/5.66 ( ( ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.45/5.66 = ( ^ [A5: int,B5: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.45/5.66 & ( ord_less_eq_int @ B5 @ A5 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Orderings.order_eq_iff
% 5.45/5.66 thf(fact_1324_order__subst1,axiom,
% 5.45/5.66 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1325_order__subst1,axiom,
% 5.45/5.66 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1326_order__subst1,axiom,
% 5.45/5.66 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1327_order__subst1,axiom,
% 5.45/5.66 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.66 => ( ! [X3: int,Y3: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1328_order__subst1,axiom,
% 5.45/5.66 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1329_order__subst1,axiom,
% 5.45/5.66 ! [A: num,F: num > num,B: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1330_order__subst1,axiom,
% 5.45/5.66 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1331_order__subst1,axiom,
% 5.45/5.66 ! [A: num,F: int > num,B: int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.66 => ( ! [X3: int,Y3: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1332_order__subst1,axiom,
% 5.45/5.66 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1333_order__subst1,axiom,
% 5.45/5.66 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst1
% 5.45/5.66 thf(fact_1334_order__subst2,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1335_order__subst2,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1336_order__subst2,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1337_order__subst2,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1338_order__subst2,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1339_order__subst2,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1340_order__subst2,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1341_order__subst2,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1342_order__subst2,axiom,
% 5.45/5.66 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1343_order__subst2,axiom,
% 5.45/5.66 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_subst2
% 5.45/5.66 thf(fact_1344_order__eq__refl,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int] :
% 5.45/5.66 ( ( X = Y )
% 5.45/5.66 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_eq_refl
% 5.45/5.66 thf(fact_1345_order__eq__refl,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ( X = Y )
% 5.45/5.66 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_eq_refl
% 5.45/5.66 thf(fact_1346_order__eq__refl,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ( X = Y )
% 5.45/5.66 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_eq_refl
% 5.45/5.66 thf(fact_1347_order__eq__refl,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( X = Y )
% 5.45/5.66 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_eq_refl
% 5.45/5.66 thf(fact_1348_order__eq__refl,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ( X = Y )
% 5.45/5.66 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_eq_refl
% 5.45/5.66 thf(fact_1349_linorder__linear,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_linear
% 5.45/5.66 thf(fact_1350_linorder__linear,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 | ( ord_less_eq_num @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_linear
% 5.45/5.66 thf(fact_1351_linorder__linear,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_linear
% 5.45/5.66 thf(fact_1352_linorder__linear,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 | ( ord_less_eq_int @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_linear
% 5.45/5.66 thf(fact_1353_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1354_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1355_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1356_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1357_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1358_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: num,F: num > num,B: num,C: num] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1359_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1360_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: int,F: num > int,B: num,C: num] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1361_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1362_ord__eq__le__subst,axiom,
% 5.45/5.66 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.45/5.66 ( ( A
% 5.45/5.66 = ( F @ B ) )
% 5.45/5.66 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_eq_le_subst
% 5.45/5.66 thf(fact_1363_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1364_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1365_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1366_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1367_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1368_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1369_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1370_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: num,B: num,F: num > int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: num,Y3: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1371_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1372_ord__le__eq__subst,axiom,
% 5.45/5.66 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.66 => ( ( ( F @ B )
% 5.45/5.66 = C )
% 5.45/5.66 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.66 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % ord_le_eq_subst
% 5.45/5.66 thf(fact_1373_linorder__le__cases,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_le_cases
% 5.45/5.66 thf(fact_1374_linorder__le__cases,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ~ ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_le_cases
% 5.45/5.66 thf(fact_1375_linorder__le__cases,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ~ ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_le_cases
% 5.45/5.66 thf(fact_1376_linorder__le__cases,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ~ ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.45/5.66
% 5.45/5.66 % linorder_le_cases
% 5.45/5.66 thf(fact_1377_order__antisym__conv,axiom,
% 5.45/5.66 ! [Y: set_int,X: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.66 = ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym_conv
% 5.45/5.66 thf(fact_1378_order__antisym__conv,axiom,
% 5.45/5.66 ! [Y: rat,X: rat] :
% 5.45/5.66 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.66 => ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.66 = ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym_conv
% 5.45/5.66 thf(fact_1379_order__antisym__conv,axiom,
% 5.45/5.66 ! [Y: num,X: num] :
% 5.45/5.66 ( ( ord_less_eq_num @ Y @ X )
% 5.45/5.66 => ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.66 = ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym_conv
% 5.45/5.66 thf(fact_1380_order__antisym__conv,axiom,
% 5.45/5.66 ! [Y: nat,X: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.66 => ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.66 = ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym_conv
% 5.45/5.66 thf(fact_1381_order__antisym__conv,axiom,
% 5.45/5.66 ! [Y: int,X: int] :
% 5.45/5.66 ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.66 => ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.66 = ( X = Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % order_antisym_conv
% 5.45/5.66 thf(fact_1382_boolean__algebra__cancel_Oinf1,axiom,
% 5.45/5.66 ! [A3: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( inf_inf_set_nat @ K @ A ) )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A3 @ B )
% 5.45/5.66 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf1
% 5.45/5.66 thf(fact_1383_boolean__algebra__cancel_Oinf1,axiom,
% 5.45/5.66 ! [A3: assn,K: assn,A: assn,B: assn] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( inf_inf_assn @ K @ A ) )
% 5.45/5.66 => ( ( inf_inf_assn @ A3 @ B )
% 5.45/5.66 = ( inf_inf_assn @ K @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf1
% 5.45/5.66 thf(fact_1384_boolean__algebra__cancel_Oinf1,axiom,
% 5.45/5.66 ! [A3: nat,K: nat,A: nat,B: nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( inf_inf_nat @ K @ A ) )
% 5.45/5.66 => ( ( inf_inf_nat @ A3 @ B )
% 5.45/5.66 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf1
% 5.45/5.66 thf(fact_1385_boolean__algebra__cancel_Oinf1,axiom,
% 5.45/5.66 ! [A3: product_unit,K: product_unit,A: product_unit,B: product_unit] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( inf_inf_Product_unit @ K @ A ) )
% 5.45/5.66 => ( ( inf_inf_Product_unit @ A3 @ B )
% 5.45/5.66 = ( inf_inf_Product_unit @ K @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf1
% 5.45/5.66 thf(fact_1386_boolean__algebra__cancel_Oinf1,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ K @ A ) )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A3 @ B )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf1
% 5.45/5.66 thf(fact_1387_boolean__algebra__cancel_Oinf2,axiom,
% 5.45/5.66 ! [B3: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( inf_inf_set_nat @ K @ B ) )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A @ B3 )
% 5.45/5.66 = ( inf_inf_set_nat @ K @ ( inf_inf_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf2
% 5.45/5.66 thf(fact_1388_boolean__algebra__cancel_Oinf2,axiom,
% 5.45/5.66 ! [B3: assn,K: assn,B: assn,A: assn] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( inf_inf_assn @ K @ B ) )
% 5.45/5.66 => ( ( inf_inf_assn @ A @ B3 )
% 5.45/5.66 = ( inf_inf_assn @ K @ ( inf_inf_assn @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf2
% 5.45/5.66 thf(fact_1389_boolean__algebra__cancel_Oinf2,axiom,
% 5.45/5.66 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( inf_inf_nat @ K @ B ) )
% 5.45/5.66 => ( ( inf_inf_nat @ A @ B3 )
% 5.45/5.66 = ( inf_inf_nat @ K @ ( inf_inf_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf2
% 5.45/5.66 thf(fact_1390_boolean__algebra__cancel_Oinf2,axiom,
% 5.45/5.66 ! [B3: product_unit,K: product_unit,B: product_unit,A: product_unit] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( inf_inf_Product_unit @ K @ B ) )
% 5.45/5.66 => ( ( inf_inf_Product_unit @ A @ B3 )
% 5.45/5.66 = ( inf_inf_Product_unit @ K @ ( inf_inf_Product_unit @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf2
% 5.45/5.66 thf(fact_1391_boolean__algebra__cancel_Oinf2,axiom,
% 5.45/5.66 ! [B3: set_Pr1261947904930325089at_nat,K: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ K @ B ) )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A @ B3 )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ K @ ( inf_in2572325071724192079at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.inf2
% 5.45/5.66 thf(fact_1392_boolean__algebra__cancel_Osup1,axiom,
% 5.45/5.66 ! [A3: set_Pr8693737435421807431at_nat,K: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ K @ A ) )
% 5.45/5.66 => ( ( sup_su718114333110466843at_nat @ A3 @ B )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ K @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup1
% 5.45/5.66 thf(fact_1393_boolean__algebra__cancel_Osup1,axiom,
% 5.45/5.66 ! [A3: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ K @ A ) )
% 5.45/5.66 => ( ( sup_su3035147773818789531at_nat @ A3 @ B )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup1
% 5.45/5.66 thf(fact_1394_boolean__algebra__cancel_Osup1,axiom,
% 5.45/5.66 ! [A3: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ K @ A ) )
% 5.45/5.66 => ( ( sup_su5525570899277871387at_nat @ A3 @ B )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup1
% 5.45/5.66 thf(fact_1395_boolean__algebra__cancel_Osup1,axiom,
% 5.45/5.66 ! [A3: set_nat,K: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( sup_sup_set_nat @ K @ A ) )
% 5.45/5.66 => ( ( sup_sup_set_nat @ A3 @ B )
% 5.45/5.66 = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup1
% 5.45/5.66 thf(fact_1396_boolean__algebra__cancel_Osup1,axiom,
% 5.45/5.66 ! [A3: nat,K: nat,A: nat,B: nat] :
% 5.45/5.66 ( ( A3
% 5.45/5.66 = ( sup_sup_nat @ K @ A ) )
% 5.45/5.66 => ( ( sup_sup_nat @ A3 @ B )
% 5.45/5.66 = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup1
% 5.45/5.66 thf(fact_1397_boolean__algebra__cancel_Osup2,axiom,
% 5.45/5.66 ! [B3: set_Pr8693737435421807431at_nat,K: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ K @ B ) )
% 5.45/5.66 => ( ( sup_su718114333110466843at_nat @ A @ B3 )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ K @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup2
% 5.45/5.66 thf(fact_1398_boolean__algebra__cancel_Osup2,axiom,
% 5.45/5.66 ! [B3: set_Pr8551490117392284871at_nat,K: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ K @ B ) )
% 5.45/5.66 => ( ( sup_su3035147773818789531at_nat @ A @ B3 )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ K @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup2
% 5.45/5.66 thf(fact_1399_boolean__algebra__cancel_Osup2,axiom,
% 5.45/5.66 ! [B3: set_Pr4329608150637261639at_nat,K: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ K @ B ) )
% 5.45/5.66 => ( ( sup_su5525570899277871387at_nat @ A @ B3 )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ K @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup2
% 5.45/5.66 thf(fact_1400_boolean__algebra__cancel_Osup2,axiom,
% 5.45/5.66 ! [B3: set_nat,K: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( sup_sup_set_nat @ K @ B ) )
% 5.45/5.66 => ( ( sup_sup_set_nat @ A @ B3 )
% 5.45/5.66 = ( sup_sup_set_nat @ K @ ( sup_sup_set_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup2
% 5.45/5.66 thf(fact_1401_boolean__algebra__cancel_Osup2,axiom,
% 5.45/5.66 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.45/5.66 ( ( B3
% 5.45/5.66 = ( sup_sup_nat @ K @ B ) )
% 5.45/5.66 => ( ( sup_sup_nat @ A @ B3 )
% 5.45/5.66 = ( sup_sup_nat @ K @ ( sup_sup_nat @ A @ B ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra_cancel.sup2
% 5.45/5.66 thf(fact_1402_bot_Oextremum,axiom,
% 5.45/5.66 ! [A: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ bot_bo2099793752762293965at_nat @ A ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum
% 5.45/5.66 thf(fact_1403_bot_Oextremum,axiom,
% 5.45/5.66 ! [A: set_o] : ( ord_less_eq_set_o @ bot_bot_set_o @ A ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum
% 5.45/5.66 thf(fact_1404_bot_Oextremum,axiom,
% 5.45/5.66 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum
% 5.45/5.66 thf(fact_1405_bot_Oextremum,axiom,
% 5.45/5.66 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum
% 5.45/5.66 thf(fact_1406_bot_Oextremum,axiom,
% 5.45/5.66 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum
% 5.45/5.66 thf(fact_1407_bot_Oextremum__unique,axiom,
% 5.45/5.66 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 5.45/5.66 = ( A = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_unique
% 5.45/5.66 thf(fact_1408_bot_Oextremum__unique,axiom,
% 5.45/5.66 ! [A: set_o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 5.45/5.66 = ( A = bot_bot_set_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_unique
% 5.45/5.66 thf(fact_1409_bot_Oextremum__unique,axiom,
% 5.45/5.66 ! [A: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.45/5.66 = ( A = bot_bot_set_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_unique
% 5.45/5.66 thf(fact_1410_bot_Oextremum__unique,axiom,
% 5.45/5.66 ! [A: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.45/5.66 = ( A = bot_bot_set_int ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_unique
% 5.45/5.66 thf(fact_1411_bot_Oextremum__unique,axiom,
% 5.45/5.66 ! [A: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.45/5.66 = ( A = bot_bot_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_unique
% 5.45/5.66 thf(fact_1412_bot_Oextremum__uniqueI,axiom,
% 5.45/5.66 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A @ bot_bo2099793752762293965at_nat )
% 5.45/5.66 => ( A = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_uniqueI
% 5.45/5.66 thf(fact_1413_bot_Oextremum__uniqueI,axiom,
% 5.45/5.66 ! [A: set_o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A @ bot_bot_set_o )
% 5.45/5.66 => ( A = bot_bot_set_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_uniqueI
% 5.45/5.66 thf(fact_1414_bot_Oextremum__uniqueI,axiom,
% 5.45/5.66 ! [A: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.45/5.66 => ( A = bot_bot_set_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_uniqueI
% 5.45/5.66 thf(fact_1415_bot_Oextremum__uniqueI,axiom,
% 5.45/5.66 ! [A: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.45/5.66 => ( A = bot_bot_set_int ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_uniqueI
% 5.45/5.66 thf(fact_1416_bot_Oextremum__uniqueI,axiom,
% 5.45/5.66 ! [A: nat] :
% 5.45/5.66 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.45/5.66 => ( A = bot_bot_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot.extremum_uniqueI
% 5.45/5.66 thf(fact_1417_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ X @ bot_bo5327735625951526323at_nat )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1418_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ X @ bot_bo8422036546324065075at_nat )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1419_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ X @ bot_bo228742789529271731at_nat )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1420_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( sup_su6327502436637775413at_nat @ X @ bot_bo2099793752762293965at_nat )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1421_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_o] :
% 5.45/5.66 ( ( sup_sup_set_o @ X @ bot_bot_set_o )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1422_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ X @ bot_bot_set_nat )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1423_boolean__algebra_Odisj__zero__right,axiom,
% 5.45/5.66 ! [X: set_int] :
% 5.45/5.66 ( ( sup_sup_set_int @ X @ bot_bot_set_int )
% 5.45/5.66 = X ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_zero_right
% 5.45/5.66 thf(fact_1424_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.66 ( ( inf_inf_assn @ X @ ( sup_sup_assn @ Y @ Z ) )
% 5.45/5.66 = ( sup_sup_assn @ ( inf_inf_assn @ X @ Y ) @ ( inf_inf_assn @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1425_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.66 ( ( inf_inf_Product_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) )
% 5.45/5.66 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) @ ( inf_inf_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1426_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) )
% 5.45/5.66 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ ( inf_in2572325071724192079at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1427_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( inf_in4302113700860409141at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) @ ( inf_in4302113700860409141at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1428_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( inf_in1697001100524423349at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ ( inf_in1697001100524423349at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1429_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( inf_in7913087082777306421at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ ( inf_in7913087082777306421at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1430_boolean__algebra_Oconj__disj__distrib,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) )
% 5.45/5.66 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ ( inf_inf_set_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib
% 5.45/5.66 thf(fact_1431_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.66 ( ( sup_sup_assn @ X @ ( inf_inf_assn @ Y @ Z ) )
% 5.45/5.66 = ( inf_inf_assn @ ( sup_sup_assn @ X @ Y ) @ ( sup_sup_assn @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1432_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.66 ( ( sup_sup_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ Z ) )
% 5.45/5.66 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ X @ Y ) @ ( sup_sup_Product_unit @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1433_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( sup_su6327502436637775413at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ Z ) )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) @ ( sup_su6327502436637775413at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1434_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ X @ ( inf_in4302113700860409141at_nat @ Y @ Z ) )
% 5.45/5.66 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) @ ( sup_su718114333110466843at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1435_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ X @ ( inf_in1697001100524423349at_nat @ Y @ Z ) )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) @ ( sup_su3035147773818789531at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1436_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ X @ ( inf_in7913087082777306421at_nat @ Y @ Z ) )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) @ ( sup_su5525570899277871387at_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1437_boolean__algebra_Odisj__conj__distrib,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ X @ ( inf_inf_set_nat @ Y @ Z ) )
% 5.45/5.66 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ X @ Y ) @ ( sup_sup_set_nat @ X @ Z ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib
% 5.45/5.66 thf(fact_1438_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: assn,Z: assn,X: assn] :
% 5.45/5.66 ( ( inf_inf_assn @ ( sup_sup_assn @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_sup_assn @ ( inf_inf_assn @ Y @ X ) @ ( inf_inf_assn @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1439_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: product_unit,Z: product_unit,X: product_unit] :
% 5.45/5.66 ( ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ X ) @ ( inf_inf_Product_unit @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1440_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ X ) @ ( inf_in2572325071724192079at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1441_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ Y @ X ) @ ( inf_in4302113700860409141at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1442_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ X ) @ ( inf_in1697001100524423349at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1443_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ X ) @ ( inf_in7913087082777306421at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1444_boolean__algebra_Oconj__disj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 5.45/5.66 ( ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ X ) @ ( inf_inf_set_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.conj_disj_distrib2
% 5.45/5.66 thf(fact_1445_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: assn,Z: assn,X: assn] :
% 5.45/5.66 ( ( sup_sup_assn @ ( inf_inf_assn @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_inf_assn @ ( sup_sup_assn @ Y @ X ) @ ( sup_sup_assn @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1446_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: product_unit,Z: product_unit,X: product_unit] :
% 5.45/5.66 ( ( sup_sup_Product_unit @ ( inf_inf_Product_unit @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_inf_Product_unit @ ( sup_sup_Product_unit @ Y @ X ) @ ( sup_sup_Product_unit @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1447_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_in2572325071724192079at_nat @ ( sup_su6327502436637775413at_nat @ Y @ X ) @ ( sup_su6327502436637775413at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1448_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat,X: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_in4302113700860409141at_nat @ ( sup_su718114333110466843at_nat @ Y @ X ) @ ( sup_su718114333110466843at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1449_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat,X: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_in1697001100524423349at_nat @ ( sup_su3035147773818789531at_nat @ Y @ X ) @ ( sup_su3035147773818789531at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1450_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat,X: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_in7913087082777306421at_nat @ ( sup_su5525570899277871387at_nat @ Y @ X ) @ ( sup_su5525570899277871387at_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1451_boolean__algebra_Odisj__conj__distrib2,axiom,
% 5.45/5.66 ! [Y: set_nat,Z: set_nat,X: set_nat] :
% 5.45/5.66 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ Y @ Z ) @ X )
% 5.45/5.66 = ( inf_inf_set_nat @ ( sup_sup_set_nat @ Y @ X ) @ ( sup_sup_set_nat @ Z @ X ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % boolean_algebra.disj_conj_distrib2
% 5.45/5.66 thf(fact_1452_sup__Some,axiom,
% 5.45/5.66 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.66 ( ( sup_su1419176701018045153at_nat @ ( some_s579751585967276588at_nat @ X ) @ ( some_s579751585967276588at_nat @ Y ) )
% 5.45/5.66 = ( some_s579751585967276588at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % sup_Some
% 5.45/5.66 thf(fact_1453_sup__Some,axiom,
% 5.45/5.66 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.66 ( ( sup_su5873096292857799009at_nat @ ( some_s287724117700012716at_nat @ X ) @ ( some_s287724117700012716at_nat @ Y ) )
% 5.45/5.66 = ( some_s287724117700012716at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % sup_Some
% 5.45/5.66 thf(fact_1454_sup__Some,axiom,
% 5.45/5.66 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.66 ( ( sup_su2273273666271716065at_nat @ ( some_s5890477192898017836at_nat @ X ) @ ( some_s5890477192898017836at_nat @ Y ) )
% 5.45/5.66 = ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % sup_Some
% 5.45/5.66 thf(fact_1455_sup__Some,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat] :
% 5.45/5.66 ( ( sup_su3598758113090618626et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 5.45/5.66 = ( some_set_nat @ ( sup_sup_set_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % sup_Some
% 5.45/5.66 thf(fact_1456_sup__Some,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( sup_sup_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.45/5.66 = ( some_nat @ ( sup_sup_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % sup_Some
% 5.45/5.66 thf(fact_1457_inf__Some,axiom,
% 5.45/5.66 ! [X: set_nat,Y: set_nat] :
% 5.45/5.66 ( ( inf_in7812914138253463912et_nat @ ( some_set_nat @ X ) @ ( some_set_nat @ Y ) )
% 5.45/5.66 = ( some_set_nat @ ( inf_inf_set_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % inf_Some
% 5.45/5.66 thf(fact_1458_inf__Some,axiom,
% 5.45/5.66 ! [X: assn,Y: assn] :
% 5.45/5.66 ( ( inf_inf_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 5.45/5.66 = ( some_assn @ ( inf_inf_assn @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % inf_Some
% 5.45/5.66 thf(fact_1459_inf__Some,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( inf_inf_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.45/5.66 = ( some_nat @ ( inf_inf_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % inf_Some
% 5.45/5.66 thf(fact_1460_inf__Some,axiom,
% 5.45/5.66 ! [X: product_unit,Y: product_unit] :
% 5.45/5.66 ( ( inf_in5800606384722953409t_unit @ ( some_Product_unit @ X ) @ ( some_Product_unit @ Y ) )
% 5.45/5.66 = ( some_Product_unit @ ( inf_inf_Product_unit @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % inf_Some
% 5.45/5.66 thf(fact_1461_inf__Some,axiom,
% 5.45/5.66 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( inf_in777885744494410645at_nat @ ( some_s147305329494351046at_nat @ X ) @ ( some_s147305329494351046at_nat @ Y ) )
% 5.45/5.66 = ( some_s147305329494351046at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % inf_Some
% 5.45/5.66 thf(fact_1462_less__eq__option__Some,axiom,
% 5.45/5.66 ! [X: set_int,Y: set_int] :
% 5.45/5.66 ( ( ord_le353528952715127954et_int @ ( some_set_int @ X ) @ ( some_set_int @ Y ) )
% 5.45/5.66 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_option_Some
% 5.45/5.66 thf(fact_1463_less__eq__option__Some,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 5.45/5.66 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_option_Some
% 5.45/5.66 thf(fact_1464_less__eq__option__Some,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 5.45/5.66 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_option_Some
% 5.45/5.66 thf(fact_1465_less__eq__option__Some,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.45/5.66 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_option_Some
% 5.45/5.66 thf(fact_1466_less__eq__option__Some,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ( ord_le1736525451366464988on_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 5.45/5.66 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_eq_option_Some
% 5.45/5.66 thf(fact_1467__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062r_Ah_H_At_O_A_092_060lbrakk_062execute_Ac_Ah_A_061_ASome_A_Ir_M_Ah_H_M_At_J_059_A_Ih_H_M_Anew__addrs_Ah_Aas1_Ah_H_J_A_092_060Turnstile_062_AQ_Ar_059_ArelH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_Ah_Ah_H_059_Alim_Ah_A_092_060le_062_Alim_Ah_H_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.45/5.66 ~ ! [R2: a,H5: heap_e7401611519738050253t_unit] :
% 5.45/5.66 ( ? [T2: nat] :
% 5.45/5.66 ( ( heap_Time_execute_a @ c @ h2 )
% 5.45/5.66 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ T2 ) ) ) )
% 5.45/5.66 => ( ( rep_assn @ ( q @ R2 ) @ ( produc7507926704131184380et_nat @ H5 @ ( hoare_new_addrs @ h2 @ as1 @ H5 ) ) )
% 5.45/5.66 => ( ( relH
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as1 ) ) )
% 5.45/5.66 @ h2
% 5.45/5.66 @ H5 )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ h2 ) @ ( lim_Product_unit @ H5 ) ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % \<open>\<And>thesis. (\<And>r h' t. \<lbrakk>execute c h = Some (r, h', t); (h', new_addrs h as1 h') \<Turnstile> Q r; relH {a. a < lim h \<and> a \<notin> as1} h h'; lim h \<le> lim h'\<rbrakk> \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.45/5.66 thf(fact_1468_option_Oinject,axiom,
% 5.45/5.66 ! [X2: produc3260487557148687353it_nat,Y2: produc3260487557148687353it_nat] :
% 5.45/5.66 ( ( ( some_P7913643980934408916it_nat @ X2 )
% 5.45/5.66 = ( some_P7913643980934408916it_nat @ Y2 ) )
% 5.45/5.66 = ( X2 = Y2 ) ) ).
% 5.45/5.66
% 5.45/5.66 % option.inject
% 5.45/5.66 thf(fact_1469_option_Oinject,axiom,
% 5.45/5.66 ! [X2: num,Y2: num] :
% 5.45/5.66 ( ( ( some_num @ X2 )
% 5.45/5.66 = ( some_num @ Y2 ) )
% 5.45/5.66 = ( X2 = Y2 ) ) ).
% 5.45/5.66
% 5.45/5.66 % option.inject
% 5.45/5.66 thf(fact_1470_option_Oinject,axiom,
% 5.45/5.66 ! [X2: produc8664842809031399944it_nat,Y2: produc8664842809031399944it_nat] :
% 5.45/5.66 ( ( ( some_P1914260805536162275it_nat @ X2 )
% 5.45/5.66 = ( some_P1914260805536162275it_nat @ Y2 ) )
% 5.45/5.66 = ( X2 = Y2 ) ) ).
% 5.45/5.66
% 5.45/5.66 % option.inject
% 5.45/5.66 thf(fact_1471_bot__empty__eq,axiom,
% 5.45/5.66 ( bot_bot_set_nat_o
% 5.45/5.66 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot_empty_eq
% 5.45/5.66 thf(fact_1472_bot__empty__eq,axiom,
% 5.45/5.66 ( bot_bo482883023278783056_nat_o
% 5.45/5.66 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot_empty_eq
% 5.45/5.66 thf(fact_1473_bot__empty__eq,axiom,
% 5.45/5.66 ( bot_bot_o_o
% 5.45/5.66 = ( ^ [X4: $o] : ( member_o @ X4 @ bot_bot_set_o ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot_empty_eq
% 5.45/5.66 thf(fact_1474_bot__empty__eq,axiom,
% 5.45/5.66 ( bot_bot_nat_o
% 5.45/5.66 = ( ^ [X4: nat] : ( member_nat @ X4 @ bot_bot_set_nat ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot_empty_eq
% 5.45/5.66 thf(fact_1475_bot__empty__eq,axiom,
% 5.45/5.66 ( bot_bot_int_o
% 5.45/5.66 = ( ^ [X4: int] : ( member_int @ X4 @ bot_bot_set_int ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % bot_empty_eq
% 5.45/5.66 thf(fact_1476_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: product_prod_int_int > $o] :
% 5.45/5.66 ( ( ( collec213857154873943460nt_int @ P )
% 5.45/5.66 = bot_bo1796632182523588997nt_int )
% 5.45/5.66 = ( P = bot_bo8147686125503663512_int_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1477_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: list_nat > $o] :
% 5.45/5.66 ( ( ( collect_list_nat @ P )
% 5.45/5.66 = bot_bot_set_list_nat )
% 5.45/5.66 = ( P = bot_bot_list_nat_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1478_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: set_nat > $o] :
% 5.45/5.66 ( ( ( collect_set_nat @ P )
% 5.45/5.66 = bot_bot_set_set_nat )
% 5.45/5.66 = ( P = bot_bot_set_nat_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1479_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: product_prod_nat_nat > $o] :
% 5.45/5.66 ( ( ( collec3392354462482085612at_nat @ P )
% 5.45/5.66 = bot_bo2099793752762293965at_nat )
% 5.45/5.66 = ( P = bot_bo482883023278783056_nat_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1480_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: $o > $o] :
% 5.45/5.66 ( ( ( collect_o @ P )
% 5.45/5.66 = bot_bot_set_o )
% 5.45/5.66 = ( P = bot_bot_o_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1481_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: nat > $o] :
% 5.45/5.66 ( ( ( collect_nat @ P )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 = ( P = bot_bot_nat_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1482_Collect__empty__eq__bot,axiom,
% 5.45/5.66 ! [P: int > $o] :
% 5.45/5.66 ( ( ( collect_int @ P )
% 5.45/5.66 = bot_bot_set_int )
% 5.45/5.66 = ( P = bot_bot_int_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_empty_eq_bot
% 5.45/5.66 thf(fact_1483_pairself_Ocases,axiom,
% 5.45/5.66 ! [X: produc7773217078559923341nt_int] :
% 5.45/5.66 ~ ! [F2: int > option6357759511663192854e_term,A4: int,B4: int] :
% 5.45/5.66 ( X
% 5.45/5.66 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ A4 @ B4 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % pairself.cases
% 5.45/5.66 thf(fact_1484_disjoint__mono,axiom,
% 5.45/5.66 ! [A: set_Pr1261947904930325089at_nat,A2: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,B2: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A @ A2 )
% 5.45/5.66 => ( ( ord_le3146513528884898305at_nat @ B @ B2 )
% 5.45/5.66 => ( ( ( inf_in2572325071724192079at_nat @ A2 @ B2 )
% 5.45/5.66 = bot_bo2099793752762293965at_nat )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.66 = bot_bo2099793752762293965at_nat ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjoint_mono
% 5.45/5.66 thf(fact_1485_disjoint__mono,axiom,
% 5.45/5.66 ! [A: set_o,A2: set_o,B: set_o,B2: set_o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A @ A2 )
% 5.45/5.66 => ( ( ord_less_eq_set_o @ B @ B2 )
% 5.45/5.66 => ( ( ( inf_inf_set_o @ A2 @ B2 )
% 5.45/5.66 = bot_bot_set_o )
% 5.45/5.66 => ( ( inf_inf_set_o @ A @ B )
% 5.45/5.66 = bot_bot_set_o ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjoint_mono
% 5.45/5.66 thf(fact_1486_disjoint__mono,axiom,
% 5.45/5.66 ! [A: set_nat,A2: set_nat,B: set_nat,B2: set_nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A @ A2 )
% 5.45/5.66 => ( ( ord_less_eq_set_nat @ B @ B2 )
% 5.45/5.66 => ( ( ( inf_inf_set_nat @ A2 @ B2 )
% 5.45/5.66 = bot_bot_set_nat )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.66 = bot_bot_set_nat ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjoint_mono
% 5.45/5.66 thf(fact_1487_disjoint__mono,axiom,
% 5.45/5.66 ! [A: set_int,A2: set_int,B: set_int,B2: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A @ A2 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B @ B2 )
% 5.45/5.66 => ( ( ( inf_inf_set_int @ A2 @ B2 )
% 5.45/5.66 = bot_bot_set_int )
% 5.45/5.66 => ( ( inf_inf_set_int @ A @ B )
% 5.45/5.66 = bot_bot_set_int ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjoint_mono
% 5.45/5.66 thf(fact_1488_disjointI,axiom,
% 5.45/5.66 ! [A: set_set_nat,B: set_set_nat] :
% 5.45/5.66 ( ! [X3: set_nat] :
% 5.45/5.66 ( ( member_set_nat @ X3 @ A )
% 5.45/5.66 => ~ ( member_set_nat @ X3 @ B ) )
% 5.45/5.66 => ( ( inf_inf_set_set_nat @ A @ B )
% 5.45/5.66 = bot_bot_set_set_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjointI
% 5.45/5.66 thf(fact_1489_disjointI,axiom,
% 5.45/5.66 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ! [X3: product_prod_nat_nat] :
% 5.45/5.66 ( ( member8440522571783428010at_nat @ X3 @ A )
% 5.45/5.66 => ~ ( member8440522571783428010at_nat @ X3 @ B ) )
% 5.45/5.66 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.66 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjointI
% 5.45/5.66 thf(fact_1490_disjointI,axiom,
% 5.45/5.66 ! [A: set_o,B: set_o] :
% 5.45/5.66 ( ! [X3: $o] :
% 5.45/5.66 ( ( member_o @ X3 @ A )
% 5.45/5.66 => ~ ( member_o @ X3 @ B ) )
% 5.45/5.66 => ( ( inf_inf_set_o @ A @ B )
% 5.45/5.66 = bot_bot_set_o ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjointI
% 5.45/5.66 thf(fact_1491_disjointI,axiom,
% 5.45/5.66 ! [A: set_nat,B: set_nat] :
% 5.45/5.66 ( ! [X3: nat] :
% 5.45/5.66 ( ( member_nat @ X3 @ A )
% 5.45/5.66 => ~ ( member_nat @ X3 @ B ) )
% 5.45/5.66 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.66 = bot_bot_set_nat ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjointI
% 5.45/5.66 thf(fact_1492_disjointI,axiom,
% 5.45/5.66 ! [A: set_int,B: set_int] :
% 5.45/5.66 ( ! [X3: int] :
% 5.45/5.66 ( ( member_int @ X3 @ A )
% 5.45/5.66 => ~ ( member_int @ X3 @ B ) )
% 5.45/5.66 => ( ( inf_inf_set_int @ A @ B )
% 5.45/5.66 = bot_bot_set_int ) ) ).
% 5.45/5.66
% 5.45/5.66 % disjointI
% 5.45/5.66 thf(fact_1493_le__some__optE,axiom,
% 5.45/5.66 ! [M: set_int,X: option_set_int] :
% 5.45/5.66 ( ( ord_le353528952715127954et_int @ ( some_set_int @ M ) @ X )
% 5.45/5.66 => ~ ! [M2: set_int] :
% 5.45/5.66 ( ( X
% 5.45/5.66 = ( some_set_int @ M2 ) )
% 5.45/5.66 => ~ ( ord_less_eq_set_int @ M @ M2 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_some_optE
% 5.45/5.66 thf(fact_1494_le__some__optE,axiom,
% 5.45/5.66 ! [M: rat,X: option_rat] :
% 5.45/5.66 ( ( ord_le2406147912482264968on_rat @ ( some_rat @ M ) @ X )
% 5.45/5.66 => ~ ! [M2: rat] :
% 5.45/5.66 ( ( X
% 5.45/5.66 = ( some_rat @ M2 ) )
% 5.45/5.66 => ~ ( ord_less_eq_rat @ M @ M2 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_some_optE
% 5.45/5.66 thf(fact_1495_le__some__optE,axiom,
% 5.45/5.66 ! [M: num,X: option_num] :
% 5.45/5.66 ( ( ord_le6622620407824499402on_num @ ( some_num @ M ) @ X )
% 5.45/5.66 => ~ ! [M2: num] :
% 5.45/5.66 ( ( X
% 5.45/5.66 = ( some_num @ M2 ) )
% 5.45/5.66 => ~ ( ord_less_eq_num @ M @ M2 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_some_optE
% 5.45/5.66 thf(fact_1496_le__some__optE,axiom,
% 5.45/5.66 ! [M: nat,X: option_nat] :
% 5.45/5.66 ( ( ord_le5914376470875661696on_nat @ ( some_nat @ M ) @ X )
% 5.45/5.66 => ~ ! [M2: nat] :
% 5.45/5.66 ( ( X
% 5.45/5.66 = ( some_nat @ M2 ) )
% 5.45/5.66 => ~ ( ord_less_eq_nat @ M @ M2 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_some_optE
% 5.45/5.66 thf(fact_1497_le__some__optE,axiom,
% 5.45/5.66 ! [M: int,X: option_int] :
% 5.45/5.66 ( ( ord_le1736525451366464988on_int @ ( some_int @ M ) @ X )
% 5.45/5.66 => ~ ! [M2: int] :
% 5.45/5.66 ( ( X
% 5.45/5.66 = ( some_int @ M2 ) )
% 5.45/5.66 => ~ ( ord_less_eq_int @ M @ M2 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % le_some_optE
% 5.45/5.66 thf(fact_1498_subsetI,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ( ! [X3: product_prod_nat_nat] :
% 5.45/5.66 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.66 => ( member8440522571783428010at_nat @ X3 @ B3 ) )
% 5.45/5.66 => ( ord_le3146513528884898305at_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetI
% 5.45/5.66 thf(fact_1499_subsetI,axiom,
% 5.45/5.66 ! [A3: set_o,B3: set_o] :
% 5.45/5.66 ( ! [X3: $o] :
% 5.45/5.66 ( ( member_o @ X3 @ A3 )
% 5.45/5.66 => ( member_o @ X3 @ B3 ) )
% 5.45/5.66 => ( ord_less_eq_set_o @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetI
% 5.45/5.66 thf(fact_1500_subsetI,axiom,
% 5.45/5.66 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.66 ( ! [X3: set_nat] :
% 5.45/5.66 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.66 => ( member_set_nat @ X3 @ B3 ) )
% 5.45/5.66 => ( ord_le6893508408891458716et_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetI
% 5.45/5.66 thf(fact_1501_subsetI,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.66 ( ! [X3: nat] :
% 5.45/5.66 ( ( member_nat @ X3 @ A3 )
% 5.45/5.66 => ( member_nat @ X3 @ B3 ) )
% 5.45/5.66 => ( ord_less_eq_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetI
% 5.45/5.66 thf(fact_1502_subsetI,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ! [X3: int] :
% 5.45/5.66 ( ( member_int @ X3 @ A3 )
% 5.45/5.66 => ( member_int @ X3 @ B3 ) )
% 5.45/5.66 => ( ord_less_eq_set_int @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetI
% 5.45/5.66 thf(fact_1503_subset__antisym,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.66 => ( A3 = B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_antisym
% 5.45/5.66 thf(fact_1504_RH1,axiom,
% 5.45/5.66 ( relH
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as1 ) ) )
% 5.45/5.66 @ h2
% 5.45/5.66 @ h ) ).
% 5.45/5.66
% 5.45/5.66 % RH1
% 5.45/5.66 thf(fact_1505_less__option__Some,axiom,
% 5.45/5.66 ! [X: assn,Y: assn] :
% 5.45/5.66 ( ( ord_less_option_assn @ ( some_assn @ X ) @ ( some_assn @ Y ) )
% 5.45/5.66 = ( ord_less_assn @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_option_Some
% 5.45/5.66 thf(fact_1506_less__option__Some,axiom,
% 5.45/5.66 ! [X: rat,Y: rat] :
% 5.45/5.66 ( ( ord_less_option_rat @ ( some_rat @ X ) @ ( some_rat @ Y ) )
% 5.45/5.66 = ( ord_less_rat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_option_Some
% 5.45/5.66 thf(fact_1507_less__option__Some,axiom,
% 5.45/5.66 ! [X: num,Y: num] :
% 5.45/5.66 ( ( ord_less_option_num @ ( some_num @ X ) @ ( some_num @ Y ) )
% 5.45/5.66 = ( ord_less_num @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_option_Some
% 5.45/5.66 thf(fact_1508_less__option__Some,axiom,
% 5.45/5.66 ! [X: nat,Y: nat] :
% 5.45/5.66 ( ( ord_less_option_nat @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.45/5.66 = ( ord_less_nat @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_option_Some
% 5.45/5.66 thf(fact_1509_less__option__Some,axiom,
% 5.45/5.66 ! [X: int,Y: int] :
% 5.45/5.66 ( ( ord_less_option_int @ ( some_int @ X ) @ ( some_int @ Y ) )
% 5.45/5.66 = ( ord_less_int @ X @ Y ) ) ).
% 5.45/5.66
% 5.45/5.66 % less_option_Some
% 5.45/5.66 thf(fact_1510__092_060open_062relH_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_Ah_Ah_H_092_060close_062,axiom,
% 5.45/5.66 ( relH
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as ) ) )
% 5.45/5.66 @ h2
% 5.45/5.66 @ h ) ).
% 5.45/5.66
% 5.45/5.66 % \<open>relH {a. a < lim h \<and> a \<notin> as} h h'\<close>
% 5.45/5.66 thf(fact_1511__092_060open_062as2_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062,axiom,
% 5.45/5.66 ( ord_less_eq_set_nat @ as2
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as1 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % \<open>as2 \<subseteq> {a. a < lim h \<and> a \<notin> as1}\<close>
% 5.45/5.66 thf(fact_1512__092_060open_062_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas_125_A_092_060subseteq_062_A_123a_O_Aa_A_060_Alim_Ah_A_092_060and_062_Aa_A_092_060notin_062_Aas1_125_092_060close_062,axiom,
% 5.45/5.66 ( ord_less_eq_set_nat
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as ) ) )
% 5.45/5.66 @ ( collect_nat
% 5.45/5.66 @ ^ [A5: nat] :
% 5.45/5.66 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ h2 ) )
% 5.45/5.66 & ~ ( member_nat @ A5 @ as1 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % \<open>{a. a < lim h \<and> a \<notin> as} \<subseteq> {a. a < lim h \<and> a \<notin> as1}\<close>
% 5.45/5.66 thf(fact_1513_in__mono,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.45/5.66 => ( member8440522571783428010at_nat @ X @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % in_mono
% 5.45/5.66 thf(fact_1514_in__mono,axiom,
% 5.45/5.66 ! [A3: set_o,B3: set_o,X: $o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.66 => ( ( member_o @ X @ A3 )
% 5.45/5.66 => ( member_o @ X @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % in_mono
% 5.45/5.66 thf(fact_1515_in__mono,axiom,
% 5.45/5.66 ! [A3: set_set_nat,B3: set_set_nat,X: set_nat] :
% 5.45/5.66 ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member_set_nat @ X @ A3 )
% 5.45/5.66 => ( member_set_nat @ X @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % in_mono
% 5.45/5.66 thf(fact_1516_in__mono,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,X: nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member_nat @ X @ A3 )
% 5.45/5.66 => ( member_nat @ X @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % in_mono
% 5.45/5.66 thf(fact_1517_in__mono,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int,X: int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ( member_int @ X @ A3 )
% 5.45/5.66 => ( member_int @ X @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % in_mono
% 5.45/5.66 thf(fact_1518_subsetD,axiom,
% 5.45/5.66 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.45/5.66 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.66 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetD
% 5.45/5.66 thf(fact_1519_subsetD,axiom,
% 5.45/5.66 ! [A3: set_o,B3: set_o,C: $o] :
% 5.45/5.66 ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.66 => ( ( member_o @ C @ A3 )
% 5.45/5.66 => ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetD
% 5.45/5.66 thf(fact_1520_subsetD,axiom,
% 5.45/5.66 ! [A3: set_set_nat,B3: set_set_nat,C: set_nat] :
% 5.45/5.66 ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member_set_nat @ C @ A3 )
% 5.45/5.66 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetD
% 5.45/5.66 thf(fact_1521_subsetD,axiom,
% 5.45/5.66 ! [A3: set_nat,B3: set_nat,C: nat] :
% 5.45/5.66 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.66 => ( ( member_nat @ C @ A3 )
% 5.45/5.66 => ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetD
% 5.45/5.66 thf(fact_1522_subsetD,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int,C: int] :
% 5.45/5.66 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ( ( member_int @ C @ A3 )
% 5.45/5.66 => ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subsetD
% 5.45/5.66 thf(fact_1523_equalityE,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( A3 = B3 )
% 5.45/5.66 => ~ ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.66 => ~ ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % equalityE
% 5.45/5.66 thf(fact_1524_subset__eq,axiom,
% 5.45/5.66 ( ord_le3146513528884898305at_nat
% 5.45/5.66 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ! [X4: product_prod_nat_nat] :
% 5.45/5.66 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.66 => ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_eq
% 5.45/5.66 thf(fact_1525_subset__eq,axiom,
% 5.45/5.66 ( ord_less_eq_set_o
% 5.45/5.66 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.66 ! [X4: $o] :
% 5.45/5.66 ( ( member_o @ X4 @ A6 )
% 5.45/5.66 => ( member_o @ X4 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_eq
% 5.45/5.66 thf(fact_1526_subset__eq,axiom,
% 5.45/5.66 ( ord_le6893508408891458716et_nat
% 5.45/5.66 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.66 ! [X4: set_nat] :
% 5.45/5.66 ( ( member_set_nat @ X4 @ A6 )
% 5.45/5.66 => ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_eq
% 5.45/5.66 thf(fact_1527_subset__eq,axiom,
% 5.45/5.66 ( ord_less_eq_set_nat
% 5.45/5.66 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.66 ! [X4: nat] :
% 5.45/5.66 ( ( member_nat @ X4 @ A6 )
% 5.45/5.66 => ( member_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_eq
% 5.45/5.66 thf(fact_1528_subset__eq,axiom,
% 5.45/5.66 ( ord_less_eq_set_int
% 5.45/5.66 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.66 ! [X4: int] :
% 5.45/5.66 ( ( member_int @ X4 @ A6 )
% 5.45/5.66 => ( member_int @ X4 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_eq
% 5.45/5.66 thf(fact_1529_equalityD1,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( A3 = B3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ A3 @ B3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % equalityD1
% 5.45/5.66 thf(fact_1530_equalityD2,axiom,
% 5.45/5.66 ! [A3: set_int,B3: set_int] :
% 5.45/5.66 ( ( A3 = B3 )
% 5.45/5.66 => ( ord_less_eq_set_int @ B3 @ A3 ) ) ).
% 5.45/5.66
% 5.45/5.66 % equalityD2
% 5.45/5.66 thf(fact_1531_subset__iff,axiom,
% 5.45/5.66 ( ord_le3146513528884898305at_nat
% 5.45/5.66 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.66 ! [T3: product_prod_nat_nat] :
% 5.45/5.66 ( ( member8440522571783428010at_nat @ T3 @ A6 )
% 5.45/5.66 => ( member8440522571783428010at_nat @ T3 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_iff
% 5.45/5.66 thf(fact_1532_subset__iff,axiom,
% 5.45/5.66 ( ord_less_eq_set_o
% 5.45/5.66 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.66 ! [T3: $o] :
% 5.45/5.66 ( ( member_o @ T3 @ A6 )
% 5.45/5.66 => ( member_o @ T3 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_iff
% 5.45/5.66 thf(fact_1533_subset__iff,axiom,
% 5.45/5.66 ( ord_le6893508408891458716et_nat
% 5.45/5.66 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.66 ! [T3: set_nat] :
% 5.45/5.66 ( ( member_set_nat @ T3 @ A6 )
% 5.45/5.66 => ( member_set_nat @ T3 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_iff
% 5.45/5.66 thf(fact_1534_subset__iff,axiom,
% 5.45/5.66 ( ord_less_eq_set_nat
% 5.45/5.66 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.66 ! [T3: nat] :
% 5.45/5.66 ( ( member_nat @ T3 @ A6 )
% 5.45/5.66 => ( member_nat @ T3 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_iff
% 5.45/5.66 thf(fact_1535_subset__iff,axiom,
% 5.45/5.66 ( ord_less_eq_set_int
% 5.45/5.66 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.66 ! [T3: int] :
% 5.45/5.66 ( ( member_int @ T3 @ A6 )
% 5.45/5.66 => ( member_int @ T3 @ B6 ) ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % subset_iff
% 5.45/5.66 thf(fact_1536_subset__refl,axiom,
% 5.45/5.66 ! [A3: set_int] : ( ord_less_eq_set_int @ A3 @ A3 ) ).
% 5.45/5.66
% 5.45/5.66 % subset_refl
% 5.45/5.66 thf(fact_1537_Collect__mono,axiom,
% 5.45/5.66 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.66 ( ! [X3: product_prod_int_int] :
% 5.45/5.66 ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) )
% 5.45/5.66 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.45/5.66
% 5.45/5.66 % Collect_mono
% 5.45/5.66 thf(fact_1538_Collect__mono,axiom,
% 5.45/5.66 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.66 ( ! [X3: list_nat] :
% 5.45/5.66 ( ( P @ X3 )
% 5.45/5.66 => ( Q @ X3 ) )
% 5.45/5.67 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono
% 5.45/5.67 thf(fact_1539_Collect__mono,axiom,
% 5.45/5.67 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.67 ( ! [X3: set_nat] :
% 5.45/5.67 ( ( P @ X3 )
% 5.45/5.67 => ( Q @ X3 ) )
% 5.45/5.67 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono
% 5.45/5.67 thf(fact_1540_Collect__mono,axiom,
% 5.45/5.67 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.67 ( ! [X3: nat] :
% 5.45/5.67 ( ( P @ X3 )
% 5.45/5.67 => ( Q @ X3 ) )
% 5.45/5.67 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono
% 5.45/5.67 thf(fact_1541_Collect__mono,axiom,
% 5.45/5.67 ! [P: int > $o,Q: int > $o] :
% 5.45/5.67 ( ! [X3: int] :
% 5.45/5.67 ( ( P @ X3 )
% 5.45/5.67 => ( Q @ X3 ) )
% 5.45/5.67 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono
% 5.45/5.67 thf(fact_1542_subset__trans,axiom,
% 5.45/5.67 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.67 => ( ( ord_less_eq_set_int @ B3 @ C3 )
% 5.45/5.67 => ( ord_less_eq_set_int @ A3 @ C3 ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_trans
% 5.45/5.67 thf(fact_1543_set__eq__subset,axiom,
% 5.45/5.67 ( ( ^ [Y5: set_int,Z3: set_int] : ( Y5 = Z3 ) )
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.45/5.67 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % set_eq_subset
% 5.45/5.67 thf(fact_1544_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( sup_su798857527126471912_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( sup_su6327502436637775413at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1545_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_o,S: set_o] :
% 5.45/5.67 ( ( sup_sup_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ R )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: $o] : ( member_o @ X4 @ ( sup_sup_set_o @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1546_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_set_nat,S: set_set_nat] :
% 5.45/5.67 ( ( sup_sup_set_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ ( sup_sup_set_set_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1547_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_int,S: set_int] :
% 5.45/5.67 ( ( sup_sup_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ R )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: int] : ( member_int @ X4 @ ( sup_sup_set_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1548_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.45/5.67 ( ( sup_su8986005896011022210_nat_o
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X4 @ ( sup_su718114333110466843at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1549_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 5.45/5.67 ( ( sup_su6256023009775730178_nat_o
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1550_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.45/5.67 ( ( sup_su2080679670758317954_nat_o
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1551_sup__Un__eq,axiom,
% 5.45/5.67 ! [R: set_nat,S: set_nat] :
% 5.45/5.67 ( ( sup_sup_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( sup_sup_set_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq
% 5.45/5.67 thf(fact_1552_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.67 ( ord_le3146513528884898305at_nat
% 5.45/5.67 @ ( collec3392354462482085612at_nat
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.67 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1553_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_o,P: $o > $o] :
% 5.45/5.67 ( ord_less_eq_set_o
% 5.45/5.67 @ ( collect_o
% 5.45/5.67 @ ^ [X4: $o] :
% 5.45/5.67 ( ( member_o @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1554_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.67 ( ord_le2843351958646193337nt_int
% 5.45/5.67 @ ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] :
% 5.45/5.67 ( ( member5262025264175285858nt_int @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1555_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_list_nat,P: list_nat > $o] :
% 5.45/5.67 ( ord_le6045566169113846134st_nat
% 5.45/5.67 @ ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] :
% 5.45/5.67 ( ( member_list_nat @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1556_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_set_nat,P: set_nat > $o] :
% 5.45/5.67 ( ord_le6893508408891458716et_nat
% 5.45/5.67 @ ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] :
% 5.45/5.67 ( ( member_set_nat @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1557_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_nat,P: nat > $o] :
% 5.45/5.67 ( ord_less_eq_set_nat
% 5.45/5.67 @ ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] :
% 5.45/5.67 ( ( member_nat @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1558_Collect__subset,axiom,
% 5.45/5.67 ! [A3: set_int,P: int > $o] :
% 5.45/5.67 ( ord_less_eq_set_int
% 5.45/5.67 @ ( collect_int
% 5.45/5.67 @ ^ [X4: int] :
% 5.45/5.67 ( ( member_int @ X4 @ A3 )
% 5.45/5.67 & ( P @ X4 ) ) )
% 5.45/5.67 @ A3 ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_subset
% 5.45/5.67 thf(fact_1559_inf__Int__eq,axiom,
% 5.45/5.67 ! [R: set_o,S: set_o] :
% 5.45/5.67 ( ( inf_inf_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ R )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: $o] : ( member_o @ X4 @ ( inf_inf_set_o @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq
% 5.45/5.67 thf(fact_1560_inf__Int__eq,axiom,
% 5.45/5.67 ! [R: set_set_nat,S: set_set_nat] :
% 5.45/5.67 ( ( inf_inf_set_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: set_nat] : ( member_set_nat @ X4 @ ( inf_inf_set_set_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq
% 5.45/5.67 thf(fact_1561_inf__Int__eq,axiom,
% 5.45/5.67 ! [R: set_int,S: set_int] :
% 5.45/5.67 ( ( inf_inf_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ R )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: int] : ( member_int @ X4 @ ( inf_inf_set_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq
% 5.45/5.67 thf(fact_1562_inf__Int__eq,axiom,
% 5.45/5.67 ! [R: set_nat,S: set_nat] :
% 5.45/5.67 ( ( inf_inf_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: nat] : ( member_nat @ X4 @ ( inf_inf_set_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq
% 5.45/5.67 thf(fact_1563_inf__Int__eq,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( inf_in5163264567034779214_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq
% 5.45/5.67 thf(fact_1564_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( sup_sup_nat_nat_o
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ ( sup_su6327502436637775413at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1565_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 5.45/5.67 ( ( sup_su1630790145277462993_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ ( sup_su7128418612487073120et_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1566_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 5.45/5.67 ( ( sup_su6535292691877529429_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ ( sup_su8975264963432250076et_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1567_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 5.45/5.67 ( ( sup_su4182031696650224058_int_o
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ ( sup_su3382966977382714213nt_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1568_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 5.45/5.67 ( ( sup_su600977994968626096_int_o
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ ( sup_su3298353300217089135nt_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1569_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 5.45/5.67 ( ( sup_su2191776239474528790_nat_o
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ ( sup_su3211442154794319707it_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1570_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8693737435421807431at_nat,S: set_Pr8693737435421807431at_nat] :
% 5.45/5.67 ( ( sup_su362511073950362882_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: product_prod_nat_nat,Y4: product_prod_nat_nat] : ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ ( sup_su718114333110466843at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1571_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8551490117392284871at_nat,S: set_Pr8551490117392284871at_nat] :
% 5.45/5.67 ( ( sup_su2200014604384089602_nat_o
% 5.45/5.67 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: multis2468970476368604999at_nat,Y4: multis2468970476368604999at_nat] : ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ X4 @ Y4 ) @ ( sup_su3035147773818789531at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1572_sup__Un__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr4329608150637261639at_nat,S: set_Pr4329608150637261639at_nat] :
% 5.45/5.67 ( ( sup_su7519161239522478338_nat_o
% 5.45/5.67 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X4 @ Y4 ) @ ( sup_su5525570899277871387at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_Un_eq2
% 5.45/5.67 thf(fact_1573_less__eq__set__def,axiom,
% 5.45/5.67 ( ord_le3146513528884898305at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ord_le704812498762024988_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_eq_set_def
% 5.45/5.67 thf(fact_1574_less__eq__set__def,axiom,
% 5.45/5.67 ( ord_less_eq_set_o
% 5.45/5.67 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.67 ( ord_less_eq_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_eq_set_def
% 5.45/5.67 thf(fact_1575_less__eq__set__def,axiom,
% 5.45/5.67 ( ord_le6893508408891458716et_nat
% 5.45/5.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.67 ( ord_le3964352015994296041_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_eq_set_def
% 5.45/5.67 thf(fact_1576_less__eq__set__def,axiom,
% 5.45/5.67 ( ord_less_eq_set_nat
% 5.45/5.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.67 ( ord_less_eq_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_eq_set_def
% 5.45/5.67 thf(fact_1577_less__eq__set__def,axiom,
% 5.45/5.67 ( ord_less_eq_set_int
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( ord_less_eq_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_eq_set_def
% 5.45/5.67 thf(fact_1578_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 5.45/5.67 ( ( inf_in3295504058751909687_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ ( inf_in1768905781608824518et_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1579_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 5.45/5.67 ( ( inf_in2641120393918057659_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ ( inf_in3088352823822785602et_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1580_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 5.45/5.67 ( ( inf_in8045883074377559328_int_o
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ ( inf_in2576786181675586251nt_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1581_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 5.45/5.67 ( ( inf_in8201999774870019094_int_o
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ ( inf_in8806012763027673301nt_int @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1582_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 5.45/5.67 ( ( inf_in8051596381320575356_nat_o
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ ( inf_in3493107508024165057it_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1583_inf__Int__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( inf_inf_nat_nat_o
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ ( inf_in2572325071724192079at_nat @ R @ S ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_Int_eq2
% 5.45/5.67 thf(fact_1584_Collect__mono__iff,axiom,
% 5.45/5.67 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.67 ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 5.45/5.67 = ( ! [X4: product_prod_int_int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 => ( Q @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono_iff
% 5.45/5.67 thf(fact_1585_Collect__mono__iff,axiom,
% 5.45/5.67 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.67 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.45/5.67 = ( ! [X4: list_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 => ( Q @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono_iff
% 5.45/5.67 thf(fact_1586_Collect__mono__iff,axiom,
% 5.45/5.67 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.67 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.45/5.67 = ( ! [X4: set_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 => ( Q @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono_iff
% 5.45/5.67 thf(fact_1587_Collect__mono__iff,axiom,
% 5.45/5.67 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.67 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.45/5.67 = ( ! [X4: nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 => ( Q @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono_iff
% 5.45/5.67 thf(fact_1588_Collect__mono__iff,axiom,
% 5.45/5.67 ! [P: int > $o,Q: int > $o] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.45/5.67 = ( ! [X4: int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 => ( Q @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_mono_iff
% 5.45/5.67 thf(fact_1589_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bo5580076615179976505_nat_o
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ bot_bo1481135142794719944et_nat ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1590_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bo3790638025767943357_nat_o
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ bot_bo5635537948650799172et_nat ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1591_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bo8662317086119403298_int_o
% 5.45/5.67 = ( ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ bot_bo572930865798478029nt_int ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1592_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bo1403522918969695512_int_o
% 5.45/5.67 = ( ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ bot_bo4508923176915781079nt_int ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1593_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bo3200480807726169982_nat_o
% 5.45/5.67 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ bot_bo8480459777671986371it_nat ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1594_bot__empty__eq2,axiom,
% 5.45/5.67 ( bot_bot_nat_nat_o
% 5.45/5.67 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % bot_empty_eq2
% 5.45/5.67 thf(fact_1595_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1596_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 5.45/5.67 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1597_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 5.45/5.67 ( ( ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1598_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 5.45/5.67 ( ( ( ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1599_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 5.45/5.67 ( ( ( ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1600_pred__equals__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 5.45/5.67 ( ( ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R ) )
% 5.45/5.67 = ( ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) ) )
% 5.45/5.67 = ( R = S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_equals_eq2
% 5.45/5.67 thf(fact_1601_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( ord_le2646555220125990790_nat_o
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: nat,Y4: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le3146513528884898305at_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1602_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr3286484037609594932et_nat,S: set_Pr3286484037609594932et_nat] :
% 5.45/5.67 ( ( ord_le8000401564054156549_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le5966269811547037844et_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1603_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr8536935166611901872et_nat,S: set_Pr8536935166611901872et_nat] :
% 5.45/5.67 ( ( ord_le6753239538765779593_nat_o
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le4763372923235995152et_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1604_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr9222295170931077689nt_int,S: set_Pr9222295170931077689nt_int] :
% 5.45/5.67 ( ( ord_le5643404153117327598_int_o
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le8725513860283290265nt_int @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1605_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr1872883991513573699nt_int,S: set_Pr1872883991513573699nt_int] :
% 5.45/5.67 ( ( ord_le2124322318746777828_int_o
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le135402666524580259nt_int @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1606_pred__subset__eq2,axiom,
% 5.45/5.67 ! [R: set_Pr7098220151150636591it_nat,S: set_Pr7098220151150636591it_nat] :
% 5.45/5.67 ( ( ord_le7992815620007647562_nat_o
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R )
% 5.45/5.67 @ ^ [X4: a,Y4: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ S ) )
% 5.45/5.67 = ( ord_le4478181985103859343it_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq2
% 5.45/5.67 thf(fact_1607_lt__ex,axiom,
% 5.45/5.67 ! [X: rat] :
% 5.45/5.67 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X ) ).
% 5.45/5.67
% 5.45/5.67 % lt_ex
% 5.45/5.67 thf(fact_1608_lt__ex,axiom,
% 5.45/5.67 ! [X: int] :
% 5.45/5.67 ? [Y3: int] : ( ord_less_int @ Y3 @ X ) ).
% 5.45/5.67
% 5.45/5.67 % lt_ex
% 5.45/5.67 thf(fact_1609_gt__ex,axiom,
% 5.45/5.67 ! [X: rat] :
% 5.45/5.67 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.45/5.67
% 5.45/5.67 % gt_ex
% 5.45/5.67 thf(fact_1610_gt__ex,axiom,
% 5.45/5.67 ! [X: nat] :
% 5.45/5.67 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.45/5.67
% 5.45/5.67 % gt_ex
% 5.45/5.67 thf(fact_1611_gt__ex,axiom,
% 5.45/5.67 ! [X: int] :
% 5.45/5.67 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.45/5.67
% 5.45/5.67 % gt_ex
% 5.45/5.67 thf(fact_1612_dense,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ? [Z2: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Z2 )
% 5.45/5.67 & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dense
% 5.45/5.67 thf(fact_1613_less__imp__neq,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_imp_neq
% 5.45/5.67 thf(fact_1614_less__imp__neq,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_imp_neq
% 5.45/5.67 thf(fact_1615_less__imp__neq,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_imp_neq
% 5.45/5.67 thf(fact_1616_less__imp__neq,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_imp_neq
% 5.45/5.67 thf(fact_1617_less__imp__neq,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_imp_neq
% 5.45/5.67 thf(fact_1618_order_Oasym,axiom,
% 5.45/5.67 ! [A: assn,B: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ~ ( ord_less_assn @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.asym
% 5.45/5.67 thf(fact_1619_order_Oasym,axiom,
% 5.45/5.67 ! [A: rat,B: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.asym
% 5.45/5.67 thf(fact_1620_order_Oasym,axiom,
% 5.45/5.67 ! [A: num,B: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.asym
% 5.45/5.67 thf(fact_1621_order_Oasym,axiom,
% 5.45/5.67 ! [A: nat,B: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.asym
% 5.45/5.67 thf(fact_1622_order_Oasym,axiom,
% 5.45/5.67 ! [A: int,B: int] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.asym
% 5.45/5.67 thf(fact_1623_ord__eq__less__trans,axiom,
% 5.45/5.67 ! [A: assn,B: assn,C: assn] :
% 5.45/5.67 ( ( A = B )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_trans
% 5.45/5.67 thf(fact_1624_ord__eq__less__trans,axiom,
% 5.45/5.67 ! [A: rat,B: rat,C: rat] :
% 5.45/5.67 ( ( A = B )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_trans
% 5.45/5.67 thf(fact_1625_ord__eq__less__trans,axiom,
% 5.45/5.67 ! [A: num,B: num,C: num] :
% 5.45/5.67 ( ( A = B )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ord_less_num @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_trans
% 5.45/5.67 thf(fact_1626_ord__eq__less__trans,axiom,
% 5.45/5.67 ! [A: nat,B: nat,C: nat] :
% 5.45/5.67 ( ( A = B )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_trans
% 5.45/5.67 thf(fact_1627_ord__eq__less__trans,axiom,
% 5.45/5.67 ! [A: int,B: int,C: int] :
% 5.45/5.67 ( ( A = B )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_trans
% 5.45/5.67 thf(fact_1628_ord__less__eq__trans,axiom,
% 5.45/5.67 ! [A: assn,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( B = C )
% 5.45/5.67 => ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_trans
% 5.45/5.67 thf(fact_1629_ord__less__eq__trans,axiom,
% 5.45/5.67 ! [A: rat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( B = C )
% 5.45/5.67 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_trans
% 5.45/5.67 thf(fact_1630_ord__less__eq__trans,axiom,
% 5.45/5.67 ! [A: num,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ( ( B = C )
% 5.45/5.67 => ( ord_less_num @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_trans
% 5.45/5.67 thf(fact_1631_ord__less__eq__trans,axiom,
% 5.45/5.67 ! [A: nat,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ( ( B = C )
% 5.45/5.67 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_trans
% 5.45/5.67 thf(fact_1632_ord__less__eq__trans,axiom,
% 5.45/5.67 ! [A: int,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ( ( B = C )
% 5.45/5.67 => ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_trans
% 5.45/5.67 thf(fact_1633_less__induct,axiom,
% 5.45/5.67 ! [P: nat > $o,A: nat] :
% 5.45/5.67 ( ! [X3: nat] :
% 5.45/5.67 ( ! [Y6: nat] :
% 5.45/5.67 ( ( ord_less_nat @ Y6 @ X3 )
% 5.45/5.67 => ( P @ Y6 ) )
% 5.45/5.67 => ( P @ X3 ) )
% 5.45/5.67 => ( P @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % less_induct
% 5.45/5.67 thf(fact_1634_antisym__conv3,axiom,
% 5.45/5.67 ! [Y: rat,X: rat] :
% 5.45/5.67 ( ~ ( ord_less_rat @ Y @ X )
% 5.45/5.67 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.45/5.67 = ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % antisym_conv3
% 5.45/5.67 thf(fact_1635_antisym__conv3,axiom,
% 5.45/5.67 ! [Y: num,X: num] :
% 5.45/5.67 ( ~ ( ord_less_num @ Y @ X )
% 5.45/5.67 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.45/5.67 = ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % antisym_conv3
% 5.45/5.67 thf(fact_1636_antisym__conv3,axiom,
% 5.45/5.67 ! [Y: nat,X: nat] :
% 5.45/5.67 ( ~ ( ord_less_nat @ Y @ X )
% 5.45/5.67 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.45/5.67 = ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % antisym_conv3
% 5.45/5.67 thf(fact_1637_antisym__conv3,axiom,
% 5.45/5.67 ! [Y: int,X: int] :
% 5.45/5.67 ( ~ ( ord_less_int @ Y @ X )
% 5.45/5.67 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.45/5.67 = ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % antisym_conv3
% 5.45/5.67 thf(fact_1638_linorder__cases,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ~ ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ( X != Y )
% 5.45/5.67 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_cases
% 5.45/5.67 thf(fact_1639_linorder__cases,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ~ ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ( X != Y )
% 5.45/5.67 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_cases
% 5.45/5.67 thf(fact_1640_linorder__cases,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ~ ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ( X != Y )
% 5.45/5.67 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_cases
% 5.45/5.67 thf(fact_1641_linorder__cases,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ~ ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ( X != Y )
% 5.45/5.67 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_cases
% 5.45/5.67 thf(fact_1642_dual__order_Oasym,axiom,
% 5.45/5.67 ! [B: assn,A: assn] :
% 5.45/5.67 ( ( ord_less_assn @ B @ A )
% 5.45/5.67 => ~ ( ord_less_assn @ A @ B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.asym
% 5.45/5.67 thf(fact_1643_dual__order_Oasym,axiom,
% 5.45/5.67 ! [B: rat,A: rat] :
% 5.45/5.67 ( ( ord_less_rat @ B @ A )
% 5.45/5.67 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.asym
% 5.45/5.67 thf(fact_1644_dual__order_Oasym,axiom,
% 5.45/5.67 ! [B: num,A: num] :
% 5.45/5.67 ( ( ord_less_num @ B @ A )
% 5.45/5.67 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.asym
% 5.45/5.67 thf(fact_1645_dual__order_Oasym,axiom,
% 5.45/5.67 ! [B: nat,A: nat] :
% 5.45/5.67 ( ( ord_less_nat @ B @ A )
% 5.45/5.67 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.asym
% 5.45/5.67 thf(fact_1646_dual__order_Oasym,axiom,
% 5.45/5.67 ! [B: int,A: int] :
% 5.45/5.67 ( ( ord_less_int @ B @ A )
% 5.45/5.67 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.asym
% 5.45/5.67 thf(fact_1647_dual__order_Oirrefl,axiom,
% 5.45/5.67 ! [A: assn] :
% 5.45/5.67 ~ ( ord_less_assn @ A @ A ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.irrefl
% 5.45/5.67 thf(fact_1648_dual__order_Oirrefl,axiom,
% 5.45/5.67 ! [A: rat] :
% 5.45/5.67 ~ ( ord_less_rat @ A @ A ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.irrefl
% 5.45/5.67 thf(fact_1649_dual__order_Oirrefl,axiom,
% 5.45/5.67 ! [A: num] :
% 5.45/5.67 ~ ( ord_less_num @ A @ A ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.irrefl
% 5.45/5.67 thf(fact_1650_dual__order_Oirrefl,axiom,
% 5.45/5.67 ! [A: nat] :
% 5.45/5.67 ~ ( ord_less_nat @ A @ A ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.irrefl
% 5.45/5.67 thf(fact_1651_dual__order_Oirrefl,axiom,
% 5.45/5.67 ! [A: int] :
% 5.45/5.67 ~ ( ord_less_int @ A @ A ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.irrefl
% 5.45/5.67 thf(fact_1652_exists__least__iff,axiom,
% 5.45/5.67 ( ( ^ [P5: nat > $o] :
% 5.45/5.67 ? [X5: nat] : ( P5 @ X5 ) )
% 5.45/5.67 = ( ^ [P4: nat > $o] :
% 5.45/5.67 ? [N: nat] :
% 5.45/5.67 ( ( P4 @ N )
% 5.45/5.67 & ! [M3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ M3 @ N )
% 5.45/5.67 => ~ ( P4 @ M3 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % exists_least_iff
% 5.45/5.67 thf(fact_1653_linorder__less__wlog,axiom,
% 5.45/5.67 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.45/5.67 ( ! [A4: rat,B4: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A4 @ B4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( ! [A4: rat] : ( P @ A4 @ A4 )
% 5.45/5.67 => ( ! [A4: rat,B4: rat] :
% 5.45/5.67 ( ( P @ B4 @ A4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( P @ A @ B ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_wlog
% 5.45/5.67 thf(fact_1654_linorder__less__wlog,axiom,
% 5.45/5.67 ! [P: num > num > $o,A: num,B: num] :
% 5.45/5.67 ( ! [A4: num,B4: num] :
% 5.45/5.67 ( ( ord_less_num @ A4 @ B4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( ! [A4: num] : ( P @ A4 @ A4 )
% 5.45/5.67 => ( ! [A4: num,B4: num] :
% 5.45/5.67 ( ( P @ B4 @ A4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( P @ A @ B ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_wlog
% 5.45/5.67 thf(fact_1655_linorder__less__wlog,axiom,
% 5.45/5.67 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.45/5.67 ( ! [A4: nat,B4: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A4 @ B4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( ! [A4: nat] : ( P @ A4 @ A4 )
% 5.45/5.67 => ( ! [A4: nat,B4: nat] :
% 5.45/5.67 ( ( P @ B4 @ A4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( P @ A @ B ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_wlog
% 5.45/5.67 thf(fact_1656_linorder__less__wlog,axiom,
% 5.45/5.67 ! [P: int > int > $o,A: int,B: int] :
% 5.45/5.67 ( ! [A4: int,B4: int] :
% 5.45/5.67 ( ( ord_less_int @ A4 @ B4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( ! [A4: int] : ( P @ A4 @ A4 )
% 5.45/5.67 => ( ! [A4: int,B4: int] :
% 5.45/5.67 ( ( P @ B4 @ A4 )
% 5.45/5.67 => ( P @ A4 @ B4 ) )
% 5.45/5.67 => ( P @ A @ B ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_wlog
% 5.45/5.67 thf(fact_1657_order_Ostrict__trans,axiom,
% 5.45/5.67 ! [A: assn,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_trans
% 5.45/5.67 thf(fact_1658_order_Ostrict__trans,axiom,
% 5.45/5.67 ! [A: rat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_trans
% 5.45/5.67 thf(fact_1659_order_Ostrict__trans,axiom,
% 5.45/5.67 ! [A: num,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ord_less_num @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_trans
% 5.45/5.67 thf(fact_1660_order_Ostrict__trans,axiom,
% 5.45/5.67 ! [A: nat,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_trans
% 5.45/5.67 thf(fact_1661_order_Ostrict__trans,axiom,
% 5.45/5.67 ! [A: int,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_trans
% 5.45/5.67 thf(fact_1662_not__less__iff__gr__or__eq,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.45/5.67 = ( ( ord_less_rat @ Y @ X )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % not_less_iff_gr_or_eq
% 5.45/5.67 thf(fact_1663_not__less__iff__gr__or__eq,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.45/5.67 = ( ( ord_less_num @ Y @ X )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % not_less_iff_gr_or_eq
% 5.45/5.67 thf(fact_1664_not__less__iff__gr__or__eq,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.45/5.67 = ( ( ord_less_nat @ Y @ X )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % not_less_iff_gr_or_eq
% 5.45/5.67 thf(fact_1665_not__less__iff__gr__or__eq,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.45/5.67 = ( ( ord_less_int @ Y @ X )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % not_less_iff_gr_or_eq
% 5.45/5.67 thf(fact_1666_dual__order_Ostrict__trans,axiom,
% 5.45/5.67 ! [B: assn,A: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ B @ A )
% 5.45/5.67 => ( ( ord_less_assn @ C @ B )
% 5.45/5.67 => ( ord_less_assn @ C @ A ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_trans
% 5.45/5.67 thf(fact_1667_dual__order_Ostrict__trans,axiom,
% 5.45/5.67 ! [B: rat,A: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ B @ A )
% 5.45/5.67 => ( ( ord_less_rat @ C @ B )
% 5.45/5.67 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_trans
% 5.45/5.67 thf(fact_1668_dual__order_Ostrict__trans,axiom,
% 5.45/5.67 ! [B: num,A: num,C: num] :
% 5.45/5.67 ( ( ord_less_num @ B @ A )
% 5.45/5.67 => ( ( ord_less_num @ C @ B )
% 5.45/5.67 => ( ord_less_num @ C @ A ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_trans
% 5.45/5.67 thf(fact_1669_dual__order_Ostrict__trans,axiom,
% 5.45/5.67 ! [B: nat,A: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_nat @ B @ A )
% 5.45/5.67 => ( ( ord_less_nat @ C @ B )
% 5.45/5.67 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_trans
% 5.45/5.67 thf(fact_1670_dual__order_Ostrict__trans,axiom,
% 5.45/5.67 ! [B: int,A: int,C: int] :
% 5.45/5.67 ( ( ord_less_int @ B @ A )
% 5.45/5.67 => ( ( ord_less_int @ C @ B )
% 5.45/5.67 => ( ord_less_int @ C @ A ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_trans
% 5.45/5.67 thf(fact_1671_order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [A: assn,B: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1672_order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [A: rat,B: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1673_order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [A: num,B: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1674_order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [A: nat,B: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1675_order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [A: int,B: int] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1676_dual__order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [B: assn,A: assn] :
% 5.45/5.67 ( ( ord_less_assn @ B @ A )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1677_dual__order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [B: rat,A: rat] :
% 5.45/5.67 ( ( ord_less_rat @ B @ A )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1678_dual__order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [B: num,A: num] :
% 5.45/5.67 ( ( ord_less_num @ B @ A )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1679_dual__order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [B: nat,A: nat] :
% 5.45/5.67 ( ( ord_less_nat @ B @ A )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1680_dual__order_Ostrict__implies__not__eq,axiom,
% 5.45/5.67 ! [B: int,A: int] :
% 5.45/5.67 ( ( ord_less_int @ B @ A )
% 5.45/5.67 => ( A != B ) ) ).
% 5.45/5.67
% 5.45/5.67 % dual_order.strict_implies_not_eq
% 5.45/5.67 thf(fact_1681_linorder__neqE,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 => ( ~ ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neqE
% 5.45/5.67 thf(fact_1682_linorder__neqE,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 => ( ~ ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neqE
% 5.45/5.67 thf(fact_1683_linorder__neqE,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 => ( ~ ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neqE
% 5.45/5.67 thf(fact_1684_linorder__neqE,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 => ( ~ ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neqE
% 5.45/5.67 thf(fact_1685_order__less__asym,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym
% 5.45/5.67 thf(fact_1686_order__less__asym,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym
% 5.45/5.67 thf(fact_1687_order__less__asym,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym
% 5.45/5.67 thf(fact_1688_order__less__asym,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym
% 5.45/5.67 thf(fact_1689_order__less__asym,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym
% 5.45/5.67 thf(fact_1690_linorder__neq__iff,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 = ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 | ( ord_less_rat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neq_iff
% 5.45/5.67 thf(fact_1691_linorder__neq__iff,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 = ( ( ord_less_num @ X @ Y )
% 5.45/5.67 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neq_iff
% 5.45/5.67 thf(fact_1692_linorder__neq__iff,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 = ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neq_iff
% 5.45/5.67 thf(fact_1693_linorder__neq__iff,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( X != Y )
% 5.45/5.67 = ( ( ord_less_int @ X @ Y )
% 5.45/5.67 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_neq_iff
% 5.45/5.67 thf(fact_1694_order__less__asym_H,axiom,
% 5.45/5.67 ! [A: assn,B: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ~ ( ord_less_assn @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym'
% 5.45/5.67 thf(fact_1695_order__less__asym_H,axiom,
% 5.45/5.67 ! [A: rat,B: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym'
% 5.45/5.67 thf(fact_1696_order__less__asym_H,axiom,
% 5.45/5.67 ! [A: num,B: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym'
% 5.45/5.67 thf(fact_1697_order__less__asym_H,axiom,
% 5.45/5.67 ! [A: nat,B: nat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym'
% 5.45/5.67 thf(fact_1698_order__less__asym_H,axiom,
% 5.45/5.67 ! [A: int,B: int] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_asym'
% 5.45/5.67 thf(fact_1699_order__less__trans,axiom,
% 5.45/5.67 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( ( ord_less_assn @ Y @ Z )
% 5.45/5.67 => ( ord_less_assn @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_trans
% 5.45/5.67 thf(fact_1700_order__less__trans,axiom,
% 5.45/5.67 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_rat @ Y @ Z )
% 5.45/5.67 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_trans
% 5.45/5.67 thf(fact_1701_order__less__trans,axiom,
% 5.45/5.67 ! [X: num,Y: num,Z: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ( ord_less_num @ Y @ Z )
% 5.45/5.67 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_trans
% 5.45/5.67 thf(fact_1702_order__less__trans,axiom,
% 5.45/5.67 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_nat @ Y @ Z )
% 5.45/5.67 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_trans
% 5.45/5.67 thf(fact_1703_order__less__trans,axiom,
% 5.45/5.67 ! [X: int,Y: int,Z: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_int @ Y @ Z )
% 5.45/5.67 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_trans
% 5.45/5.67 thf(fact_1704_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: assn,F: assn > assn,B: assn,C: assn] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1705_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: rat,F: assn > rat,B: assn,C: assn] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1706_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: num,F: assn > num,B: assn,C: assn] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1707_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: nat,F: assn > nat,B: assn,C: assn] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1708_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: int,F: assn > int,B: assn,C: assn] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1709_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: assn,F: rat > assn,B: rat,C: rat] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1710_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1711_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1712_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1713_ord__eq__less__subst,axiom,
% 5.45/5.67 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.45/5.67 ( ( A
% 5.45/5.67 = ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_eq_less_subst
% 5.45/5.67 thf(fact_1714_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1715_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1716_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > num,C: num] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1717_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1718_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > int,C: int] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1719_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1720_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1721_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1722_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1723_ord__less__eq__subst,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ( F @ B )
% 5.45/5.67 = C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % ord_less_eq_subst
% 5.45/5.67 thf(fact_1724_order__less__irrefl,axiom,
% 5.45/5.67 ! [X: assn] :
% 5.45/5.67 ~ ( ord_less_assn @ X @ X ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_irrefl
% 5.45/5.67 thf(fact_1725_order__less__irrefl,axiom,
% 5.45/5.67 ! [X: rat] :
% 5.45/5.67 ~ ( ord_less_rat @ X @ X ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_irrefl
% 5.45/5.67 thf(fact_1726_order__less__irrefl,axiom,
% 5.45/5.67 ! [X: num] :
% 5.45/5.67 ~ ( ord_less_num @ X @ X ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_irrefl
% 5.45/5.67 thf(fact_1727_order__less__irrefl,axiom,
% 5.45/5.67 ! [X: nat] :
% 5.45/5.67 ~ ( ord_less_nat @ X @ X ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_irrefl
% 5.45/5.67 thf(fact_1728_order__less__irrefl,axiom,
% 5.45/5.67 ! [X: int] :
% 5.45/5.67 ~ ( ord_less_int @ X @ X ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_irrefl
% 5.45/5.67 thf(fact_1729_order__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: assn > assn,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1730_order__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: rat > assn,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1731_order__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: num > assn,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1732_order__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: nat > assn,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1733_order__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: int > assn,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1734_order__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: assn > rat,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1735_order__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1736_order__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1737_order__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1738_order__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst1
% 5.45/5.67 thf(fact_1739_order__less__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1740_order__less__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1741_order__less__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > num,C: num] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1742_order__less__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1743_order__less__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > int,C: int] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1744_order__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1745_order__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1746_order__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1747_order__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1748_order__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_subst2
% 5.45/5.67 thf(fact_1749_order__less__not__sym,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_not_sym
% 5.45/5.67 thf(fact_1750_order__less__not__sym,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_not_sym
% 5.45/5.67 thf(fact_1751_order__less__not__sym,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_not_sym
% 5.45/5.67 thf(fact_1752_order__less__not__sym,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_not_sym
% 5.45/5.67 thf(fact_1753_order__less__not__sym,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_not_sym
% 5.45/5.67 thf(fact_1754_order__less__imp__triv,axiom,
% 5.45/5.67 ! [X: assn,Y: assn,P: $o] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( ( ord_less_assn @ Y @ X )
% 5.45/5.67 => P ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_triv
% 5.45/5.67 thf(fact_1755_order__less__imp__triv,axiom,
% 5.45/5.67 ! [X: rat,Y: rat,P: $o] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_rat @ Y @ X )
% 5.45/5.67 => P ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_triv
% 5.45/5.67 thf(fact_1756_order__less__imp__triv,axiom,
% 5.45/5.67 ! [X: num,Y: num,P: $o] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ( ord_less_num @ Y @ X )
% 5.45/5.67 => P ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_triv
% 5.45/5.67 thf(fact_1757_order__less__imp__triv,axiom,
% 5.45/5.67 ! [X: nat,Y: nat,P: $o] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_nat @ Y @ X )
% 5.45/5.67 => P ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_triv
% 5.45/5.67 thf(fact_1758_order__less__imp__triv,axiom,
% 5.45/5.67 ! [X: int,Y: int,P: $o] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_int @ Y @ X )
% 5.45/5.67 => P ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_triv
% 5.45/5.67 thf(fact_1759_linorder__less__linear,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 | ( X = Y )
% 5.45/5.67 | ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_linear
% 5.45/5.67 thf(fact_1760_linorder__less__linear,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 | ( X = Y )
% 5.45/5.67 | ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_linear
% 5.45/5.67 thf(fact_1761_linorder__less__linear,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 | ( X = Y )
% 5.45/5.67 | ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_linear
% 5.45/5.67 thf(fact_1762_linorder__less__linear,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 | ( X = Y )
% 5.45/5.67 | ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_less_linear
% 5.45/5.67 thf(fact_1763_order__less__imp__not__eq,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq
% 5.45/5.67 thf(fact_1764_order__less__imp__not__eq,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq
% 5.45/5.67 thf(fact_1765_order__less__imp__not__eq,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq
% 5.45/5.67 thf(fact_1766_order__less__imp__not__eq,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq
% 5.45/5.67 thf(fact_1767_order__less__imp__not__eq,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( X != Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq
% 5.45/5.67 thf(fact_1768_order__less__imp__not__eq2,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( Y != X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq2
% 5.45/5.67 thf(fact_1769_order__less__imp__not__eq2,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( Y != X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq2
% 5.45/5.67 thf(fact_1770_order__less__imp__not__eq2,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( Y != X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq2
% 5.45/5.67 thf(fact_1771_order__less__imp__not__eq2,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( Y != X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq2
% 5.45/5.67 thf(fact_1772_order__less__imp__not__eq2,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( Y != X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_eq2
% 5.45/5.67 thf(fact_1773_order__less__imp__not__less,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_assn @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_less
% 5.45/5.67 thf(fact_1774_order__less__imp__not__less,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_less
% 5.45/5.67 thf(fact_1775_order__less__imp__not__less,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_less
% 5.45/5.67 thf(fact_1776_order__less__imp__not__less,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_less
% 5.45/5.67 thf(fact_1777_order__less__imp__not__less,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_not_less
% 5.45/5.67 thf(fact_1778_subset__Collect__conv,axiom,
% 5.45/5.67 ! [S: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.67 ( ( ord_le2843351958646193337nt_int @ S @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.67 = ( ! [X4: product_prod_int_int] :
% 5.45/5.67 ( ( member5262025264175285858nt_int @ X4 @ S )
% 5.45/5.67 => ( P @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_Collect_conv
% 5.45/5.67 thf(fact_1779_subset__Collect__conv,axiom,
% 5.45/5.67 ! [S: set_list_nat,P: list_nat > $o] :
% 5.45/5.67 ( ( ord_le6045566169113846134st_nat @ S @ ( collect_list_nat @ P ) )
% 5.45/5.67 = ( ! [X4: list_nat] :
% 5.45/5.67 ( ( member_list_nat @ X4 @ S )
% 5.45/5.67 => ( P @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_Collect_conv
% 5.45/5.67 thf(fact_1780_subset__Collect__conv,axiom,
% 5.45/5.67 ! [S: set_set_nat,P: set_nat > $o] :
% 5.45/5.67 ( ( ord_le6893508408891458716et_nat @ S @ ( collect_set_nat @ P ) )
% 5.45/5.67 = ( ! [X4: set_nat] :
% 5.45/5.67 ( ( member_set_nat @ X4 @ S )
% 5.45/5.67 => ( P @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_Collect_conv
% 5.45/5.67 thf(fact_1781_subset__Collect__conv,axiom,
% 5.45/5.67 ! [S: set_nat,P: nat > $o] :
% 5.45/5.67 ( ( ord_less_eq_set_nat @ S @ ( collect_nat @ P ) )
% 5.45/5.67 = ( ! [X4: nat] :
% 5.45/5.67 ( ( member_nat @ X4 @ S )
% 5.45/5.67 => ( P @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_Collect_conv
% 5.45/5.67 thf(fact_1782_subset__Collect__conv,axiom,
% 5.45/5.67 ! [S: set_int,P: int > $o] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ S @ ( collect_int @ P ) )
% 5.45/5.67 = ( ! [X4: int] :
% 5.45/5.67 ( ( member_int @ X4 @ S )
% 5.45/5.67 => ( P @ X4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % subset_Collect_conv
% 5.45/5.67 thf(fact_1783_pred__subset__eq,axiom,
% 5.45/5.67 ! [R: set_Pr1261947904930325089at_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( ( ord_le704812498762024988_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ S ) )
% 5.45/5.67 = ( ord_le3146513528884898305at_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq
% 5.45/5.67 thf(fact_1784_pred__subset__eq,axiom,
% 5.45/5.67 ! [R: set_o,S: set_o] :
% 5.45/5.67 ( ( ord_less_eq_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ R )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ S ) )
% 5.45/5.67 = ( ord_less_eq_set_o @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq
% 5.45/5.67 thf(fact_1785_pred__subset__eq,axiom,
% 5.45/5.67 ! [R: set_set_nat,S: set_set_nat] :
% 5.45/5.67 ( ( ord_le3964352015994296041_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ S ) )
% 5.45/5.67 = ( ord_le6893508408891458716et_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq
% 5.45/5.67 thf(fact_1786_pred__subset__eq,axiom,
% 5.45/5.67 ! [R: set_nat,S: set_nat] :
% 5.45/5.67 ( ( ord_less_eq_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ R )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ S ) )
% 5.45/5.67 = ( ord_less_eq_set_nat @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq
% 5.45/5.67 thf(fact_1787_pred__subset__eq,axiom,
% 5.45/5.67 ! [R: set_int,S: set_int] :
% 5.45/5.67 ( ( ord_less_eq_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ R )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ S ) )
% 5.45/5.67 = ( ord_less_eq_set_int @ R @ S ) ) ).
% 5.45/5.67
% 5.45/5.67 % pred_subset_eq
% 5.45/5.67 thf(fact_1788_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bo1796632182523588997nt_int
% 5.45/5.67 = ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1789_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bot_set_list_nat
% 5.45/5.67 = ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1790_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bot_set_set_nat
% 5.45/5.67 = ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1791_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bo2099793752762293965at_nat
% 5.45/5.67 = ( collec3392354462482085612at_nat
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1792_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bot_set_o
% 5.45/5.67 = ( collect_o
% 5.45/5.67 @ ^ [X4: $o] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1793_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bot_set_nat
% 5.45/5.67 = ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1794_Set_Oempty__def,axiom,
% 5.45/5.67 ( bot_bot_set_int
% 5.45/5.67 = ( collect_int
% 5.45/5.67 @ ^ [X4: int] : $false ) ) ).
% 5.45/5.67
% 5.45/5.67 % Set.empty_def
% 5.45/5.67 thf(fact_1795_Int__def,axiom,
% 5.45/5.67 ( inf_inf_set_o
% 5.45/5.67 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.67 ( collect_o
% 5.45/5.67 @ ^ [X4: $o] :
% 5.45/5.67 ( ( member_o @ X4 @ A6 )
% 5.45/5.67 & ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1796_Int__def,axiom,
% 5.45/5.67 ( inf_in2269163501485487111nt_int
% 5.45/5.67 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.67 ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] :
% 5.45/5.67 ( ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.67 & ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1797_Int__def,axiom,
% 5.45/5.67 ( inf_inf_set_list_nat
% 5.45/5.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.67 ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] :
% 5.45/5.67 ( ( member_list_nat @ X4 @ A6 )
% 5.45/5.67 & ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1798_Int__def,axiom,
% 5.45/5.67 ( inf_inf_set_set_nat
% 5.45/5.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.67 ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] :
% 5.45/5.67 ( ( member_set_nat @ X4 @ A6 )
% 5.45/5.67 & ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1799_Int__def,axiom,
% 5.45/5.67 ( inf_inf_set_int
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( collect_int
% 5.45/5.67 @ ^ [X4: int] :
% 5.45/5.67 ( ( member_int @ X4 @ A6 )
% 5.45/5.67 & ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1800_Int__def,axiom,
% 5.45/5.67 ( inf_inf_set_nat
% 5.45/5.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.67 ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] :
% 5.45/5.67 ( ( member_nat @ X4 @ A6 )
% 5.45/5.67 & ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1801_Int__def,axiom,
% 5.45/5.67 ( inf_in2572325071724192079at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( collec3392354462482085612at_nat
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.67 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.67 & ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_def
% 5.45/5.67 thf(fact_1802_Int__Collect,axiom,
% 5.45/5.67 ! [X: $o,A3: set_o,P: $o > $o] :
% 5.45/5.67 ( ( member_o @ X @ ( inf_inf_set_o @ A3 @ ( collect_o @ P ) ) )
% 5.45/5.67 = ( ( member_o @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1803_Int__Collect,axiom,
% 5.45/5.67 ! [X: product_prod_int_int,A3: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.67 ( ( member5262025264175285858nt_int @ X @ ( inf_in2269163501485487111nt_int @ A3 @ ( collec213857154873943460nt_int @ P ) ) )
% 5.45/5.67 = ( ( member5262025264175285858nt_int @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1804_Int__Collect,axiom,
% 5.45/5.67 ! [X: list_nat,A3: set_list_nat,P: list_nat > $o] :
% 5.45/5.67 ( ( member_list_nat @ X @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P ) ) )
% 5.45/5.67 = ( ( member_list_nat @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1805_Int__Collect,axiom,
% 5.45/5.67 ! [X: set_nat,A3: set_set_nat,P: set_nat > $o] :
% 5.45/5.67 ( ( member_set_nat @ X @ ( inf_inf_set_set_nat @ A3 @ ( collect_set_nat @ P ) ) )
% 5.45/5.67 = ( ( member_set_nat @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1806_Int__Collect,axiom,
% 5.45/5.67 ! [X: int,A3: set_int,P: int > $o] :
% 5.45/5.67 ( ( member_int @ X @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) )
% 5.45/5.67 = ( ( member_int @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1807_Int__Collect,axiom,
% 5.45/5.67 ! [X: nat,A3: set_nat,P: nat > $o] :
% 5.45/5.67 ( ( member_nat @ X @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) )
% 5.45/5.67 = ( ( member_nat @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1808_Int__Collect,axiom,
% 5.45/5.67 ! [X: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.67 ( ( member8440522571783428010at_nat @ X @ ( inf_in2572325071724192079at_nat @ A3 @ ( collec3392354462482085612at_nat @ P ) ) )
% 5.45/5.67 = ( ( member8440522571783428010at_nat @ X @ A3 )
% 5.45/5.67 & ( P @ X ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Int_Collect
% 5.45/5.67 thf(fact_1809_inf__set__def,axiom,
% 5.45/5.67 ( inf_inf_set_o
% 5.45/5.67 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.67 ( collect_o
% 5.45/5.67 @ ( inf_inf_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1810_inf__set__def,axiom,
% 5.45/5.67 ( inf_in2269163501485487111nt_int
% 5.45/5.67 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.67 ( collec213857154873943460nt_int
% 5.45/5.67 @ ( inf_in3604695632404883862_int_o
% 5.45/5.67 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1811_inf__set__def,axiom,
% 5.45/5.67 ( inf_inf_set_list_nat
% 5.45/5.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.67 ( collect_list_nat
% 5.45/5.67 @ ( inf_inf_list_nat_o
% 5.45/5.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1812_inf__set__def,axiom,
% 5.45/5.67 ( inf_inf_set_set_nat
% 5.45/5.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.67 ( collect_set_nat
% 5.45/5.67 @ ( inf_inf_set_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1813_inf__set__def,axiom,
% 5.45/5.67 ( inf_inf_set_int
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( collect_int
% 5.45/5.67 @ ( inf_inf_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1814_inf__set__def,axiom,
% 5.45/5.67 ( inf_inf_set_nat
% 5.45/5.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.67 ( collect_nat
% 5.45/5.67 @ ( inf_inf_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1815_inf__set__def,axiom,
% 5.45/5.67 ( inf_in2572325071724192079at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( collec3392354462482085612at_nat
% 5.45/5.67 @ ( inf_in5163264567034779214_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % inf_set_def
% 5.45/5.67 thf(fact_1816_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.67 ( ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_in2269163501485487111nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1817_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.67 ( ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_inf_set_list_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1818_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.67 ( ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_inf_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1819_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: int > $o,Q: int > $o] :
% 5.45/5.67 ( ( collect_int
% 5.45/5.67 @ ^ [X4: int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_inf_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1820_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.67 ( ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_inf_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1821_Collect__conj__eq,axiom,
% 5.45/5.67 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.45/5.67 ( ( collec3392354462482085612at_nat
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 & ( Q @ X4 ) ) )
% 5.45/5.67 = ( inf_in2572325071724192079at_nat @ ( collec3392354462482085612at_nat @ P ) @ ( collec3392354462482085612at_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_conj_eq
% 5.45/5.67 thf(fact_1822_Un__def,axiom,
% 5.45/5.67 ( sup_su6327502436637775413at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( collec3392354462482085612at_nat
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.67 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.67 | ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1823_Un__def,axiom,
% 5.45/5.67 ( sup_sup_set_o
% 5.45/5.67 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.67 ( collect_o
% 5.45/5.67 @ ^ [X4: $o] :
% 5.45/5.67 ( ( member_o @ X4 @ A6 )
% 5.45/5.67 | ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1824_Un__def,axiom,
% 5.45/5.67 ( sup_su6024340866399070445nt_int
% 5.45/5.67 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.67 ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] :
% 5.45/5.67 ( ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.67 | ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1825_Un__def,axiom,
% 5.45/5.67 ( sup_sup_set_list_nat
% 5.45/5.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.67 ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] :
% 5.45/5.67 ( ( member_list_nat @ X4 @ A6 )
% 5.45/5.67 | ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1826_Un__def,axiom,
% 5.45/5.67 ( sup_sup_set_set_nat
% 5.45/5.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.67 ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] :
% 5.45/5.67 ( ( member_set_nat @ X4 @ A6 )
% 5.45/5.67 | ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1827_Un__def,axiom,
% 5.45/5.67 ( sup_sup_set_int
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( collect_int
% 5.45/5.67 @ ^ [X4: int] :
% 5.45/5.67 ( ( member_int @ X4 @ A6 )
% 5.45/5.67 | ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1828_Un__def,axiom,
% 5.45/5.67 ( sup_su718114333110466843at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.45/5.67 ( collec7088162979684241874at_nat
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] :
% 5.45/5.67 ( ( member8206827879206165904at_nat @ X4 @ A6 )
% 5.45/5.67 | ( member8206827879206165904at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1829_Un__def,axiom,
% 5.45/5.67 ( sup_su3035147773818789531at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 5.45/5.67 ( collec5204685387357076818at_nat
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] :
% 5.45/5.67 ( ( member6689249552917799696at_nat @ X4 @ A6 )
% 5.45/5.67 | ( member6689249552917799696at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1830_Un__def,axiom,
% 5.45/5.67 ( sup_su5525570899277871387at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.45/5.67 ( collec6321179662152712658at_nat
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] :
% 5.45/5.67 ( ( member8757157785044589968at_nat @ X4 @ A6 )
% 5.45/5.67 | ( member8757157785044589968at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1831_Un__def,axiom,
% 5.45/5.67 ( sup_sup_set_nat
% 5.45/5.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.67 ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] :
% 5.45/5.67 ( ( member_nat @ X4 @ A6 )
% 5.45/5.67 | ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Un_def
% 5.45/5.67 thf(fact_1832_sup__set__def,axiom,
% 5.45/5.67 ( sup_su6327502436637775413at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.67 ( collec3392354462482085612at_nat
% 5.45/5.67 @ ( sup_su798857527126471912_nat_o
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1833_sup__set__def,axiom,
% 5.45/5.67 ( sup_sup_set_o
% 5.45/5.67 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.67 ( collect_o
% 5.45/5.67 @ ( sup_sup_o_o
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1834_sup__set__def,axiom,
% 5.45/5.67 ( sup_su6024340866399070445nt_int
% 5.45/5.67 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.67 ( collec213857154873943460nt_int
% 5.45/5.67 @ ( sup_su8463660629351352368_int_o
% 5.45/5.67 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1835_sup__set__def,axiom,
% 5.45/5.67 ( sup_sup_set_list_nat
% 5.45/5.67 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.67 ( collect_list_nat
% 5.45/5.67 @ ( sup_sup_list_nat_o
% 5.45/5.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1836_sup__set__def,axiom,
% 5.45/5.67 ( sup_sup_set_set_nat
% 5.45/5.67 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.67 ( collect_set_nat
% 5.45/5.67 @ ( sup_sup_set_nat_o
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1837_sup__set__def,axiom,
% 5.45/5.67 ( sup_sup_set_int
% 5.45/5.67 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.67 ( collect_int
% 5.45/5.67 @ ( sup_sup_int_o
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1838_sup__set__def,axiom,
% 5.45/5.67 ( sup_su718114333110466843at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr8693737435421807431at_nat,B6: set_Pr8693737435421807431at_nat] :
% 5.45/5.67 ( collec7088162979684241874at_nat
% 5.45/5.67 @ ( sup_su8986005896011022210_nat_o
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] : ( member8206827879206165904at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1839_sup__set__def,axiom,
% 5.45/5.67 ( sup_su3035147773818789531at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr8551490117392284871at_nat,B6: set_Pr8551490117392284871at_nat] :
% 5.45/5.67 ( collec5204685387357076818at_nat
% 5.45/5.67 @ ( sup_su6256023009775730178_nat_o
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] : ( member6689249552917799696at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1840_sup__set__def,axiom,
% 5.45/5.67 ( sup_su5525570899277871387at_nat
% 5.45/5.67 = ( ^ [A6: set_Pr4329608150637261639at_nat,B6: set_Pr4329608150637261639at_nat] :
% 5.45/5.67 ( collec6321179662152712658at_nat
% 5.45/5.67 @ ( sup_su2080679670758317954_nat_o
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] : ( member8757157785044589968at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1841_sup__set__def,axiom,
% 5.45/5.67 ( sup_sup_set_nat
% 5.45/5.67 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.67 ( collect_nat
% 5.45/5.67 @ ( sup_sup_nat_o
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 5.45/5.67 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % sup_set_def
% 5.45/5.67 thf(fact_1842_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.67 ( ( collec213857154873943460nt_int
% 5.45/5.67 @ ^ [X4: product_prod_int_int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_su6024340866399070445nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1843_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.67 ( ( collect_list_nat
% 5.45/5.67 @ ^ [X4: list_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_sup_set_list_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1844_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.67 ( ( collect_set_nat
% 5.45/5.67 @ ^ [X4: set_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_sup_set_set_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1845_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: int > $o,Q: int > $o] :
% 5.45/5.67 ( ( collect_int
% 5.45/5.67 @ ^ [X4: int] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_sup_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1846_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: produc859450856879609959at_nat > $o,Q: produc859450856879609959at_nat > $o] :
% 5.45/5.67 ( ( collec7088162979684241874at_nat
% 5.45/5.67 @ ^ [X4: produc859450856879609959at_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_su718114333110466843at_nat @ ( collec7088162979684241874at_nat @ P ) @ ( collec7088162979684241874at_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1847_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: produc4166570645942440679at_nat > $o,Q: produc4166570645942440679at_nat > $o] :
% 5.45/5.67 ( ( collec5204685387357076818at_nat
% 5.45/5.67 @ ^ [X4: produc4166570645942440679at_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_su3035147773818789531at_nat @ ( collec5204685387357076818at_nat @ P ) @ ( collec5204685387357076818at_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1848_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > $o] :
% 5.45/5.67 ( ( collec6321179662152712658at_nat
% 5.45/5.67 @ ^ [X4: produc3843707927480180839at_nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_su5525570899277871387at_nat @ ( collec6321179662152712658at_nat @ P ) @ ( collec6321179662152712658at_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1849_Collect__disj__eq,axiom,
% 5.45/5.67 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.67 ( ( collect_nat
% 5.45/5.67 @ ^ [X4: nat] :
% 5.45/5.67 ( ( P @ X4 )
% 5.45/5.67 | ( Q @ X4 ) ) )
% 5.45/5.67 = ( sup_sup_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % Collect_disj_eq
% 5.45/5.67 thf(fact_1850_exists__leI,axiom,
% 5.45/5.67 ! [N2: nat,P: nat > $o] :
% 5.45/5.67 ( ( ! [N3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ N3 @ N2 )
% 5.45/5.67 => ~ ( P @ N3 ) )
% 5.45/5.67 => ( P @ N2 ) )
% 5.45/5.67 => ? [N4: nat] :
% 5.45/5.67 ( ( ord_less_eq_nat @ N4 @ N2 )
% 5.45/5.67 & ( P @ N4 ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % exists_leI
% 5.45/5.67 thf(fact_1851_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.67 => ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1852_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: set_int,Y: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_set_int @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1853_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1854_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.67 => ( ( ord_less_num @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1855_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1856_order__le__imp__less__or__eq,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_int @ X @ Y )
% 5.45/5.67 | ( X = Y ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_imp_less_or_eq
% 5.45/5.67 thf(fact_1857_linorder__le__less__linear,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.67 | ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_le_less_linear
% 5.45/5.67 thf(fact_1858_linorder__le__less__linear,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.67 | ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_le_less_linear
% 5.45/5.67 thf(fact_1859_linorder__le__less__linear,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.67 | ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_le_less_linear
% 5.45/5.67 thf(fact_1860_linorder__le__less__linear,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.67 | ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_le_less_linear
% 5.45/5.67 thf(fact_1861_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1862_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1863_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1864_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: nat,B: nat,F: nat > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1865_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: int,B: int,F: int > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1866_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: assn,B: assn,F: assn > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1867_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1868_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1869_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1870_order__less__le__subst2,axiom,
% 5.45/5.67 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_int @ A @ B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst2
% 5.45/5.67 thf(fact_1871_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: rat > assn,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1872_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1873_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1874_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1875_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1876_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: num > assn,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1877_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1878_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: num,F: num > num,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1879_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1880_order__less__le__subst1,axiom,
% 5.45/5.67 ! [A: int,F: num > int,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_subst1
% 5.45/5.67 thf(fact_1881_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1882_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1883_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1884_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1885_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1886_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > assn,C: assn] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_assn @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1887_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1888_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > num,C: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_num @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1889_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1890_order__le__less__subst2,axiom,
% 5.45/5.67 ! [A: num,B: num,F: num > int,C: int] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_eq_int @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst2
% 5.45/5.67 thf(fact_1891_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: assn > assn,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1892_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: rat > assn,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1893_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: num > assn,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1894_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: nat > assn,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1895_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: assn,F: int > assn,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_assn @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_assn @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1896_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: assn > rat,B: assn,C: assn] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_assn @ B @ C )
% 5.45/5.67 => ( ! [X3: assn,Y3: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1897_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_rat @ B @ C )
% 5.45/5.67 => ( ! [X3: rat,Y3: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1898_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_num @ B @ C )
% 5.45/5.67 => ( ! [X3: num,Y3: num] :
% 5.45/5.67 ( ( ord_less_num @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1899_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_nat @ B @ C )
% 5.45/5.67 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1900_order__le__less__subst1,axiom,
% 5.45/5.67 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.45/5.67 => ( ( ord_less_int @ B @ C )
% 5.45/5.67 => ( ! [X3: int,Y3: int] :
% 5.45/5.67 ( ( ord_less_int @ X3 @ Y3 )
% 5.45/5.67 => ( ord_less_rat @ ( F @ X3 ) @ ( F @ Y3 ) ) )
% 5.45/5.67 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_subst1
% 5.45/5.67 thf(fact_1901_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_assn @ Y @ Z )
% 5.45/5.67 => ( ord_less_assn @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1902_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.67 ( ( ord_less_set_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.45/5.67 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1903_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.45/5.67 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1904_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: num,Y: num,Z: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_num @ Y @ Z )
% 5.45/5.67 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1905_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.45/5.67 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1906_order__less__le__trans,axiom,
% 5.45/5.67 ! [X: int,Y: int,Z: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_eq_int @ Y @ Z )
% 5.45/5.67 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le_trans
% 5.45/5.67 thf(fact_1907_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.67 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.67 => ( ( ord_less_assn @ Y @ Z )
% 5.45/5.67 => ( ord_less_assn @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1908_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_set_int @ Y @ Z )
% 5.45/5.67 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1909_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_rat @ Y @ Z )
% 5.45/5.67 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1910_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: num,Y: num,Z: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.67 => ( ( ord_less_num @ Y @ Z )
% 5.45/5.67 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1911_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: nat,Y: nat,Z: nat] :
% 5.45/5.67 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.67 => ( ( ord_less_nat @ Y @ Z )
% 5.45/5.67 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1912_order__le__less__trans,axiom,
% 5.45/5.67 ! [X: int,Y: int,Z: int] :
% 5.45/5.67 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.67 => ( ( ord_less_int @ Y @ Z )
% 5.45/5.67 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_less_trans
% 5.45/5.67 thf(fact_1913_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: assn,B: assn] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.67 => ( ord_less_assn @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1914_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: set_int,B: set_int] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.67 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1915_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: rat,B: rat] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1916_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: num,B: num] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ord_less_num @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1917_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: nat,B: nat] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.67 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1918_order__neq__le__trans,axiom,
% 5.45/5.67 ! [A: int,B: int] :
% 5.45/5.67 ( ( A != B )
% 5.45/5.67 => ( ( ord_less_eq_int @ A @ B )
% 5.45/5.67 => ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_neq_le_trans
% 5.45/5.67 thf(fact_1919_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: assn,B: assn] :
% 5.45/5.67 ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_assn @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1920_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: set_int,B: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1921_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: rat,B: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1922_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: num,B: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_num @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1923_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: nat,B: nat] :
% 5.45/5.67 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1924_order__le__neq__trans,axiom,
% 5.45/5.67 ! [A: int,B: int] :
% 5.45/5.67 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.67 => ( ( A != B )
% 5.45/5.67 => ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_le_neq_trans
% 5.45/5.67 thf(fact_1925_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: assn,Y: assn] :
% 5.45/5.67 ( ( ord_less_assn @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_assn @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1926_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: set_int,Y: set_int] :
% 5.45/5.67 ( ( ord_less_set_int @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1927_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ord_less_rat @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1928_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ord_less_num @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1929_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ord_less_nat @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1930_order__less__imp__le,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ord_less_int @ X @ Y )
% 5.45/5.67 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_imp_le
% 5.45/5.67 thf(fact_1931_linorder__not__less,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.45/5.67 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_less
% 5.45/5.67 thf(fact_1932_linorder__not__less,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.45/5.67 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_less
% 5.45/5.67 thf(fact_1933_linorder__not__less,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.45/5.67 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_less
% 5.45/5.67 thf(fact_1934_linorder__not__less,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.45/5.67 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_less
% 5.45/5.67 thf(fact_1935_linorder__not__le,axiom,
% 5.45/5.67 ! [X: rat,Y: rat] :
% 5.45/5.67 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 5.45/5.67 = ( ord_less_rat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_le
% 5.45/5.67 thf(fact_1936_linorder__not__le,axiom,
% 5.45/5.67 ! [X: num,Y: num] :
% 5.45/5.67 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.45/5.67 = ( ord_less_num @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_le
% 5.45/5.67 thf(fact_1937_linorder__not__le,axiom,
% 5.45/5.67 ! [X: nat,Y: nat] :
% 5.45/5.67 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.45/5.67 = ( ord_less_nat @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_le
% 5.45/5.67 thf(fact_1938_linorder__not__le,axiom,
% 5.45/5.67 ! [X: int,Y: int] :
% 5.45/5.67 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.45/5.67 = ( ord_less_int @ Y @ X ) ) ).
% 5.45/5.67
% 5.45/5.67 % linorder_not_le
% 5.45/5.67 thf(fact_1939_order__less__le,axiom,
% 5.45/5.67 ( ord_less_assn
% 5.45/5.67 = ( ^ [X4: assn,Y4: assn] :
% 5.45/5.67 ( ( ord_less_eq_assn @ X4 @ Y4 )
% 5.45/5.67 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le
% 5.45/5.67 thf(fact_1940_order__less__le,axiom,
% 5.45/5.67 ( ord_less_set_int
% 5.45/5.67 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.67 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 5.45/5.67 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le
% 5.45/5.67 thf(fact_1941_order__less__le,axiom,
% 5.45/5.67 ( ord_less_rat
% 5.45/5.67 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.67 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.45/5.67 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le
% 5.45/5.67 thf(fact_1942_order__less__le,axiom,
% 5.45/5.67 ( ord_less_num
% 5.45/5.67 = ( ^ [X4: num,Y4: num] :
% 5.45/5.67 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.45/5.67 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.67
% 5.45/5.67 % order_less_le
% 5.45/5.67 thf(fact_1943_order__less__le,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.45/5.68 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_less_le
% 5.45/5.68 thf(fact_1944_order__less__le,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [X4: int,Y4: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.45/5.68 & ( X4 != Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_less_le
% 5.45/5.68 thf(fact_1945_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_assn
% 5.45/5.68 = ( ^ [X4: assn,Y4: assn] :
% 5.45/5.68 ( ( ord_less_assn @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1946_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_set_int
% 5.45/5.68 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1947_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_rat
% 5.45/5.68 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1948_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_num
% 5.45/5.68 = ( ^ [X4: num,Y4: num] :
% 5.45/5.68 ( ( ord_less_num @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1949_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_nat
% 5.45/5.68 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.68 ( ( ord_less_nat @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1950_order__le__less,axiom,
% 5.45/5.68 ( ord_less_eq_int
% 5.45/5.68 = ( ^ [X4: int,Y4: int] :
% 5.45/5.68 ( ( ord_less_int @ X4 @ Y4 )
% 5.45/5.68 | ( X4 = Y4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order_le_less
% 5.45/5.68 thf(fact_1951_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ A )
% 5.45/5.68 => ( ord_less_eq_assn @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1952_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: set_int,A: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ B @ A )
% 5.45/5.68 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1953_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ A )
% 5.45/5.68 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1954_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: num,A: num] :
% 5.45/5.68 ( ( ord_less_num @ B @ A )
% 5.45/5.68 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1955_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ A )
% 5.45/5.68 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1956_dual__order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [B: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ A )
% 5.45/5.68 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_implies_order
% 5.45/5.68 thf(fact_1957_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ B )
% 5.45/5.68 => ( ord_less_eq_assn @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1958_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: set_int,B: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A @ B )
% 5.45/5.68 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1959_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ B )
% 5.45/5.68 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1960_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: num,B: num] :
% 5.45/5.68 ( ( ord_less_num @ A @ B )
% 5.45/5.68 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1961_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1962_order_Ostrict__implies__order,axiom,
% 5.45/5.68 ! [A: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_implies_order
% 5.45/5.68 thf(fact_1963_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_assn @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1964_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_set_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1965_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_rat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1966_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_num
% 5.45/5.68 = ( ^ [B5: num,A5: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_num @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1967_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_nat @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1968_dual__order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [B5: int,A5: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.45/5.68 & ~ ( ord_less_eq_int @ A5 @ B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_not
% 5.45/5.68 thf(fact_1969_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: assn,A: assn,C: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_assn @ C @ B )
% 5.45/5.68 => ( ord_less_assn @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1970_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: set_int,A: set_int,C: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ C @ B )
% 5.45/5.68 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1971_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: rat,A: rat,C: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_rat @ C @ B )
% 5.45/5.68 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1972_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: num,A: num,C: num] :
% 5.45/5.68 ( ( ord_less_num @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_num @ C @ B )
% 5.45/5.68 => ( ord_less_num @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1973_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: nat,A: nat,C: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_nat @ C @ B )
% 5.45/5.68 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1974_dual__order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [B: int,A: int,C: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ A )
% 5.45/5.68 => ( ( ord_less_eq_int @ C @ B )
% 5.45/5.68 => ( ord_less_int @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans2
% 5.45/5.68 thf(fact_1975_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: assn,A: assn,C: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ B @ A )
% 5.45/5.68 => ( ( ord_less_assn @ C @ B )
% 5.45/5.68 => ( ord_less_assn @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1976_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: set_int,A: set_int,C: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.68 => ( ( ord_less_set_int @ C @ B )
% 5.45/5.68 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1977_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: rat,A: rat,C: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.68 => ( ( ord_less_rat @ C @ B )
% 5.45/5.68 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1978_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: num,A: num,C: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ B @ A )
% 5.45/5.68 => ( ( ord_less_num @ C @ B )
% 5.45/5.68 => ( ord_less_num @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1979_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: nat,A: nat,C: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.68 => ( ( ord_less_nat @ C @ B )
% 5.45/5.68 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1980_dual__order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [B: int,A: int,C: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.68 => ( ( ord_less_int @ C @ B )
% 5.45/5.68 => ( ord_less_int @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_trans1
% 5.45/5.68 thf(fact_1981_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1982_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1983_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1984_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_num
% 5.45/5.68 = ( ^ [B5: num,A5: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1985_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1986_dual__order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [B5: int,A5: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ B5 @ A5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.strict_iff_order
% 5.45/5.68 thf(fact_1987_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_assn
% 5.45/5.68 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1988_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_set_int
% 5.45/5.68 = ( ^ [B5: set_int,A5: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1989_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_rat
% 5.45/5.68 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1990_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_num
% 5.45/5.68 = ( ^ [B5: num,A5: num] :
% 5.45/5.68 ( ( ord_less_num @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1991_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_nat
% 5.45/5.68 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1992_dual__order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_int
% 5.45/5.68 = ( ^ [B5: int,A5: int] :
% 5.45/5.68 ( ( ord_less_int @ B5 @ A5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dual_order.order_iff_strict
% 5.45/5.68 thf(fact_1993_dense__le__bounded,axiom,
% 5.45/5.68 ! [X: rat,Y: rat,Z: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X @ Y )
% 5.45/5.68 => ( ! [W: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X @ W )
% 5.45/5.68 => ( ( ord_less_rat @ W @ Y )
% 5.45/5.68 => ( ord_less_eq_rat @ W @ Z ) ) )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dense_le_bounded
% 5.45/5.68 thf(fact_1994_dense__ge__bounded,axiom,
% 5.45/5.68 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z @ X )
% 5.45/5.68 => ( ! [W: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z @ W )
% 5.45/5.68 => ( ( ord_less_rat @ W @ X )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ W ) ) )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % dense_ge_bounded
% 5.45/5.68 thf(fact_1995_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_assn @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_1996_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_set_int @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_1997_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_rat @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_1998_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_num
% 5.45/5.68 = ( ^ [A5: num,B5: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_num @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_1999_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_nat @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_2000_order_Ostrict__iff__not,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [A5: int,B5: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.45/5.68 & ~ ( ord_less_eq_int @ B5 @ A5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_not
% 5.45/5.68 thf(fact_2001_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: assn,B: assn,C: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_assn @ B @ C )
% 5.45/5.68 => ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2002_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ B @ C )
% 5.45/5.68 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2003_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: rat,B: rat,C: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.68 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2004_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: num,B: num,C: num] :
% 5.45/5.68 ( ( ord_less_num @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.68 => ( ord_less_num @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2005_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: nat,B: nat,C: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.68 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2006_order_Ostrict__trans2,axiom,
% 5.45/5.68 ! [A: int,B: int,C: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.68 => ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans2
% 5.45/5.68 thf(fact_2007_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: assn,B: assn,C: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.68 => ( ( ord_less_assn @ B @ C )
% 5.45/5.68 => ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2008_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: set_int,B: set_int,C: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.68 => ( ( ord_less_set_int @ B @ C )
% 5.45/5.68 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2009_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: rat,B: rat,C: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.68 => ( ( ord_less_rat @ B @ C )
% 5.45/5.68 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2010_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: num,B: num,C: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ A @ B )
% 5.45/5.68 => ( ( ord_less_num @ B @ C )
% 5.45/5.68 => ( ord_less_num @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2011_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: nat,B: nat,C: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.68 => ( ( ord_less_nat @ B @ C )
% 5.45/5.68 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2012_order_Ostrict__trans1,axiom,
% 5.45/5.68 ! [A: int,B: int,C: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.68 => ( ( ord_less_int @ B @ C )
% 5.45/5.68 => ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_trans1
% 5.45/5.68 thf(fact_2013_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2014_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2015_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2016_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_num
% 5.45/5.68 = ( ^ [A5: num,B5: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2017_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2018_order_Ostrict__iff__order,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [A5: int,B5: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.strict_iff_order
% 5.45/5.68 thf(fact_2019_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_assn
% 5.45/5.68 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2020_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_set_int
% 5.45/5.68 = ( ^ [A5: set_int,B5: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2021_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_rat
% 5.45/5.68 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2022_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_num
% 5.45/5.68 = ( ^ [A5: num,B5: num] :
% 5.45/5.68 ( ( ord_less_num @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2023_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_nat
% 5.45/5.68 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2024_order_Oorder__iff__strict,axiom,
% 5.45/5.68 ( ord_less_eq_int
% 5.45/5.68 = ( ^ [A5: int,B5: int] :
% 5.45/5.68 ( ( ord_less_int @ A5 @ B5 )
% 5.45/5.68 | ( A5 = B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % order.order_iff_strict
% 5.45/5.68 thf(fact_2025_not__le__imp__less,axiom,
% 5.45/5.68 ! [Y: rat,X: rat] :
% 5.45/5.68 ( ~ ( ord_less_eq_rat @ Y @ X )
% 5.45/5.68 => ( ord_less_rat @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % not_le_imp_less
% 5.45/5.68 thf(fact_2026_not__le__imp__less,axiom,
% 5.45/5.68 ! [Y: num,X: num] :
% 5.45/5.68 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.45/5.68 => ( ord_less_num @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % not_le_imp_less
% 5.45/5.68 thf(fact_2027_not__le__imp__less,axiom,
% 5.45/5.68 ! [Y: nat,X: nat] :
% 5.45/5.68 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.45/5.68 => ( ord_less_nat @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % not_le_imp_less
% 5.45/5.68 thf(fact_2028_not__le__imp__less,axiom,
% 5.45/5.68 ! [Y: int,X: int] :
% 5.45/5.68 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.45/5.68 => ( ord_less_int @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % not_le_imp_less
% 5.45/5.68 thf(fact_2029_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [X4: assn,Y4: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_assn @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2030_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [X4: set_int,Y4: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_set_int @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2031_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [X4: rat,Y4: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_rat @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2032_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_num
% 5.45/5.68 = ( ^ [X4: num,Y4: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_num @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2033_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [X4: nat,Y4: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_nat @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2034_less__le__not__le,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [X4: int,Y4: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ X4 @ Y4 )
% 5.45/5.68 & ~ ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_le_not_le
% 5.45/5.68 thf(fact_2035_dense__le,axiom,
% 5.45/5.68 ! [Y: rat,Z: rat] :
% 5.45/5.68 ( ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X3 @ Y )
% 5.45/5.68 => ( ord_less_eq_rat @ X3 @ Z ) )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.45/5.68
% 5.45/5.68 % dense_le
% 5.45/5.68 thf(fact_2036_dense__ge,axiom,
% 5.45/5.68 ! [Z: rat,Y: rat] :
% 5.45/5.68 ( ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z @ X3 )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ X3 ) )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.45/5.68
% 5.45/5.68 % dense_ge
% 5.45/5.68 thf(fact_2037_antisym__conv2,axiom,
% 5.45/5.68 ! [X: assn,Y: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_assn @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2038_antisym__conv2,axiom,
% 5.45/5.68 ! [X: set_int,Y: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2039_antisym__conv2,axiom,
% 5.45/5.68 ! [X: rat,Y: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2040_antisym__conv2,axiom,
% 5.45/5.68 ! [X: num,Y: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2041_antisym__conv2,axiom,
% 5.45/5.68 ! [X: nat,Y: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2042_antisym__conv2,axiom,
% 5.45/5.68 ! [X: int,Y: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.68 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv2
% 5.45/5.68 thf(fact_2043_antisym__conv1,axiom,
% 5.45/5.68 ! [X: assn,Y: assn] :
% 5.45/5.68 ( ~ ( ord_less_assn @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2044_antisym__conv1,axiom,
% 5.45/5.68 ! [X: set_int,Y: set_int] :
% 5.45/5.68 ( ~ ( ord_less_set_int @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2045_antisym__conv1,axiom,
% 5.45/5.68 ! [X: rat,Y: rat] :
% 5.45/5.68 ( ~ ( ord_less_rat @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2046_antisym__conv1,axiom,
% 5.45/5.68 ! [X: num,Y: num] :
% 5.45/5.68 ( ~ ( ord_less_num @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_num @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2047_antisym__conv1,axiom,
% 5.45/5.68 ! [X: nat,Y: nat] :
% 5.45/5.68 ( ~ ( ord_less_nat @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_nat @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2048_antisym__conv1,axiom,
% 5.45/5.68 ! [X: int,Y: int] :
% 5.45/5.68 ( ~ ( ord_less_int @ X @ Y )
% 5.45/5.68 => ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.68 = ( X = Y ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % antisym_conv1
% 5.45/5.68 thf(fact_2049_nless__le,axiom,
% 5.45/5.68 ! [A: assn,B: assn] :
% 5.45/5.68 ( ( ~ ( ord_less_assn @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_assn @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2050_nless__le,axiom,
% 5.45/5.68 ! [A: set_int,B: set_int] :
% 5.45/5.68 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2051_nless__le,axiom,
% 5.45/5.68 ! [A: rat,B: rat] :
% 5.45/5.68 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2052_nless__le,axiom,
% 5.45/5.68 ! [A: num,B: num] :
% 5.45/5.68 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2053_nless__le,axiom,
% 5.45/5.68 ! [A: nat,B: nat] :
% 5.45/5.68 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2054_nless__le,axiom,
% 5.45/5.68 ! [A: int,B: int] :
% 5.45/5.68 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.45/5.68 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.45/5.68 | ( A = B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nless_le
% 5.45/5.68 thf(fact_2055_leI,axiom,
% 5.45/5.68 ! [X: rat,Y: rat] :
% 5.45/5.68 ( ~ ( ord_less_rat @ X @ Y )
% 5.45/5.68 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % leI
% 5.45/5.68 thf(fact_2056_leI,axiom,
% 5.45/5.68 ! [X: num,Y: num] :
% 5.45/5.68 ( ~ ( ord_less_num @ X @ Y )
% 5.45/5.68 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % leI
% 5.45/5.68 thf(fact_2057_leI,axiom,
% 5.45/5.68 ! [X: nat,Y: nat] :
% 5.45/5.68 ( ~ ( ord_less_nat @ X @ Y )
% 5.45/5.68 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % leI
% 5.45/5.68 thf(fact_2058_leI,axiom,
% 5.45/5.68 ! [X: int,Y: int] :
% 5.45/5.68 ( ~ ( ord_less_int @ X @ Y )
% 5.45/5.68 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % leI
% 5.45/5.68 thf(fact_2059_leD,axiom,
% 5.45/5.68 ! [Y: assn,X: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_assn @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2060_leD,axiom,
% 5.45/5.68 ! [Y: set_int,X: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2061_leD,axiom,
% 5.45/5.68 ! [Y: rat,X: rat] :
% 5.45/5.68 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2062_leD,axiom,
% 5.45/5.68 ! [Y: num,X: num] :
% 5.45/5.68 ( ( ord_less_eq_num @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2063_leD,axiom,
% 5.45/5.68 ! [Y: nat,X: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2064_leD,axiom,
% 5.45/5.68 ! [Y: int,X: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ Y @ X )
% 5.45/5.68 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.45/5.68
% 5.45/5.68 % leD
% 5.45/5.68 thf(fact_2065_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( A != bot_bo2099793752762293965at_nat )
% 5.45/5.68 = ( ord_le7866589430770878221at_nat @ bot_bo2099793752762293965at_nat @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2066_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: set_o] :
% 5.45/5.68 ( ( A != bot_bot_set_o )
% 5.45/5.68 = ( ord_less_set_o @ bot_bot_set_o @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2067_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: set_nat] :
% 5.45/5.68 ( ( A != bot_bot_set_nat )
% 5.45/5.68 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2068_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: set_int] :
% 5.45/5.68 ( ( A != bot_bot_set_int )
% 5.45/5.68 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2069_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: assn] :
% 5.45/5.68 ( ( A != bot_bot_assn )
% 5.45/5.68 = ( ord_less_assn @ bot_bot_assn @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2070_bot_Onot__eq__extremum,axiom,
% 5.45/5.68 ! [A: nat] :
% 5.45/5.68 ( ( A != bot_bot_nat )
% 5.45/5.68 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % bot.not_eq_extremum
% 5.45/5.68 thf(fact_2071_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ~ ( ord_le7866589430770878221at_nat @ A @ bot_bo2099793752762293965at_nat ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2072_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: set_o] :
% 5.45/5.68 ~ ( ord_less_set_o @ A @ bot_bot_set_o ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2073_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: set_nat] :
% 5.45/5.68 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2074_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: set_int] :
% 5.45/5.68 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2075_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: assn] :
% 5.45/5.68 ~ ( ord_less_assn @ A @ bot_bot_assn ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2076_bot_Oextremum__strict,axiom,
% 5.45/5.68 ! [A: nat] :
% 5.45/5.68 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.45/5.68
% 5.45/5.68 % bot.extremum_strict
% 5.45/5.68 thf(fact_2077_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: set_nat,C: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ B @ C )
% 5.45/5.68 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2078_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: product_unit,C: product_unit,A: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ B @ C )
% 5.45/5.68 => ( ord_le361264281704409273t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2079_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ B @ C )
% 5.45/5.68 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2080_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: assn,C: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ C )
% 5.45/5.68 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2081_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: rat,C: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ C )
% 5.45/5.68 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2082_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: nat,C: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ C )
% 5.45/5.68 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2083_inf_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [B: int,C: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ C )
% 5.45/5.68 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI2
% 5.45/5.68 thf(fact_2084_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: set_nat,C: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A @ C )
% 5.45/5.68 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2085_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: product_unit,C: product_unit,B: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ A @ C )
% 5.45/5.68 => ( ord_le361264281704409273t_unit @ ( inf_inf_Product_unit @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2086_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ A @ C )
% 5.45/5.68 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2087_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: assn,C: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ C )
% 5.45/5.68 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2088_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: rat,C: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ C )
% 5.45/5.68 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2089_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: nat,C: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ C )
% 5.45/5.68 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2090_inf_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [A: int,C: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ C )
% 5.45/5.68 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ C ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_coboundedI1
% 5.45/5.68 thf(fact_2091_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_set_nat
% 5.45/5.68 = ( ^ [A5: set_nat,B5: set_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_set_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2092_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_le361264281704409273t_unit
% 5.45/5.68 = ( ^ [A5: product_unit,B5: product_unit] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_Product_unit @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2093_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_le7866589430770878221at_nat
% 5.45/5.68 = ( ^ [A5: set_Pr1261947904930325089at_nat,B5: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_in2572325071724192079at_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2094_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_assn @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2095_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [A5: rat,B5: rat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_rat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2096_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2097_inf_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [A5: int,B5: int] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( inf_inf_int @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_order_iff
% 5.45/5.68 thf(fact_2098_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: set_nat,B: set_nat,C: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A @ ( inf_inf_set_nat @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_less_set_nat @ A @ B )
% 5.45/5.68 => ~ ( ord_less_set_nat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2099_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: product_unit,B: product_unit,C: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ A @ ( inf_inf_Product_unit @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_le361264281704409273t_unit @ A @ B )
% 5.45/5.68 => ~ ( ord_le361264281704409273t_unit @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2100_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat,C: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ A @ ( inf_in2572325071724192079at_nat @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_le7866589430770878221at_nat @ A @ B )
% 5.45/5.68 => ~ ( ord_le7866589430770878221at_nat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2101_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: assn,B: assn,C: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ ( inf_inf_assn @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_less_assn @ A @ B )
% 5.45/5.68 => ~ ( ord_less_assn @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2102_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: rat,B: rat,C: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ ( inf_inf_rat @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_less_rat @ A @ B )
% 5.45/5.68 => ~ ( ord_less_rat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2103_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: nat,B: nat,C: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ ( inf_inf_nat @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ~ ( ord_less_nat @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2104_inf_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [A: int,B: int,C: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ ( inf_inf_int @ B @ C ) )
% 5.45/5.68 => ~ ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ~ ( ord_less_int @ A @ C ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.strict_boundedE
% 5.45/5.68 thf(fact_2105_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ B @ A )
% 5.45/5.68 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2106_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: product_unit,A: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ B @ A )
% 5.45/5.68 => ( ( inf_inf_Product_unit @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2107_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ B @ A )
% 5.45/5.68 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2108_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ A )
% 5.45/5.68 => ( ( inf_inf_assn @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2109_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ A )
% 5.45/5.68 => ( ( inf_inf_rat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2110_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ A )
% 5.45/5.68 => ( ( inf_inf_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2111_inf_Oabsorb4,axiom,
% 5.45/5.68 ! [B: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ A )
% 5.45/5.68 => ( ( inf_inf_int @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb4
% 5.45/5.68 thf(fact_2112_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A @ B )
% 5.45/5.68 => ( ( inf_inf_set_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2113_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: product_unit,B: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ A @ B )
% 5.45/5.68 => ( ( inf_inf_Product_unit @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2114_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ A @ B )
% 5.45/5.68 => ( ( inf_in2572325071724192079at_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2115_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ B )
% 5.45/5.68 => ( ( inf_inf_assn @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2116_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ B )
% 5.45/5.68 => ( ( inf_inf_rat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2117_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ( ( inf_inf_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2118_inf_Oabsorb3,axiom,
% 5.45/5.68 ! [A: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ( ( inf_inf_int @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % inf.absorb3
% 5.45/5.68 thf(fact_2119_less__infI2,axiom,
% 5.45/5.68 ! [B: set_nat,X: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ B @ X )
% 5.45/5.68 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2120_less__infI2,axiom,
% 5.45/5.68 ! [B: product_unit,X: product_unit,A: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ B @ X )
% 5.45/5.68 => ( ord_le361264281704409273t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2121_less__infI2,axiom,
% 5.45/5.68 ! [B: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ B @ X )
% 5.45/5.68 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2122_less__infI2,axiom,
% 5.45/5.68 ! [B: assn,X: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ X )
% 5.45/5.68 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2123_less__infI2,axiom,
% 5.45/5.68 ! [B: rat,X: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ X )
% 5.45/5.68 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2124_less__infI2,axiom,
% 5.45/5.68 ! [B: nat,X: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ X )
% 5.45/5.68 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2125_less__infI2,axiom,
% 5.45/5.68 ! [B: int,X: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ X )
% 5.45/5.68 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI2
% 5.45/5.68 thf(fact_2126_less__infI1,axiom,
% 5.45/5.68 ! [A: set_nat,X: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A @ X )
% 5.45/5.68 => ( ord_less_set_nat @ ( inf_inf_set_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2127_less__infI1,axiom,
% 5.45/5.68 ! [A: product_unit,X: product_unit,B: product_unit] :
% 5.45/5.68 ( ( ord_le361264281704409273t_unit @ A @ X )
% 5.45/5.68 => ( ord_le361264281704409273t_unit @ ( inf_inf_Product_unit @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2128_less__infI1,axiom,
% 5.45/5.68 ! [A: set_Pr1261947904930325089at_nat,X: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ A @ X )
% 5.45/5.68 => ( ord_le7866589430770878221at_nat @ ( inf_in2572325071724192079at_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2129_less__infI1,axiom,
% 5.45/5.68 ! [A: assn,X: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ X )
% 5.45/5.68 => ( ord_less_assn @ ( inf_inf_assn @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2130_less__infI1,axiom,
% 5.45/5.68 ! [A: rat,X: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ X )
% 5.45/5.68 => ( ord_less_rat @ ( inf_inf_rat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2131_less__infI1,axiom,
% 5.45/5.68 ! [A: nat,X: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ X )
% 5.45/5.68 => ( ord_less_nat @ ( inf_inf_nat @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2132_less__infI1,axiom,
% 5.45/5.68 ! [A: int,X: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ X )
% 5.45/5.68 => ( ord_less_int @ ( inf_inf_int @ A @ B ) @ X ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_infI1
% 5.45/5.68 thf(fact_2133_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ C @ B )
% 5.45/5.68 => ( ord_le6428140832669894131at_nat @ C @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2134_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ C @ B )
% 5.45/5.68 => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2135_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ C @ B )
% 5.45/5.68 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2136_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ C @ B )
% 5.45/5.68 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2137_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: assn,B: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ C @ B )
% 5.45/5.68 => ( ord_less_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2138_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: rat,B: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ C @ B )
% 5.45/5.68 => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2139_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: nat,B: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ C @ B )
% 5.45/5.68 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2140_sup_Ostrict__coboundedI2,axiom,
% 5.45/5.68 ! [C: int,B: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ C @ B )
% 5.45/5.68 => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI2
% 5.45/5.68 thf(fact_2141_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ C @ A )
% 5.45/5.68 => ( ord_le6428140832669894131at_nat @ C @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2142_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ C @ A )
% 5.45/5.68 => ( ord_le7642048601412989811at_nat @ C @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2143_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ C @ A )
% 5.45/5.68 => ( ord_le2604355607129572851at_nat @ C @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2144_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ C @ A )
% 5.45/5.68 => ( ord_less_set_nat @ C @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2145_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: assn,A: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ C @ A )
% 5.45/5.68 => ( ord_less_assn @ C @ ( sup_sup_assn @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2146_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: rat,A: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ C @ A )
% 5.45/5.68 => ( ord_less_rat @ C @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2147_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: nat,A: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ C @ A )
% 5.45/5.68 => ( ord_less_nat @ C @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2148_sup_Ostrict__coboundedI1,axiom,
% 5.45/5.68 ! [C: int,A: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ C @ A )
% 5.45/5.68 => ( ord_less_int @ C @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_coboundedI1
% 5.45/5.68 thf(fact_2149_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_le6428140832669894131at_nat
% 5.45/5.68 = ( ^ [B5: set_Pr8693737435421807431at_nat,A5: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_su718114333110466843at_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2150_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_le7642048601412989811at_nat
% 5.45/5.68 = ( ^ [B5: set_Pr8551490117392284871at_nat,A5: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_su3035147773818789531at_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2151_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_le2604355607129572851at_nat
% 5.45/5.68 = ( ^ [B5: set_Pr4329608150637261639at_nat,A5: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_su5525570899277871387at_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2152_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_set_nat
% 5.45/5.68 = ( ^ [B5: set_nat,A5: set_nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_sup_set_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2153_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_sup_assn @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2154_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_rat
% 5.45/5.68 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_sup_rat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2155_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_sup_nat @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2156_sup_Ostrict__order__iff,axiom,
% 5.45/5.68 ( ord_less_int
% 5.45/5.68 = ( ^ [B5: int,A5: int] :
% 5.45/5.68 ( ( A5
% 5.45/5.68 = ( sup_sup_int @ A5 @ B5 ) )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_order_iff
% 5.45/5.68 thf(fact_2157_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: set_Pr8693737435421807431at_nat,C: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ ( sup_su718114333110466843at_nat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_le6428140832669894131at_nat @ B @ A )
% 5.45/5.68 => ~ ( ord_le6428140832669894131at_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2158_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: set_Pr8551490117392284871at_nat,C: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ ( sup_su3035147773818789531at_nat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_le7642048601412989811at_nat @ B @ A )
% 5.45/5.68 => ~ ( ord_le7642048601412989811at_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2159_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: set_Pr4329608150637261639at_nat,C: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ ( sup_su5525570899277871387at_nat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_le2604355607129572851at_nat @ B @ A )
% 5.45/5.68 => ~ ( ord_le2604355607129572851at_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2160_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: set_nat,C: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ ( sup_sup_set_nat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_less_set_nat @ B @ A )
% 5.45/5.68 => ~ ( ord_less_set_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2161_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: assn,C: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ ( sup_sup_assn @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_less_assn @ B @ A )
% 5.45/5.68 => ~ ( ord_less_assn @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2162_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: rat,C: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ ( sup_sup_rat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_less_rat @ B @ A )
% 5.45/5.68 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2163_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: nat,C: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ ( sup_sup_nat @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_less_nat @ B @ A )
% 5.45/5.68 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2164_sup_Ostrict__boundedE,axiom,
% 5.45/5.68 ! [B: int,C: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ ( sup_sup_int @ B @ C ) @ A )
% 5.45/5.68 => ~ ( ( ord_less_int @ B @ A )
% 5.45/5.68 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.strict_boundedE
% 5.45/5.68 thf(fact_2165_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ A @ B )
% 5.45/5.68 => ( ( sup_su718114333110466843at_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2166_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ A @ B )
% 5.45/5.68 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2167_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ A @ B )
% 5.45/5.68 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2168_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A @ B )
% 5.45/5.68 => ( ( sup_sup_set_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2169_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ A @ B )
% 5.45/5.68 => ( ( sup_sup_assn @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2170_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ A @ B )
% 5.45/5.68 => ( ( sup_sup_rat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2171_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ( ( sup_sup_nat @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2172_sup_Oabsorb4,axiom,
% 5.45/5.68 ! [A: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ( ( sup_sup_int @ A @ B )
% 5.45/5.68 = B ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb4
% 5.45/5.68 thf(fact_2173_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ B @ A )
% 5.45/5.68 => ( ( sup_su718114333110466843at_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2174_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ B @ A )
% 5.45/5.68 => ( ( sup_su3035147773818789531at_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2175_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ B @ A )
% 5.45/5.68 => ( ( sup_su5525570899277871387at_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2176_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ B @ A )
% 5.45/5.68 => ( ( sup_sup_set_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2177_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ B @ A )
% 5.45/5.68 => ( ( sup_sup_assn @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2178_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ B @ A )
% 5.45/5.68 => ( ( sup_sup_rat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2179_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ B @ A )
% 5.45/5.68 => ( ( sup_sup_nat @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2180_sup_Oabsorb3,axiom,
% 5.45/5.68 ! [B: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ B @ A )
% 5.45/5.68 => ( ( sup_sup_int @ A @ B )
% 5.45/5.68 = A ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup.absorb3
% 5.45/5.68 thf(fact_2181_less__supI2,axiom,
% 5.45/5.68 ! [X: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ X @ B )
% 5.45/5.68 => ( ord_le6428140832669894131at_nat @ X @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2182_less__supI2,axiom,
% 5.45/5.68 ! [X: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ X @ B )
% 5.45/5.68 => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2183_less__supI2,axiom,
% 5.45/5.68 ! [X: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ X @ B )
% 5.45/5.68 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2184_less__supI2,axiom,
% 5.45/5.68 ! [X: set_nat,B: set_nat,A: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ X @ B )
% 5.45/5.68 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2185_less__supI2,axiom,
% 5.45/5.68 ! [X: assn,B: assn,A: assn] :
% 5.45/5.68 ( ( ord_less_assn @ X @ B )
% 5.45/5.68 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2186_less__supI2,axiom,
% 5.45/5.68 ! [X: rat,B: rat,A: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X @ B )
% 5.45/5.68 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2187_less__supI2,axiom,
% 5.45/5.68 ! [X: nat,B: nat,A: nat] :
% 5.45/5.68 ( ( ord_less_nat @ X @ B )
% 5.45/5.68 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2188_less__supI2,axiom,
% 5.45/5.68 ! [X: int,B: int,A: int] :
% 5.45/5.68 ( ( ord_less_int @ X @ B )
% 5.45/5.68 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI2
% 5.45/5.68 thf(fact_2189_less__supI1,axiom,
% 5.45/5.68 ! [X: set_Pr8693737435421807431at_nat,A: set_Pr8693737435421807431at_nat,B: set_Pr8693737435421807431at_nat] :
% 5.45/5.68 ( ( ord_le6428140832669894131at_nat @ X @ A )
% 5.45/5.68 => ( ord_le6428140832669894131at_nat @ X @ ( sup_su718114333110466843at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2190_less__supI1,axiom,
% 5.45/5.68 ! [X: set_Pr8551490117392284871at_nat,A: set_Pr8551490117392284871at_nat,B: set_Pr8551490117392284871at_nat] :
% 5.45/5.68 ( ( ord_le7642048601412989811at_nat @ X @ A )
% 5.45/5.68 => ( ord_le7642048601412989811at_nat @ X @ ( sup_su3035147773818789531at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2191_less__supI1,axiom,
% 5.45/5.68 ! [X: set_Pr4329608150637261639at_nat,A: set_Pr4329608150637261639at_nat,B: set_Pr4329608150637261639at_nat] :
% 5.45/5.68 ( ( ord_le2604355607129572851at_nat @ X @ A )
% 5.45/5.68 => ( ord_le2604355607129572851at_nat @ X @ ( sup_su5525570899277871387at_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2192_less__supI1,axiom,
% 5.45/5.68 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ X @ A )
% 5.45/5.68 => ( ord_less_set_nat @ X @ ( sup_sup_set_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2193_less__supI1,axiom,
% 5.45/5.68 ! [X: assn,A: assn,B: assn] :
% 5.45/5.68 ( ( ord_less_assn @ X @ A )
% 5.45/5.68 => ( ord_less_assn @ X @ ( sup_sup_assn @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2194_less__supI1,axiom,
% 5.45/5.68 ! [X: rat,A: rat,B: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X @ A )
% 5.45/5.68 => ( ord_less_rat @ X @ ( sup_sup_rat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2195_less__supI1,axiom,
% 5.45/5.68 ! [X: nat,A: nat,B: nat] :
% 5.45/5.68 ( ( ord_less_nat @ X @ A )
% 5.45/5.68 => ( ord_less_nat @ X @ ( sup_sup_nat @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2196_less__supI1,axiom,
% 5.45/5.68 ! [X: int,A: int,B: int] :
% 5.45/5.68 ( ( ord_less_int @ X @ A )
% 5.45/5.68 => ( ord_less_int @ X @ ( sup_sup_int @ A @ B ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_supI1
% 5.45/5.68 thf(fact_2197_new__addrs__def,axiom,
% 5.45/5.68 ( hoare_new_addrs
% 5.45/5.68 = ( ^ [H6: heap_e7401611519738050253t_unit,As5: set_nat,H7: heap_e7401611519738050253t_unit] :
% 5.45/5.68 ( sup_sup_set_nat @ As5
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ A5 )
% 5.45/5.68 & ( ord_less_nat @ A5 @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % new_addrs_def
% 5.45/5.68 thf(fact_2198_ord__eq__le__eq__trans,axiom,
% 5.45/5.68 ! [A: set_int,B: set_int,C: set_int,D2: set_int] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ B @ C )
% 5.45/5.68 => ( ( C = D2 )
% 5.45/5.68 => ( ord_less_eq_set_int @ A @ D2 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ord_eq_le_eq_trans
% 5.45/5.68 thf(fact_2199_ord__eq__le__eq__trans,axiom,
% 5.45/5.68 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.68 => ( ( C = D2 )
% 5.45/5.68 => ( ord_less_eq_rat @ A @ D2 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ord_eq_le_eq_trans
% 5.45/5.68 thf(fact_2200_ord__eq__le__eq__trans,axiom,
% 5.45/5.68 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 => ( ( ord_less_eq_num @ B @ C )
% 5.45/5.68 => ( ( C = D2 )
% 5.45/5.68 => ( ord_less_eq_num @ A @ D2 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ord_eq_le_eq_trans
% 5.45/5.68 thf(fact_2201_ord__eq__le__eq__trans,axiom,
% 5.45/5.68 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.68 => ( ( C = D2 )
% 5.45/5.68 => ( ord_less_eq_nat @ A @ D2 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ord_eq_le_eq_trans
% 5.45/5.68 thf(fact_2202_ord__eq__le__eq__trans,axiom,
% 5.45/5.68 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.68 => ( ( C = D2 )
% 5.45/5.68 => ( ord_less_eq_int @ A @ D2 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ord_eq_le_eq_trans
% 5.45/5.68 thf(fact_2203_bex2I,axiom,
% 5.45/5.68 ! [A: nat,B: nat,S: set_Pr1261947904930325089at_nat,P: nat > nat > $o] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: nat,B4: nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2204_bex2I,axiom,
% 5.45/5.68 ! [A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat,S: set_Pr3286484037609594932et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 5.45/5.68 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 5.45/5.68 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2205_bex2I,axiom,
% 5.45/5.68 ! [A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat,S: set_Pr8536935166611901872et_nat,P: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 5.45/5.68 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 5.45/5.68 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2206_bex2I,axiom,
% 5.45/5.68 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr9222295170931077689nt_int,P: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.45/5.68 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.45/5.68 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2207_bex2I,axiom,
% 5.45/5.68 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,S: set_Pr1872883991513573699nt_int,P: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.45/5.68 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.45/5.68 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2208_bex2I,axiom,
% 5.45/5.68 ! [A: a,B: produc6653097349344004940it_nat,S: set_Pr7098220151150636591it_nat,P: a > produc6653097349344004940it_nat > $o] :
% 5.45/5.68 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 5.45/5.68 => ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ S )
% 5.45/5.68 => ( P @ A @ B ) )
% 5.45/5.68 => ? [A4: a,B4: produc6653097349344004940it_nat] :
% 5.45/5.68 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A4 @ B4 ) @ S )
% 5.45/5.68 & ( P @ A4 @ B4 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % bex2I
% 5.45/5.68 thf(fact_2209_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr1261947904930325089at_nat,S2: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ! [X3: nat,Y3: nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le3146513528884898305at_nat @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2210_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr3286484037609594932et_nat,S2: set_Pr3286484037609594932et_nat] :
% 5.45/5.68 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 5.45/5.68 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le5966269811547037844et_nat @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2211_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr8536935166611901872et_nat,S2: set_Pr8536935166611901872et_nat] :
% 5.45/5.68 ( ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 5.45/5.68 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le4763372923235995152et_nat @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2212_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr9222295170931077689nt_int,S2: set_Pr9222295170931077689nt_int] :
% 5.45/5.68 ( ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.45/5.68 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le8725513860283290265nt_int @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2213_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr1872883991513573699nt_int,S2: set_Pr1872883991513573699nt_int] :
% 5.45/5.68 ( ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.45/5.68 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le135402666524580259nt_int @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2214_subrelI,axiom,
% 5.45/5.68 ! [R3: set_Pr7098220151150636591it_nat,S2: set_Pr7098220151150636591it_nat] :
% 5.45/5.68 ( ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.45/5.68 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X3 @ Y3 ) @ R3 )
% 5.45/5.68 => ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X3 @ Y3 ) @ S2 ) )
% 5.45/5.68 => ( ord_le4478181985103859343it_nat @ R3 @ S2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % subrelI
% 5.45/5.68 thf(fact_2215_memb__imp__not__empty,axiom,
% 5.45/5.68 ! [X: set_nat,S: set_set_nat] :
% 5.45/5.68 ( ( member_set_nat @ X @ S )
% 5.45/5.68 => ( S != bot_bot_set_set_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % memb_imp_not_empty
% 5.45/5.68 thf(fact_2216_memb__imp__not__empty,axiom,
% 5.45/5.68 ! [X: product_prod_nat_nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ X @ S )
% 5.45/5.68 => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % memb_imp_not_empty
% 5.45/5.68 thf(fact_2217_memb__imp__not__empty,axiom,
% 5.45/5.68 ! [X: $o,S: set_o] :
% 5.45/5.68 ( ( member_o @ X @ S )
% 5.45/5.68 => ( S != bot_bot_set_o ) ) ).
% 5.45/5.68
% 5.45/5.68 % memb_imp_not_empty
% 5.45/5.68 thf(fact_2218_memb__imp__not__empty,axiom,
% 5.45/5.68 ! [X: nat,S: set_nat] :
% 5.45/5.68 ( ( member_nat @ X @ S )
% 5.45/5.68 => ( S != bot_bot_set_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % memb_imp_not_empty
% 5.45/5.68 thf(fact_2219_memb__imp__not__empty,axiom,
% 5.45/5.68 ! [X: int,S: set_int] :
% 5.45/5.68 ( ( member_int @ X @ S )
% 5.45/5.68 => ( S != bot_bot_set_int ) ) ).
% 5.45/5.68
% 5.45/5.68 % memb_imp_not_empty
% 5.45/5.68 thf(fact_2220_set__notEmptyE,axiom,
% 5.45/5.68 ! [S: set_set_nat] :
% 5.45/5.68 ( ( S != bot_bot_set_set_nat )
% 5.45/5.68 => ~ ! [X3: set_nat] :
% 5.45/5.68 ~ ( member_set_nat @ X3 @ S ) ) ).
% 5.45/5.68
% 5.45/5.68 % set_notEmptyE
% 5.45/5.68 thf(fact_2221_set__notEmptyE,axiom,
% 5.45/5.68 ! [S: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( S != bot_bo2099793752762293965at_nat )
% 5.45/5.68 => ~ ! [X3: product_prod_nat_nat] :
% 5.45/5.68 ~ ( member8440522571783428010at_nat @ X3 @ S ) ) ).
% 5.45/5.68
% 5.45/5.68 % set_notEmptyE
% 5.45/5.68 thf(fact_2222_set__notEmptyE,axiom,
% 5.45/5.68 ! [S: set_o] :
% 5.45/5.68 ( ( S != bot_bot_set_o )
% 5.45/5.68 => ~ ! [X3: $o] :
% 5.45/5.68 ~ ( member_o @ X3 @ S ) ) ).
% 5.45/5.68
% 5.45/5.68 % set_notEmptyE
% 5.45/5.68 thf(fact_2223_set__notEmptyE,axiom,
% 5.45/5.68 ! [S: set_nat] :
% 5.45/5.68 ( ( S != bot_bot_set_nat )
% 5.45/5.68 => ~ ! [X3: nat] :
% 5.45/5.68 ~ ( member_nat @ X3 @ S ) ) ).
% 5.45/5.68
% 5.45/5.68 % set_notEmptyE
% 5.45/5.68 thf(fact_2224_set__notEmptyE,axiom,
% 5.45/5.68 ! [S: set_int] :
% 5.45/5.68 ( ( S != bot_bot_set_int )
% 5.45/5.68 => ~ ! [X3: int] :
% 5.45/5.68 ~ ( member_int @ X3 @ S ) ) ).
% 5.45/5.68
% 5.45/5.68 % set_notEmptyE
% 5.45/5.68 thf(fact_2225_inter__eq__subsetI,axiom,
% 5.45/5.68 ! [S: set_nat,S3: set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.68 ( ( ord_less_eq_set_nat @ S @ S3 )
% 5.45/5.68 => ( ( ( inf_inf_set_nat @ A3 @ S3 )
% 5.45/5.68 = ( inf_inf_set_nat @ B3 @ S3 ) )
% 5.45/5.68 => ( ( inf_inf_set_nat @ A3 @ S )
% 5.45/5.68 = ( inf_inf_set_nat @ B3 @ S ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inter_eq_subsetI
% 5.45/5.68 thf(fact_2226_inter__eq__subsetI,axiom,
% 5.45/5.68 ! [S: set_Pr1261947904930325089at_nat,S3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( ord_le3146513528884898305at_nat @ S @ S3 )
% 5.45/5.68 => ( ( ( inf_in2572325071724192079at_nat @ A3 @ S3 )
% 5.45/5.68 = ( inf_in2572325071724192079at_nat @ B3 @ S3 ) )
% 5.45/5.68 => ( ( inf_in2572325071724192079at_nat @ A3 @ S )
% 5.45/5.68 = ( inf_in2572325071724192079at_nat @ B3 @ S ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inter_eq_subsetI
% 5.45/5.68 thf(fact_2227_inter__eq__subsetI,axiom,
% 5.45/5.68 ! [S: set_int,S3: set_int,A3: set_int,B3: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ S @ S3 )
% 5.45/5.68 => ( ( ( inf_inf_set_int @ A3 @ S3 )
% 5.45/5.68 = ( inf_inf_set_int @ B3 @ S3 ) )
% 5.45/5.68 => ( ( inf_inf_set_int @ A3 @ S )
% 5.45/5.68 = ( inf_inf_set_int @ B3 @ S ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % inter_eq_subsetI
% 5.45/5.68 thf(fact_2228_hoare__triple__def,axiom,
% 5.45/5.68 ( hoare_8945653483474564448t_unit
% 5.45/5.68 = ( ^ [P4: assn,C4: heap_T5738788834812785303t_unit,Q3: product_unit > assn] :
% 5.45/5.68 ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 5.45/5.68 ( ( rep_assn @ P4 @ ( produc7507926704131184380et_nat @ H6 @ As5 ) )
% 5.45/5.68 => ? [R4: product_unit,H7: heap_e7401611519738050253t_unit] :
% 5.45/5.68 ( ? [T3: nat] :
% 5.45/5.68 ( ( heap_T875086893843062177t_unit @ C4 @ H6 )
% 5.45/5.68 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H7 @ T3 ) ) ) )
% 5.45/5.68 & ( rep_assn @ ( Q3 @ R4 ) @ ( produc7507926704131184380et_nat @ H7 @ ( hoare_new_addrs @ H6 @ As5 @ H7 ) ) )
% 5.45/5.68 & ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H6 ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As5 ) ) )
% 5.45/5.68 @ H6
% 5.45/5.68 @ H7 )
% 5.45/5.68 & ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_triple_def
% 5.45/5.68 thf(fact_2229_hoare__triple__def,axiom,
% 5.45/5.68 ( hoare_hoare_triple_a
% 5.45/5.68 = ( ^ [P4: assn,C4: heap_Time_Heap_a,Q3: a > assn] :
% 5.45/5.68 ! [H6: heap_e7401611519738050253t_unit,As5: set_nat] :
% 5.45/5.68 ( ( rep_assn @ P4 @ ( produc7507926704131184380et_nat @ H6 @ As5 ) )
% 5.45/5.68 => ? [R4: a,H7: heap_e7401611519738050253t_unit] :
% 5.45/5.68 ( ? [T3: nat] :
% 5.45/5.68 ( ( heap_Time_execute_a @ C4 @ H6 )
% 5.45/5.68 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H7 @ T3 ) ) ) )
% 5.45/5.68 & ( rep_assn @ ( Q3 @ R4 ) @ ( produc7507926704131184380et_nat @ H7 @ ( hoare_new_addrs @ H6 @ As5 @ H7 ) ) )
% 5.45/5.68 & ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H6 ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As5 ) ) )
% 5.45/5.68 @ H6
% 5.45/5.68 @ H7 )
% 5.45/5.68 & ( ord_less_eq_nat @ ( lim_Product_unit @ H6 ) @ ( lim_Product_unit @ H7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_triple_def
% 5.45/5.68 thf(fact_2230_hoare__tripleI,axiom,
% 5.45/5.68 ! [P: assn,C: heap_T5738788834812785303t_unit,Q: product_unit > assn] :
% 5.45/5.68 ( ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.68 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.68 => ? [R5: product_unit,H8: heap_e7401611519738050253t_unit,T4: nat] :
% 5.45/5.68 ( ( ( heap_T875086893843062177t_unit @ C @ H4 )
% 5.45/5.68 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R5 @ ( produc584006145561248582it_nat @ H8 @ T4 ) ) ) )
% 5.45/5.68 & ( rep_assn @ ( Q @ R5 ) @ ( produc7507926704131184380et_nat @ H8 @ ( hoare_new_addrs @ H4 @ As4 @ H8 ) ) )
% 5.45/5.68 & ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H4 ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As4 ) ) )
% 5.45/5.68 @ H4
% 5.45/5.68 @ H8 )
% 5.45/5.68 & ( ord_less_eq_nat @ ( lim_Product_unit @ H4 ) @ ( lim_Product_unit @ H8 ) ) ) )
% 5.45/5.68 => ( hoare_8945653483474564448t_unit @ P @ C @ Q ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_tripleI
% 5.45/5.68 thf(fact_2231_hoare__tripleI,axiom,
% 5.45/5.68 ! [P: assn,C: heap_Time_Heap_a,Q: a > assn] :
% 5.45/5.68 ( ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.68 ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.68 => ? [R5: a,H8: heap_e7401611519738050253t_unit,T4: nat] :
% 5.45/5.68 ( ( ( heap_Time_execute_a @ C @ H4 )
% 5.45/5.68 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R5 @ ( produc584006145561248582it_nat @ H8 @ T4 ) ) ) )
% 5.45/5.68 & ( rep_assn @ ( Q @ R5 ) @ ( produc7507926704131184380et_nat @ H8 @ ( hoare_new_addrs @ H4 @ As4 @ H8 ) ) )
% 5.45/5.68 & ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H4 ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As4 ) ) )
% 5.45/5.68 @ H4
% 5.45/5.68 @ H8 )
% 5.45/5.68 & ( ord_less_eq_nat @ ( lim_Product_unit @ H4 ) @ ( lim_Product_unit @ H8 ) ) ) )
% 5.45/5.68 => ( hoare_hoare_triple_a @ P @ C @ Q ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_tripleI
% 5.45/5.68 thf(fact_2232_hoare__tripleE,axiom,
% 5.45/5.68 ! [P: assn,C: heap_T5738788834812785303t_unit,Q: product_unit > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.68 ( ( hoare_8945653483474564448t_unit @ P @ C @ Q )
% 5.45/5.68 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.68 => ~ ! [R2: product_unit,H5: heap_e7401611519738050253t_unit] :
% 5.45/5.68 ( ? [T2: nat] :
% 5.45/5.68 ( ( heap_T875086893843062177t_unit @ C @ H )
% 5.45/5.68 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ T2 ) ) ) )
% 5.45/5.68 => ( ( rep_assn @ ( Q @ R2 ) @ ( produc7507926704131184380et_nat @ H5 @ ( hoare_new_addrs @ H @ As @ H5 ) ) )
% 5.45/5.68 => ( ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As ) ) )
% 5.45/5.68 @ H
% 5.45/5.68 @ H5 )
% 5.45/5.68 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ H ) @ ( lim_Product_unit @ H5 ) ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_tripleE
% 5.45/5.68 thf(fact_2233_hoare__tripleE,axiom,
% 5.45/5.68 ! [P: assn,C: heap_Time_Heap_a,Q: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.68 ( ( hoare_hoare_triple_a @ P @ C @ Q )
% 5.45/5.68 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.68 => ~ ! [R2: a,H5: heap_e7401611519738050253t_unit] :
% 5.45/5.68 ( ? [T2: nat] :
% 5.45/5.68 ( ( heap_Time_execute_a @ C @ H )
% 5.45/5.68 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H5 @ T2 ) ) ) )
% 5.45/5.68 => ( ( rep_assn @ ( Q @ R2 ) @ ( produc7507926704131184380et_nat @ H5 @ ( hoare_new_addrs @ H @ As @ H5 ) ) )
% 5.45/5.68 => ( ( relH
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [A5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ A5 @ ( lim_Product_unit @ H ) )
% 5.45/5.68 & ~ ( member_nat @ A5 @ As ) ) )
% 5.45/5.68 @ H
% 5.45/5.68 @ H5 )
% 5.45/5.68 => ~ ( ord_less_eq_nat @ ( lim_Product_unit @ H ) @ ( lim_Product_unit @ H5 ) ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % hoare_tripleE
% 5.45/5.68 thf(fact_2234_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila1307241728879085301at_nat @ sup_su718114333110466843at_nat @ bot_bo5327735625951526323at_nat
% 5.45/5.68 @ ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le6428140832669894131at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2235_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila5207306265035627125at_nat @ sup_su3035147773818789531at_nat @ bot_bo8422036546324065075at_nat
% 5.45/5.68 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2236_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila6534579987270727413at_nat @ sup_su5525570899277871387at_nat @ bot_bo228742789529271731at_nat
% 5.45/5.68 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2237_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila4918476307565957903at_nat @ sup_su6327502436637775413at_nat @ bot_bo2099793752762293965at_nat
% 5.45/5.68 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2238_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila2554085542299052326_set_o @ sup_sup_set_o @ bot_bot_set_o
% 5.45/5.68 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2239_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila1667268886620078168et_nat @ sup_sup_set_nat @ bot_bot_set_nat
% 5.45/5.68 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2240_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila8603258263270017530r_assn @ sup_sup_assn @ bot_bot_assn
% 5.45/5.68 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2241_sup__bot_Osemilattice__neutr__order__axioms,axiom,
% 5.45/5.68 ( semila6712789903965657268et_int @ sup_sup_set_int @ bot_bot_set_int
% 5.45/5.68 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 5.45/5.68 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 ) ) ).
% 5.45/5.68
% 5.45/5.68 % sup_bot.semilattice_neutr_order_axioms
% 5.45/5.68 thf(fact_2242_nat__descend__induct,axiom,
% 5.45/5.68 ! [N2: nat,P: nat > $o,M: nat] :
% 5.45/5.68 ( ! [K2: nat] :
% 5.45/5.68 ( ( ord_less_nat @ N2 @ K2 )
% 5.45/5.68 => ( P @ K2 ) )
% 5.45/5.68 => ( ! [K2: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.45/5.68 => ( ! [I: nat] :
% 5.45/5.68 ( ( ord_less_nat @ K2 @ I )
% 5.45/5.68 => ( P @ I ) )
% 5.45/5.68 => ( P @ K2 ) ) )
% 5.45/5.68 => ( P @ M ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nat_descend_induct
% 5.45/5.68 thf(fact_2243_less__mono__imp__le__mono,axiom,
% 5.45/5.68 ! [F: nat > nat,I2: nat,J: nat] :
% 5.45/5.68 ( ! [I3: nat,J2: nat] :
% 5.45/5.68 ( ( ord_less_nat @ I3 @ J2 )
% 5.45/5.68 => ( ord_less_nat @ ( F @ I3 ) @ ( F @ J2 ) ) )
% 5.45/5.68 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.68 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_mono_imp_le_mono
% 5.45/5.68 thf(fact_2244_le__neq__implies__less,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.68 => ( ( M != N2 )
% 5.45/5.68 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % le_neq_implies_less
% 5.45/5.68 thf(fact_2245_less__or__eq__imp__le,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( ( ord_less_nat @ M @ N2 )
% 5.45/5.68 | ( M = N2 ) )
% 5.45/5.68 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_or_eq_imp_le
% 5.45/5.68 thf(fact_2246_le__eq__less__or__eq,axiom,
% 5.45/5.68 ( ord_less_eq_nat
% 5.45/5.68 = ( ^ [M3: nat,N: nat] :
% 5.45/5.68 ( ( ord_less_nat @ M3 @ N )
% 5.45/5.68 | ( M3 = N ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % le_eq_less_or_eq
% 5.45/5.68 thf(fact_2247_less__imp__le__nat,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.68 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_imp_le_nat
% 5.45/5.68 thf(fact_2248_nat__less__le,axiom,
% 5.45/5.68 ( ord_less_nat
% 5.45/5.68 = ( ^ [M3: nat,N: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ M3 @ N )
% 5.45/5.68 & ( M3 != N ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nat_less_le
% 5.45/5.68 thf(fact_2249_subset__emptyI,axiom,
% 5.45/5.68 ! [A3: set_set_nat] :
% 5.45/5.68 ( ! [X3: set_nat] :
% 5.45/5.68 ~ ( member_set_nat @ X3 @ A3 )
% 5.45/5.68 => ( ord_le6893508408891458716et_nat @ A3 @ bot_bot_set_set_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_emptyI
% 5.45/5.68 thf(fact_2250_subset__emptyI,axiom,
% 5.45/5.68 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ! [X3: product_prod_nat_nat] :
% 5.45/5.68 ~ ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.68 => ( ord_le3146513528884898305at_nat @ A3 @ bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_emptyI
% 5.45/5.68 thf(fact_2251_subset__emptyI,axiom,
% 5.45/5.68 ! [A3: set_o] :
% 5.45/5.68 ( ! [X3: $o] :
% 5.45/5.68 ~ ( member_o @ X3 @ A3 )
% 5.45/5.68 => ( ord_less_eq_set_o @ A3 @ bot_bot_set_o ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_emptyI
% 5.45/5.68 thf(fact_2252_subset__emptyI,axiom,
% 5.45/5.68 ! [A3: set_nat] :
% 5.45/5.68 ( ! [X3: nat] :
% 5.45/5.68 ~ ( member_nat @ X3 @ A3 )
% 5.45/5.68 => ( ord_less_eq_set_nat @ A3 @ bot_bot_set_nat ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_emptyI
% 5.45/5.68 thf(fact_2253_subset__emptyI,axiom,
% 5.45/5.68 ! [A3: set_int] :
% 5.45/5.68 ( ! [X3: int] :
% 5.45/5.68 ~ ( member_int @ X3 @ A3 )
% 5.45/5.68 => ( ord_less_eq_set_int @ A3 @ bot_bot_set_int ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_emptyI
% 5.45/5.68 thf(fact_2254_psubsetI,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ( A3 != B3 )
% 5.45/5.68 => ( ord_less_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetI
% 5.45/5.68 thf(fact_2255_less__by__empty,axiom,
% 5.45/5.68 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.45/5.68 => ( ord_le3146513528884898305at_nat @ A3 @ B3 ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_by_empty
% 5.45/5.68 thf(fact_2256_semilattice__neutr__order_Oneutr__eq__iff,axiom,
% 5.45/5.68 ! [F: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 5.45/5.68 ( ( semila1623282765462674594er_nat @ F @ Z @ Less_eq @ Less )
% 5.45/5.68 => ( ( Z
% 5.45/5.68 = ( F @ A @ B ) )
% 5.45/5.68 = ( ( A = Z )
% 5.45/5.68 & ( B = Z ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % semilattice_neutr_order.neutr_eq_iff
% 5.45/5.68 thf(fact_2257_semilattice__neutr__order_Oeq__neutr__iff,axiom,
% 5.45/5.68 ! [F: nat > nat > nat,Z: nat,Less_eq: nat > nat > $o,Less: nat > nat > $o,A: nat,B: nat] :
% 5.45/5.68 ( ( semila1623282765462674594er_nat @ F @ Z @ Less_eq @ Less )
% 5.45/5.68 => ( ( ( F @ A @ B )
% 5.45/5.68 = Z )
% 5.45/5.68 = ( ( A = Z )
% 5.45/5.68 & ( B = Z ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % semilattice_neutr_order.eq_neutr_iff
% 5.45/5.68 thf(fact_2258_not__psubset__empty,axiom,
% 5.45/5.68 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ~ ( ord_le7866589430770878221at_nat @ A3 @ bot_bo2099793752762293965at_nat ) ).
% 5.45/5.68
% 5.45/5.68 % not_psubset_empty
% 5.45/5.68 thf(fact_2259_not__psubset__empty,axiom,
% 5.45/5.68 ! [A3: set_o] :
% 5.45/5.68 ~ ( ord_less_set_o @ A3 @ bot_bot_set_o ) ).
% 5.45/5.68
% 5.45/5.68 % not_psubset_empty
% 5.45/5.68 thf(fact_2260_not__psubset__empty,axiom,
% 5.45/5.68 ! [A3: set_nat] :
% 5.45/5.68 ~ ( ord_less_set_nat @ A3 @ bot_bot_set_nat ) ).
% 5.45/5.68
% 5.45/5.68 % not_psubset_empty
% 5.45/5.68 thf(fact_2261_not__psubset__empty,axiom,
% 5.45/5.68 ! [A3: set_int] :
% 5.45/5.68 ~ ( ord_less_set_int @ A3 @ bot_bot_set_int ) ).
% 5.45/5.68
% 5.45/5.68 % not_psubset_empty
% 5.45/5.68 thf(fact_2262_subset__iff__psubset__eq,axiom,
% 5.45/5.68 ( ord_less_eq_set_int
% 5.45/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A6 @ B6 )
% 5.45/5.68 | ( A6 = B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_iff_psubset_eq
% 5.45/5.68 thf(fact_2263_subset__psubset__trans,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ( ord_less_set_int @ B3 @ C3 )
% 5.45/5.68 => ( ord_less_set_int @ A3 @ C3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_psubset_trans
% 5.45/5.68 thf(fact_2264_subset__not__subset__eq,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.45/5.68 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % subset_not_subset_eq
% 5.45/5.68 thf(fact_2265_psubset__subset__trans,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ B3 @ C3 )
% 5.45/5.68 => ( ord_less_set_int @ A3 @ C3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubset_subset_trans
% 5.45/5.68 thf(fact_2266_psubset__imp__subset,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ord_less_eq_set_int @ A3 @ B3 ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubset_imp_subset
% 5.45/5.68 thf(fact_2267_psubset__eq,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.68 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.45/5.68 & ( A6 != B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubset_eq
% 5.45/5.68 thf(fact_2268_psubsetE,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int] :
% 5.45/5.68 ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.68 => ~ ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ord_less_eq_set_int @ B3 @ A3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetE
% 5.45/5.68 thf(fact_2269_less__assn__def,axiom,
% 5.45/5.68 ( ord_less_assn
% 5.45/5.68 = ( ^ [A5: assn,B5: assn] :
% 5.45/5.68 ( ( ord_less_eq_assn @ A5 @ B5 )
% 5.45/5.68 & ( A5 != B5 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_assn_def
% 5.45/5.68 thf(fact_2270_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: nat,S2: nat,R: set_Pr1261947904930325089at_nat,S4: nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2271_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: produc3658429121746597890et_nat > $o,S2: produc3658429121746597890et_nat,R: set_Pr3286484037609594932et_nat,S4: produc3658429121746597890et_nat] :
% 5.45/5.68 ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2272_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: produc3658429121746597890et_nat > $o,S2: produc3925858234332021118et_nat,R: set_Pr8536935166611901872et_nat,S4: produc3925858234332021118et_nat] :
% 5.45/5.68 ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2273_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: produc8551481072490612790e_term > option6357759511663192854e_term,S2: product_prod_int_int,R: set_Pr9222295170931077689nt_int,S4: product_prod_int_int] :
% 5.45/5.68 ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2274_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: int > option6357759511663192854e_term,S2: product_prod_int_int,R: set_Pr1872883991513573699nt_int,S4: product_prod_int_int] :
% 5.45/5.68 ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2275_ssubst__Pair__rhs,axiom,
% 5.45/5.68 ! [R3: a,S2: produc6653097349344004940it_nat,R: set_Pr7098220151150636591it_nat,S4: produc6653097349344004940it_nat] :
% 5.45/5.68 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R3 @ S2 ) @ R )
% 5.45/5.68 => ( ( S4 = S2 )
% 5.45/5.68 => ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ R3 @ S4 ) @ R ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % ssubst_Pair_rhs
% 5.45/5.68 thf(fact_2276_nat__neq__iff,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( M != N2 )
% 5.45/5.68 = ( ( ord_less_nat @ M @ N2 )
% 5.45/5.68 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % nat_neq_iff
% 5.45/5.68 thf(fact_2277_less__not__refl,axiom,
% 5.45/5.68 ! [N2: nat] :
% 5.45/5.68 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.45/5.68
% 5.45/5.68 % less_not_refl
% 5.45/5.68 thf(fact_2278_less__not__refl2,axiom,
% 5.45/5.68 ! [N2: nat,M: nat] :
% 5.45/5.68 ( ( ord_less_nat @ N2 @ M )
% 5.45/5.68 => ( M != N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_not_refl2
% 5.45/5.68 thf(fact_2279_less__not__refl3,axiom,
% 5.45/5.68 ! [S2: nat,T5: nat] :
% 5.45/5.68 ( ( ord_less_nat @ S2 @ T5 )
% 5.45/5.68 => ( S2 != T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_not_refl3
% 5.45/5.68 thf(fact_2280_less__irrefl__nat,axiom,
% 5.45/5.68 ! [N2: nat] :
% 5.45/5.68 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.45/5.68
% 5.45/5.68 % less_irrefl_nat
% 5.45/5.68 thf(fact_2281_nat__less__induct,axiom,
% 5.45/5.68 ! [P: nat > $o,N2: nat] :
% 5.45/5.68 ( ! [N5: nat] :
% 5.45/5.68 ( ! [M4: nat] :
% 5.45/5.68 ( ( ord_less_nat @ M4 @ N5 )
% 5.45/5.68 => ( P @ M4 ) )
% 5.45/5.68 => ( P @ N5 ) )
% 5.45/5.68 => ( P @ N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % nat_less_induct
% 5.45/5.68 thf(fact_2282_infinite__descent,axiom,
% 5.45/5.68 ! [P: nat > $o,N2: nat] :
% 5.45/5.68 ( ! [N5: nat] :
% 5.45/5.68 ( ~ ( P @ N5 )
% 5.45/5.68 => ? [M4: nat] :
% 5.45/5.68 ( ( ord_less_nat @ M4 @ N5 )
% 5.45/5.68 & ~ ( P @ M4 ) ) )
% 5.45/5.68 => ( P @ N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % infinite_descent
% 5.45/5.68 thf(fact_2283_linorder__neqE__nat,axiom,
% 5.45/5.68 ! [X: nat,Y: nat] :
% 5.45/5.68 ( ( X != Y )
% 5.45/5.68 => ( ~ ( ord_less_nat @ X @ Y )
% 5.45/5.68 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % linorder_neqE_nat
% 5.45/5.68 thf(fact_2284_le__refl,axiom,
% 5.45/5.68 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 5.45/5.68
% 5.45/5.68 % le_refl
% 5.45/5.68 thf(fact_2285_le__trans,axiom,
% 5.45/5.68 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.68 => ( ( ord_less_eq_nat @ J @ K )
% 5.45/5.68 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % le_trans
% 5.45/5.68 thf(fact_2286_eq__imp__le,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( M = N2 )
% 5.45/5.68 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % eq_imp_le
% 5.45/5.68 thf(fact_2287_le__antisym,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.68 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.68 => ( M = N2 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % le_antisym
% 5.45/5.68 thf(fact_2288_nat__le__linear,axiom,
% 5.45/5.68 ! [M: nat,N2: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.68 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.45/5.68
% 5.45/5.68 % nat_le_linear
% 5.45/5.68 thf(fact_2289_Nat_Oex__has__greatest__nat,axiom,
% 5.45/5.68 ! [P: nat > $o,K: nat,B: nat] :
% 5.45/5.68 ( ( P @ K )
% 5.45/5.68 => ( ! [Y3: nat] :
% 5.45/5.68 ( ( P @ Y3 )
% 5.45/5.68 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.45/5.68 => ? [X3: nat] :
% 5.45/5.68 ( ( P @ X3 )
% 5.45/5.68 & ! [Y6: nat] :
% 5.45/5.68 ( ( P @ Y6 )
% 5.45/5.68 => ( ord_less_eq_nat @ Y6 @ X3 ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % Nat.ex_has_greatest_nat
% 5.45/5.68 thf(fact_2290_prop__restrict,axiom,
% 5.45/5.68 ! [X: product_prod_nat_nat,Z4: set_Pr1261947904930325089at_nat,X6: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ X @ Z4 )
% 5.45/5.68 => ( ( ord_le3146513528884898305at_nat @ Z4
% 5.45/5.68 @ ( collec3392354462482085612at_nat
% 5.45/5.68 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2291_prop__restrict,axiom,
% 5.45/5.68 ! [X: $o,Z4: set_o,X6: set_o,P: $o > $o] :
% 5.45/5.68 ( ( member_o @ X @ Z4 )
% 5.45/5.68 => ( ( ord_less_eq_set_o @ Z4
% 5.45/5.68 @ ( collect_o
% 5.45/5.68 @ ^ [X4: $o] :
% 5.45/5.68 ( ( member_o @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2292_prop__restrict,axiom,
% 5.45/5.68 ! [X: product_prod_int_int,Z4: set_Pr958786334691620121nt_int,X6: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.68 ( ( member5262025264175285858nt_int @ X @ Z4 )
% 5.45/5.68 => ( ( ord_le2843351958646193337nt_int @ Z4
% 5.45/5.68 @ ( collec213857154873943460nt_int
% 5.45/5.68 @ ^ [X4: product_prod_int_int] :
% 5.45/5.68 ( ( member5262025264175285858nt_int @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2293_prop__restrict,axiom,
% 5.45/5.68 ! [X: list_nat,Z4: set_list_nat,X6: set_list_nat,P: list_nat > $o] :
% 5.45/5.68 ( ( member_list_nat @ X @ Z4 )
% 5.45/5.68 => ( ( ord_le6045566169113846134st_nat @ Z4
% 5.45/5.68 @ ( collect_list_nat
% 5.45/5.68 @ ^ [X4: list_nat] :
% 5.45/5.68 ( ( member_list_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2294_prop__restrict,axiom,
% 5.45/5.68 ! [X: set_nat,Z4: set_set_nat,X6: set_set_nat,P: set_nat > $o] :
% 5.45/5.68 ( ( member_set_nat @ X @ Z4 )
% 5.45/5.68 => ( ( ord_le6893508408891458716et_nat @ Z4
% 5.45/5.68 @ ( collect_set_nat
% 5.45/5.68 @ ^ [X4: set_nat] :
% 5.45/5.68 ( ( member_set_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2295_prop__restrict,axiom,
% 5.45/5.68 ! [X: nat,Z4: set_nat,X6: set_nat,P: nat > $o] :
% 5.45/5.68 ( ( member_nat @ X @ Z4 )
% 5.45/5.68 => ( ( ord_less_eq_set_nat @ Z4
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [X4: nat] :
% 5.45/5.68 ( ( member_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2296_prop__restrict,axiom,
% 5.45/5.68 ! [X: int,Z4: set_int,X6: set_int,P: int > $o] :
% 5.45/5.68 ( ( member_int @ X @ Z4 )
% 5.45/5.68 => ( ( ord_less_eq_set_int @ Z4
% 5.45/5.68 @ ( collect_int
% 5.45/5.68 @ ^ [X4: int] :
% 5.45/5.68 ( ( member_int @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) ) )
% 5.45/5.68 => ( P @ X ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % prop_restrict
% 5.45/5.68 thf(fact_2297_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.68 ( ord_le3146513528884898305at_nat
% 5.45/5.68 @ ( collec3392354462482085612at_nat
% 5.45/5.68 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.68 ( ( member8440522571783428010at_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2298_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_o,P: $o > $o] :
% 5.45/5.68 ( ord_less_eq_set_o
% 5.45/5.68 @ ( collect_o
% 5.45/5.68 @ ^ [X4: $o] :
% 5.45/5.68 ( ( member_o @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2299_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.68 ( ord_le2843351958646193337nt_int
% 5.45/5.68 @ ( collec213857154873943460nt_int
% 5.45/5.68 @ ^ [X4: product_prod_int_int] :
% 5.45/5.68 ( ( member5262025264175285858nt_int @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2300_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_list_nat,P: list_nat > $o] :
% 5.45/5.68 ( ord_le6045566169113846134st_nat
% 5.45/5.68 @ ( collect_list_nat
% 5.45/5.68 @ ^ [X4: list_nat] :
% 5.45/5.68 ( ( member_list_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2301_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_set_nat,P: set_nat > $o] :
% 5.45/5.68 ( ord_le6893508408891458716et_nat
% 5.45/5.68 @ ( collect_set_nat
% 5.45/5.68 @ ^ [X4: set_nat] :
% 5.45/5.68 ( ( member_set_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2302_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_nat,P: nat > $o] :
% 5.45/5.68 ( ord_less_eq_set_nat
% 5.45/5.68 @ ( collect_nat
% 5.45/5.68 @ ^ [X4: nat] :
% 5.45/5.68 ( ( member_nat @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2303_Collect__restrict,axiom,
% 5.45/5.68 ! [X6: set_int,P: int > $o] :
% 5.45/5.68 ( ord_less_eq_set_int
% 5.45/5.68 @ ( collect_int
% 5.45/5.68 @ ^ [X4: int] :
% 5.45/5.68 ( ( member_int @ X4 @ X6 )
% 5.45/5.68 & ( P @ X4 ) ) )
% 5.45/5.68 @ X6 ) ).
% 5.45/5.68
% 5.45/5.68 % Collect_restrict
% 5.45/5.68 thf(fact_2304_minf_I8_J,axiom,
% 5.45/5.68 ! [T5: rat] :
% 5.45/5.68 ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.68 => ~ ( ord_less_eq_rat @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(8)
% 5.45/5.68 thf(fact_2305_minf_I8_J,axiom,
% 5.45/5.68 ! [T5: num] :
% 5.45/5.68 ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.68 => ~ ( ord_less_eq_num @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(8)
% 5.45/5.68 thf(fact_2306_minf_I8_J,axiom,
% 5.45/5.68 ! [T5: nat] :
% 5.45/5.68 ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.68 => ~ ( ord_less_eq_nat @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(8)
% 5.45/5.68 thf(fact_2307_minf_I8_J,axiom,
% 5.45/5.68 ! [T5: int] :
% 5.45/5.68 ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.68 => ~ ( ord_less_eq_int @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(8)
% 5.45/5.68 thf(fact_2308_minf_I6_J,axiom,
% 5.45/5.68 ! [T5: rat] :
% 5.45/5.68 ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.68 => ( ord_less_eq_rat @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(6)
% 5.45/5.68 thf(fact_2309_minf_I6_J,axiom,
% 5.45/5.68 ! [T5: num] :
% 5.45/5.68 ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.68 => ( ord_less_eq_num @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(6)
% 5.45/5.68 thf(fact_2310_minf_I6_J,axiom,
% 5.45/5.68 ! [T5: nat] :
% 5.45/5.68 ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.68 => ( ord_less_eq_nat @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(6)
% 5.45/5.68 thf(fact_2311_minf_I6_J,axiom,
% 5.45/5.68 ! [T5: int] :
% 5.45/5.68 ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.68 => ( ord_less_eq_int @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % minf(6)
% 5.45/5.68 thf(fact_2312_pinf_I8_J,axiom,
% 5.45/5.68 ! [T5: rat] :
% 5.45/5.68 ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.68 => ( ord_less_eq_rat @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(8)
% 5.45/5.68 thf(fact_2313_pinf_I8_J,axiom,
% 5.45/5.68 ! [T5: num] :
% 5.45/5.68 ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.68 => ( ord_less_eq_num @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(8)
% 5.45/5.68 thf(fact_2314_pinf_I8_J,axiom,
% 5.45/5.68 ! [T5: nat] :
% 5.45/5.68 ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.68 => ( ord_less_eq_nat @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(8)
% 5.45/5.68 thf(fact_2315_pinf_I8_J,axiom,
% 5.45/5.68 ! [T5: int] :
% 5.45/5.68 ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.68 => ( ord_less_eq_int @ T5 @ X7 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(8)
% 5.45/5.68 thf(fact_2316_pinf_I6_J,axiom,
% 5.45/5.68 ! [T5: rat] :
% 5.45/5.68 ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.68 => ~ ( ord_less_eq_rat @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(6)
% 5.45/5.68 thf(fact_2317_pinf_I6_J,axiom,
% 5.45/5.68 ! [T5: num] :
% 5.45/5.68 ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.68 => ~ ( ord_less_eq_num @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(6)
% 5.45/5.68 thf(fact_2318_pinf_I6_J,axiom,
% 5.45/5.68 ! [T5: nat] :
% 5.45/5.68 ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.68 => ~ ( ord_less_eq_nat @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(6)
% 5.45/5.68 thf(fact_2319_pinf_I6_J,axiom,
% 5.45/5.68 ! [T5: int] :
% 5.45/5.68 ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.68 => ~ ( ord_less_eq_int @ X7 @ T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(6)
% 5.45/5.68 thf(fact_2320_verit__comp__simplify1_I3_J,axiom,
% 5.45/5.68 ! [B2: rat,A2: rat] :
% 5.45/5.68 ( ( ~ ( ord_less_eq_rat @ B2 @ A2 ) )
% 5.45/5.68 = ( ord_less_rat @ A2 @ B2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(3)
% 5.45/5.68 thf(fact_2321_verit__comp__simplify1_I3_J,axiom,
% 5.45/5.68 ! [B2: num,A2: num] :
% 5.45/5.68 ( ( ~ ( ord_less_eq_num @ B2 @ A2 ) )
% 5.45/5.68 = ( ord_less_num @ A2 @ B2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(3)
% 5.45/5.68 thf(fact_2322_verit__comp__simplify1_I3_J,axiom,
% 5.45/5.68 ! [B2: nat,A2: nat] :
% 5.45/5.68 ( ( ~ ( ord_less_eq_nat @ B2 @ A2 ) )
% 5.45/5.68 = ( ord_less_nat @ A2 @ B2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(3)
% 5.45/5.68 thf(fact_2323_verit__comp__simplify1_I3_J,axiom,
% 5.45/5.68 ! [B2: int,A2: int] :
% 5.45/5.68 ( ( ~ ( ord_less_eq_int @ B2 @ A2 ) )
% 5.45/5.68 = ( ord_less_int @ A2 @ B2 ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(3)
% 5.45/5.68 thf(fact_2324_complete__interval,axiom,
% 5.45/5.68 ! [A: nat,B: nat,P: nat > $o] :
% 5.45/5.68 ( ( ord_less_nat @ A @ B )
% 5.45/5.68 => ( ( P @ A )
% 5.45/5.68 => ( ~ ( P @ B )
% 5.45/5.68 => ? [C2: nat] :
% 5.45/5.68 ( ( ord_less_eq_nat @ A @ C2 )
% 5.45/5.68 & ( ord_less_eq_nat @ C2 @ B )
% 5.45/5.68 & ! [X7: nat] :
% 5.45/5.68 ( ( ( ord_less_eq_nat @ A @ X7 )
% 5.45/5.68 & ( ord_less_nat @ X7 @ C2 ) )
% 5.45/5.68 => ( P @ X7 ) )
% 5.45/5.68 & ! [D4: nat] :
% 5.45/5.68 ( ! [X3: nat] :
% 5.45/5.68 ( ( ( ord_less_eq_nat @ A @ X3 )
% 5.45/5.68 & ( ord_less_nat @ X3 @ D4 ) )
% 5.45/5.68 => ( P @ X3 ) )
% 5.45/5.68 => ( ord_less_eq_nat @ D4 @ C2 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % complete_interval
% 5.45/5.68 thf(fact_2325_complete__interval,axiom,
% 5.45/5.68 ! [A: int,B: int,P: int > $o] :
% 5.45/5.68 ( ( ord_less_int @ A @ B )
% 5.45/5.68 => ( ( P @ A )
% 5.45/5.68 => ( ~ ( P @ B )
% 5.45/5.68 => ? [C2: int] :
% 5.45/5.68 ( ( ord_less_eq_int @ A @ C2 )
% 5.45/5.68 & ( ord_less_eq_int @ C2 @ B )
% 5.45/5.68 & ! [X7: int] :
% 5.45/5.68 ( ( ( ord_less_eq_int @ A @ X7 )
% 5.45/5.68 & ( ord_less_int @ X7 @ C2 ) )
% 5.45/5.68 => ( P @ X7 ) )
% 5.45/5.68 & ! [D4: int] :
% 5.45/5.68 ( ! [X3: int] :
% 5.45/5.68 ( ( ( ord_less_eq_int @ A @ X3 )
% 5.45/5.68 & ( ord_less_int @ X3 @ D4 ) )
% 5.45/5.68 => ( P @ X3 ) )
% 5.45/5.68 => ( ord_less_eq_int @ D4 @ C2 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % complete_interval
% 5.45/5.68 thf(fact_2326_bijective__Empty,axiom,
% 5.45/5.68 bijective_nat_nat @ bot_bo2099793752762293965at_nat ).
% 5.45/5.68
% 5.45/5.68 % bijective_Empty
% 5.45/5.68 thf(fact_2327_the__dflt__None__nonempty,axiom,
% 5.45/5.68 ! [S: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ( S != bot_bo2099793752762293965at_nat )
% 5.45/5.68 => ( ( dflt_N6592383573632408824at_nat @ S )
% 5.45/5.68 = ( some_s147305329494351046at_nat @ S ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % the_dflt_None_nonempty
% 5.45/5.68 thf(fact_2328_the__dflt__None__nonempty,axiom,
% 5.45/5.68 ! [S: set_o] :
% 5.45/5.68 ( ( S != bot_bot_set_o )
% 5.45/5.68 => ( ( dflt_None_set_o @ S )
% 5.45/5.68 = ( some_set_o @ S ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % the_dflt_None_nonempty
% 5.45/5.68 thf(fact_2329_the__dflt__None__nonempty,axiom,
% 5.45/5.68 ! [S: set_nat] :
% 5.45/5.68 ( ( S != bot_bot_set_nat )
% 5.45/5.68 => ( ( dflt_None_set_nat @ S )
% 5.45/5.68 = ( some_set_nat @ S ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % the_dflt_None_nonempty
% 5.45/5.68 thf(fact_2330_the__dflt__None__nonempty,axiom,
% 5.45/5.68 ! [S: set_int] :
% 5.45/5.68 ( ( S != bot_bot_set_int )
% 5.45/5.68 => ( ( dflt_None_set_int @ S )
% 5.45/5.68 = ( some_set_int @ S ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % the_dflt_None_nonempty
% 5.45/5.68 thf(fact_2331_times__assn__raw_Opelims_I3_J,axiom,
% 5.45/5.68 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.68 ( ~ ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.68 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.68 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.68 ( ( Xb
% 5.45/5.68 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.68 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) )
% 5.45/5.68 => ? [As13: set_nat,As23: set_nat] :
% 5.45/5.68 ( ( As4
% 5.45/5.68 = ( sup_sup_set_nat @ As13 @ As23 ) )
% 5.45/5.68 & ( ( inf_inf_set_nat @ As13 @ As23 )
% 5.45/5.68 = bot_bot_set_nat )
% 5.45/5.68 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As13 ) )
% 5.45/5.68 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As23 ) ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % times_assn_raw.pelims(3)
% 5.45/5.68 thf(fact_2332_psubsetD,axiom,
% 5.45/5.68 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.45/5.68 ( ( ord_le7866589430770878221at_nat @ A3 @ B3 )
% 5.45/5.68 => ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.68 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetD
% 5.45/5.68 thf(fact_2333_psubsetD,axiom,
% 5.45/5.68 ! [A3: set_o,B3: set_o,C: $o] :
% 5.45/5.68 ( ( ord_less_set_o @ A3 @ B3 )
% 5.45/5.68 => ( ( member_o @ C @ A3 )
% 5.45/5.68 => ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetD
% 5.45/5.68 thf(fact_2334_psubsetD,axiom,
% 5.45/5.68 ! [A3: set_set_nat,B3: set_set_nat,C: set_nat] :
% 5.45/5.68 ( ( ord_less_set_set_nat @ A3 @ B3 )
% 5.45/5.68 => ( ( member_set_nat @ C @ A3 )
% 5.45/5.68 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetD
% 5.45/5.68 thf(fact_2335_psubsetD,axiom,
% 5.45/5.68 ! [A3: set_nat,B3: set_nat,C: nat] :
% 5.45/5.68 ( ( ord_less_set_nat @ A3 @ B3 )
% 5.45/5.68 => ( ( member_nat @ C @ A3 )
% 5.45/5.68 => ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetD
% 5.45/5.68 thf(fact_2336_psubsetD,axiom,
% 5.45/5.68 ! [A3: set_int,B3: set_int,C: int] :
% 5.45/5.68 ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.68 => ( ( member_int @ C @ A3 )
% 5.45/5.68 => ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % psubsetD
% 5.45/5.68 thf(fact_2337_less__set__def,axiom,
% 5.45/5.68 ( ord_le7866589430770878221at_nat
% 5.45/5.68 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.68 ( ord_le549003669493604880_nat_o
% 5.45/5.68 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.68 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_set_def
% 5.45/5.68 thf(fact_2338_less__set__def,axiom,
% 5.45/5.68 ( ord_less_set_o
% 5.45/5.68 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.68 ( ord_less_o_o
% 5.45/5.68 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 5.45/5.68 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_set_def
% 5.45/5.68 thf(fact_2339_less__set__def,axiom,
% 5.45/5.68 ( ord_less_set_set_nat
% 5.45/5.68 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.68 ( ord_less_set_nat_o
% 5.45/5.68 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 5.45/5.68 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_set_def
% 5.45/5.68 thf(fact_2340_less__set__def,axiom,
% 5.45/5.68 ( ord_less_set_nat
% 5.45/5.68 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.68 ( ord_less_nat_o
% 5.45/5.68 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 5.45/5.68 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_set_def
% 5.45/5.68 thf(fact_2341_less__set__def,axiom,
% 5.45/5.68 ( ord_less_set_int
% 5.45/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.68 ( ord_less_int_o
% 5.45/5.68 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 5.45/5.68 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % less_set_def
% 5.45/5.68 thf(fact_2342_verit__la__disequality,axiom,
% 5.45/5.68 ! [A: rat,B: rat] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 | ~ ( ord_less_eq_rat @ A @ B )
% 5.45/5.68 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_la_disequality
% 5.45/5.68 thf(fact_2343_verit__la__disequality,axiom,
% 5.45/5.68 ! [A: num,B: num] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 | ~ ( ord_less_eq_num @ A @ B )
% 5.45/5.68 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_la_disequality
% 5.45/5.68 thf(fact_2344_verit__la__disequality,axiom,
% 5.45/5.68 ! [A: nat,B: nat] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 | ~ ( ord_less_eq_nat @ A @ B )
% 5.45/5.68 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_la_disequality
% 5.45/5.68 thf(fact_2345_verit__la__disequality,axiom,
% 5.45/5.68 ! [A: int,B: int] :
% 5.45/5.68 ( ( A = B )
% 5.45/5.68 | ~ ( ord_less_eq_int @ A @ B )
% 5.45/5.68 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.45/5.68
% 5.45/5.68 % verit_la_disequality
% 5.45/5.68 thf(fact_2346_verit__comp__simplify1_I2_J,axiom,
% 5.45/5.68 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(2)
% 5.45/5.68 thf(fact_2347_verit__comp__simplify1_I2_J,axiom,
% 5.45/5.68 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(2)
% 5.45/5.68 thf(fact_2348_verit__comp__simplify1_I2_J,axiom,
% 5.45/5.68 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(2)
% 5.45/5.68 thf(fact_2349_verit__comp__simplify1_I2_J,axiom,
% 5.45/5.68 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(2)
% 5.45/5.68 thf(fact_2350_verit__comp__simplify1_I2_J,axiom,
% 5.45/5.68 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(2)
% 5.45/5.68 thf(fact_2351_verit__comp__simplify1_I1_J,axiom,
% 5.45/5.68 ! [A: assn] :
% 5.45/5.68 ~ ( ord_less_assn @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(1)
% 5.45/5.68 thf(fact_2352_verit__comp__simplify1_I1_J,axiom,
% 5.45/5.68 ! [A: rat] :
% 5.45/5.68 ~ ( ord_less_rat @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(1)
% 5.45/5.68 thf(fact_2353_verit__comp__simplify1_I1_J,axiom,
% 5.45/5.68 ! [A: num] :
% 5.45/5.68 ~ ( ord_less_num @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(1)
% 5.45/5.68 thf(fact_2354_verit__comp__simplify1_I1_J,axiom,
% 5.45/5.68 ! [A: nat] :
% 5.45/5.68 ~ ( ord_less_nat @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(1)
% 5.45/5.68 thf(fact_2355_verit__comp__simplify1_I1_J,axiom,
% 5.45/5.68 ! [A: int] :
% 5.45/5.68 ~ ( ord_less_int @ A @ A ) ).
% 5.45/5.68
% 5.45/5.68 % verit_comp_simplify1(1)
% 5.45/5.68 thf(fact_2356_pinf_I1_J,axiom,
% 5.45/5.68 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 5.45/5.68 ( ? [Z5: rat] :
% 5.45/5.68 ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: rat] :
% 5.45/5.68 ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 & ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(1)
% 5.45/5.68 thf(fact_2357_pinf_I1_J,axiom,
% 5.45/5.68 ! [P: num > $o,P6: num > $o,Q: num > $o,Q4: num > $o] :
% 5.45/5.68 ( ? [Z5: num] :
% 5.45/5.68 ! [X3: num] :
% 5.45/5.68 ( ( ord_less_num @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: num] :
% 5.45/5.68 ! [X3: num] :
% 5.45/5.68 ( ( ord_less_num @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 & ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(1)
% 5.45/5.68 thf(fact_2358_pinf_I1_J,axiom,
% 5.45/5.68 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 5.45/5.68 ( ? [Z5: nat] :
% 5.45/5.68 ! [X3: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: nat] :
% 5.45/5.68 ! [X3: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 & ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(1)
% 5.45/5.68 thf(fact_2359_pinf_I1_J,axiom,
% 5.45/5.68 ! [P: int > $o,P6: int > $o,Q: int > $o,Q4: int > $o] :
% 5.45/5.68 ( ? [Z5: int] :
% 5.45/5.68 ! [X3: int] :
% 5.45/5.68 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: int] :
% 5.45/5.68 ! [X3: int] :
% 5.45/5.68 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 & ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(1)
% 5.45/5.68 thf(fact_2360_pinf_I2_J,axiom,
% 5.45/5.68 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 5.45/5.68 ( ? [Z5: rat] :
% 5.45/5.68 ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: rat] :
% 5.45/5.68 ! [X3: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 | ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(2)
% 5.45/5.68 thf(fact_2361_pinf_I2_J,axiom,
% 5.45/5.68 ! [P: num > $o,P6: num > $o,Q: num > $o,Q4: num > $o] :
% 5.45/5.68 ( ? [Z5: num] :
% 5.45/5.68 ! [X3: num] :
% 5.45/5.68 ( ( ord_less_num @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: num] :
% 5.45/5.68 ! [X3: num] :
% 5.45/5.68 ( ( ord_less_num @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 | ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(2)
% 5.45/5.68 thf(fact_2362_pinf_I2_J,axiom,
% 5.45/5.68 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 5.45/5.68 ( ? [Z5: nat] :
% 5.45/5.68 ! [X3: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: nat] :
% 5.45/5.68 ! [X3: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 | ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(2)
% 5.45/5.68 thf(fact_2363_pinf_I2_J,axiom,
% 5.45/5.68 ! [P: int > $o,P6: int > $o,Q: int > $o,Q4: int > $o] :
% 5.45/5.68 ( ? [Z5: int] :
% 5.45/5.68 ! [X3: int] :
% 5.45/5.68 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.68 => ( ( P @ X3 )
% 5.45/5.68 = ( P6 @ X3 ) ) )
% 5.45/5.68 => ( ? [Z5: int] :
% 5.45/5.68 ! [X3: int] :
% 5.45/5.68 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.68 => ( ( Q @ X3 )
% 5.45/5.68 = ( Q4 @ X3 ) ) )
% 5.45/5.68 => ? [Z2: int] :
% 5.45/5.68 ! [X7: int] :
% 5.45/5.68 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.68 => ( ( ( P @ X7 )
% 5.45/5.68 | ( Q @ X7 ) )
% 5.45/5.68 = ( ( P6 @ X7 )
% 5.45/5.68 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(2)
% 5.45/5.68 thf(fact_2364_pinf_I3_J,axiom,
% 5.45/5.68 ! [T5: rat] :
% 5.45/5.68 ? [Z2: rat] :
% 5.45/5.68 ! [X7: rat] :
% 5.45/5.68 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.68 => ( X7 != T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(3)
% 5.45/5.68 thf(fact_2365_pinf_I3_J,axiom,
% 5.45/5.68 ! [T5: num] :
% 5.45/5.68 ? [Z2: num] :
% 5.45/5.68 ! [X7: num] :
% 5.45/5.68 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.68 => ( X7 != T5 ) ) ).
% 5.45/5.68
% 5.45/5.68 % pinf(3)
% 5.45/5.68 thf(fact_2366_pinf_I3_J,axiom,
% 5.45/5.68 ! [T5: nat] :
% 5.45/5.68 ? [Z2: nat] :
% 5.45/5.68 ! [X7: nat] :
% 5.45/5.68 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(3)
% 5.45/5.69 thf(fact_2367_pinf_I3_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(3)
% 5.45/5.69 thf(fact_2368_pinf_I4_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(4)
% 5.45/5.69 thf(fact_2369_pinf_I4_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(4)
% 5.45/5.69 thf(fact_2370_pinf_I4_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(4)
% 5.45/5.69 thf(fact_2371_pinf_I4_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(4)
% 5.45/5.69 thf(fact_2372_pinf_I5_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.69 => ~ ( ord_less_rat @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(5)
% 5.45/5.69 thf(fact_2373_pinf_I5_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.69 => ~ ( ord_less_num @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(5)
% 5.45/5.69 thf(fact_2374_pinf_I5_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.69 => ~ ( ord_less_nat @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(5)
% 5.45/5.69 thf(fact_2375_pinf_I5_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.69 => ~ ( ord_less_int @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(5)
% 5.45/5.69 thf(fact_2376_pinf_I7_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.69 => ( ord_less_rat @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(7)
% 5.45/5.69 thf(fact_2377_pinf_I7_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ Z2 @ X7 )
% 5.45/5.69 => ( ord_less_num @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(7)
% 5.45/5.69 thf(fact_2378_pinf_I7_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.69 => ( ord_less_nat @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(7)
% 5.45/5.69 thf(fact_2379_pinf_I7_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.69 => ( ord_less_int @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % pinf(7)
% 5.45/5.69 thf(fact_2380_minf_I1_J,axiom,
% 5.45/5.69 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 5.45/5.69 ( ? [Z5: rat] :
% 5.45/5.69 ! [X3: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: rat] :
% 5.45/5.69 ! [X3: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 & ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(1)
% 5.45/5.69 thf(fact_2381_minf_I1_J,axiom,
% 5.45/5.69 ! [P: num > $o,P6: num > $o,Q: num > $o,Q4: num > $o] :
% 5.45/5.69 ( ? [Z5: num] :
% 5.45/5.69 ! [X3: num] :
% 5.45/5.69 ( ( ord_less_num @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: num] :
% 5.45/5.69 ! [X3: num] :
% 5.45/5.69 ( ( ord_less_num @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 & ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(1)
% 5.45/5.69 thf(fact_2382_minf_I1_J,axiom,
% 5.45/5.69 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 5.45/5.69 ( ? [Z5: nat] :
% 5.45/5.69 ! [X3: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: nat] :
% 5.45/5.69 ! [X3: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 & ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(1)
% 5.45/5.69 thf(fact_2383_minf_I1_J,axiom,
% 5.45/5.69 ! [P: int > $o,P6: int > $o,Q: int > $o,Q4: int > $o] :
% 5.45/5.69 ( ? [Z5: int] :
% 5.45/5.69 ! [X3: int] :
% 5.45/5.69 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: int] :
% 5.45/5.69 ! [X3: int] :
% 5.45/5.69 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 & ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 & ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(1)
% 5.45/5.69 thf(fact_2384_minf_I2_J,axiom,
% 5.45/5.69 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q4: rat > $o] :
% 5.45/5.69 ( ? [Z5: rat] :
% 5.45/5.69 ! [X3: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: rat] :
% 5.45/5.69 ! [X3: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 | ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(2)
% 5.45/5.69 thf(fact_2385_minf_I2_J,axiom,
% 5.45/5.69 ! [P: num > $o,P6: num > $o,Q: num > $o,Q4: num > $o] :
% 5.45/5.69 ( ? [Z5: num] :
% 5.45/5.69 ! [X3: num] :
% 5.45/5.69 ( ( ord_less_num @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: num] :
% 5.45/5.69 ! [X3: num] :
% 5.45/5.69 ( ( ord_less_num @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 | ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(2)
% 5.45/5.69 thf(fact_2386_minf_I2_J,axiom,
% 5.45/5.69 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q4: nat > $o] :
% 5.45/5.69 ( ? [Z5: nat] :
% 5.45/5.69 ! [X3: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: nat] :
% 5.45/5.69 ! [X3: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 | ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(2)
% 5.45/5.69 thf(fact_2387_minf_I2_J,axiom,
% 5.45/5.69 ! [P: int > $o,P6: int > $o,Q: int > $o,Q4: int > $o] :
% 5.45/5.69 ( ? [Z5: int] :
% 5.45/5.69 ! [X3: int] :
% 5.45/5.69 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.69 => ( ( P @ X3 )
% 5.45/5.69 = ( P6 @ X3 ) ) )
% 5.45/5.69 => ( ? [Z5: int] :
% 5.45/5.69 ! [X3: int] :
% 5.45/5.69 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 = ( Q4 @ X3 ) ) )
% 5.45/5.69 => ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ( ( ( P @ X7 )
% 5.45/5.69 | ( Q @ X7 ) )
% 5.45/5.69 = ( ( P6 @ X7 )
% 5.45/5.69 | ( Q4 @ X7 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(2)
% 5.45/5.69 thf(fact_2388_minf_I3_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(3)
% 5.45/5.69 thf(fact_2389_minf_I3_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(3)
% 5.45/5.69 thf(fact_2390_minf_I3_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(3)
% 5.45/5.69 thf(fact_2391_minf_I3_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(3)
% 5.45/5.69 thf(fact_2392_minf_I4_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(4)
% 5.45/5.69 thf(fact_2393_minf_I4_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(4)
% 5.45/5.69 thf(fact_2394_minf_I4_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(4)
% 5.45/5.69 thf(fact_2395_minf_I4_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ( X7 != T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(4)
% 5.45/5.69 thf(fact_2396_minf_I5_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ( ord_less_rat @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(5)
% 5.45/5.69 thf(fact_2397_minf_I5_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ( ord_less_num @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(5)
% 5.45/5.69 thf(fact_2398_minf_I5_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ( ord_less_nat @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(5)
% 5.45/5.69 thf(fact_2399_minf_I5_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ( ord_less_int @ X7 @ T5 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(5)
% 5.45/5.69 thf(fact_2400_minf_I7_J,axiom,
% 5.45/5.69 ! [T5: rat] :
% 5.45/5.69 ? [Z2: rat] :
% 5.45/5.69 ! [X7: rat] :
% 5.45/5.69 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.69 => ~ ( ord_less_rat @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(7)
% 5.45/5.69 thf(fact_2401_minf_I7_J,axiom,
% 5.45/5.69 ! [T5: num] :
% 5.45/5.69 ? [Z2: num] :
% 5.45/5.69 ! [X7: num] :
% 5.45/5.69 ( ( ord_less_num @ X7 @ Z2 )
% 5.45/5.69 => ~ ( ord_less_num @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(7)
% 5.45/5.69 thf(fact_2402_minf_I7_J,axiom,
% 5.45/5.69 ! [T5: nat] :
% 5.45/5.69 ? [Z2: nat] :
% 5.45/5.69 ! [X7: nat] :
% 5.45/5.69 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.69 => ~ ( ord_less_nat @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(7)
% 5.45/5.69 thf(fact_2403_minf_I7_J,axiom,
% 5.45/5.69 ! [T5: int] :
% 5.45/5.69 ? [Z2: int] :
% 5.45/5.69 ! [X7: int] :
% 5.45/5.69 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.69 => ~ ( ord_less_int @ T5 @ X7 ) ) ).
% 5.45/5.69
% 5.45/5.69 % minf(7)
% 5.45/5.69 thf(fact_2404_bijective__def,axiom,
% 5.45/5.69 ( bijective_nat_nat
% 5.45/5.69 = ( ^ [R6: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ! [X4: nat,Y4: nat,Z6: nat] :
% 5.45/5.69 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: nat,Y4: nat,Z6: nat] :
% 5.45/5.69 ( ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2405_bijective__def,axiom,
% 5.45/5.69 ( biject2615096655818420098et_nat
% 5.45/5.69 = ( ^ [R6: set_Pr3286484037609594932et_nat] :
% 5.45/5.69 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat,Z6: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z6: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2406_bijective__def,axiom,
% 5.45/5.69 ( biject1468766312547416318et_nat
% 5.45/5.69 = ( ^ [R6: set_Pr8536935166611901872et_nat] :
% 5.45/5.69 ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat,Z6: produc3925858234332021118et_nat] :
% 5.45/5.69 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat > $o,Z6: produc3925858234332021118et_nat] :
% 5.45/5.69 ( ( ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2407_bijective__def,axiom,
% 5.45/5.69 ( biject383251550997737151nt_int
% 5.45/5.69 = ( ^ [R6: set_Pr9222295170931077689nt_int] :
% 5.45/5.69 ( ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int,Z6: product_prod_int_int] :
% 5.45/5.69 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: produc8551481072490612790e_term > option6357759511663192854e_term,Z6: product_prod_int_int] :
% 5.45/5.69 ( ( ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2408_bijective__def,axiom,
% 5.45/5.69 ( biject576505603616484041nt_int
% 5.45/5.69 = ( ^ [R6: set_Pr1872883991513573699nt_int] :
% 5.45/5.69 ( ! [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int,Z6: product_prod_int_int] :
% 5.45/5.69 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: int > option6357759511663192854e_term,Y4: int > option6357759511663192854e_term,Z6: product_prod_int_int] :
% 5.45/5.69 ( ( ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2409_bijective__def,axiom,
% 5.45/5.69 ( biject8592306251674886141it_nat
% 5.45/5.69 = ( ^ [R6: set_Pr7098220151150636591it_nat] :
% 5.45/5.69 ( ! [X4: a,Y4: produc6653097349344004940it_nat,Z6: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) @ R6 )
% 5.45/5.69 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( Y4 = Z6 ) )
% 5.45/5.69 & ! [X4: a,Y4: a,Z6: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ X4 @ Z6 ) @ R6 )
% 5.45/5.69 & ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ Y4 @ Z6 ) @ R6 ) )
% 5.45/5.69 => ( X4 = Y4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % bijective_def
% 5.45/5.69 thf(fact_2410_times__assn__raw_Opelims_I1_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( ? [As12: set_nat,As22: set_nat] :
% 5.45/5.69 ( ( As4
% 5.45/5.69 = ( sup_sup_set_nat @ As12 @ As22 ) )
% 5.45/5.69 & ( ( inf_inf_set_nat @ As12 @ As22 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As12 ) )
% 5.45/5.69 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As22 ) ) ) ) )
% 5.45/5.69 => ~ ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % times_assn_raw.pelims(1)
% 5.45/5.69 thf(fact_2411_times__assn__raw_Opelims_I2_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( times_assn_raw @ X @ Xa @ Xb )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ times_assn_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) )
% 5.45/5.69 => ~ ? [As1: set_nat,As2: set_nat] :
% 5.45/5.69 ( ( As4
% 5.45/5.69 = ( sup_sup_set_nat @ As1 @ As2 ) )
% 5.45/5.69 & ( ( inf_inf_set_nat @ As1 @ As2 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H4 @ As1 ) )
% 5.45/5.69 & ( Xa @ ( produc7507926704131184380et_nat @ H4 @ As2 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % times_assn_raw.pelims(2)
% 5.45/5.69 thf(fact_2412_the__dflt__None__set,axiom,
% 5.45/5.69 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( the_de3668382347305825784at_nat @ bot_bo2099793752762293965at_nat @ ( dflt_N6592383573632408824at_nat @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_set
% 5.45/5.69 thf(fact_2413_the__dflt__None__set,axiom,
% 5.45/5.69 ! [X: set_o] :
% 5.45/5.69 ( ( the_default_set_o @ bot_bot_set_o @ ( dflt_None_set_o @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_set
% 5.45/5.69 thf(fact_2414_the__dflt__None__set,axiom,
% 5.45/5.69 ! [X: set_nat] :
% 5.45/5.69 ( ( the_default_set_nat @ bot_bot_set_nat @ ( dflt_None_set_nat @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_set
% 5.45/5.69 thf(fact_2415_the__dflt__None__set,axiom,
% 5.45/5.69 ! [X: set_int] :
% 5.45/5.69 ( ( the_default_set_int @ bot_bot_set_int @ ( dflt_None_set_int @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_set
% 5.45/5.69 thf(fact_2416_accp__subset,axiom,
% 5.45/5.69 ! [R1: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o,R22: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o] :
% 5.45/5.69 ( ( ord_le3355651325779393058_nat_o @ R1 @ R22 )
% 5.45/5.69 => ( ord_le729326519192465773_nat_o @ ( accp_P5801069581201407417et_nat @ R22 ) @ ( accp_P5801069581201407417et_nat @ R1 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset
% 5.45/5.69 thf(fact_2417_accp__subset,axiom,
% 5.45/5.69 ! [R1: product_prod_num_num > product_prod_num_num > $o,R22: product_prod_num_num > product_prod_num_num > $o] :
% 5.45/5.69 ( ( ord_le2556027599737686990_num_o @ R1 @ R22 )
% 5.45/5.69 => ( ord_le2239182809043710856_num_o @ ( accp_P3113834385874906142um_num @ R22 ) @ ( accp_P3113834385874906142um_num @ R1 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset
% 5.45/5.69 thf(fact_2418_accp__subset,axiom,
% 5.45/5.69 ! [R1: product_prod_nat_nat > product_prod_nat_nat > $o,R22: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.45/5.69 ( ( ord_le5604493270027003598_nat_o @ R1 @ R22 )
% 5.45/5.69 => ( ord_le704812498762024988_nat_o @ ( accp_P4275260045618599050at_nat @ R22 ) @ ( accp_P4275260045618599050at_nat @ R1 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset
% 5.45/5.69 thf(fact_2419_accp__subset,axiom,
% 5.45/5.69 ! [R1: product_prod_int_int > product_prod_int_int > $o,R22: product_prod_int_int > product_prod_int_int > $o] :
% 5.45/5.69 ( ( ord_le1598226405681992910_int_o @ R1 @ R22 )
% 5.45/5.69 => ( ord_le8369615600986905444_int_o @ ( accp_P1096762738010456898nt_int @ R22 ) @ ( accp_P1096762738010456898nt_int @ R1 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset
% 5.45/5.69 thf(fact_2420_accp__subset,axiom,
% 5.45/5.69 ! [R1: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,R22: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o] :
% 5.45/5.69 ( ( ord_le7226304311989208114_nat_o @ R1 @ R22 )
% 5.45/5.69 => ( ord_le1658592502415435381_nat_o @ ( accp_P1862375125659990705et_nat @ R22 ) @ ( accp_P1862375125659990705et_nat @ R1 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset
% 5.45/5.69 thf(fact_2421_accp__subset__induct,axiom,
% 5.45/5.69 ! [D3: produc3658429121746597890et_nat > $o,R: produc3658429121746597890et_nat > produc3658429121746597890et_nat > $o,X: produc3658429121746597890et_nat,P: produc3658429121746597890et_nat > $o] :
% 5.45/5.69 ( ( ord_le729326519192465773_nat_o @ D3 @ ( accp_P5801069581201407417et_nat @ R ) )
% 5.45/5.69 => ( ! [X3: produc3658429121746597890et_nat,Z2: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ( R @ Z2 @ X3 )
% 5.45/5.69 => ( D3 @ Z2 ) ) )
% 5.45/5.69 => ( ( D3 @ X )
% 5.45/5.69 => ( ! [X3: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ! [Z5: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( R @ Z5 @ X3 )
% 5.45/5.69 => ( P @ Z5 ) )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( P @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset_induct
% 5.45/5.69 thf(fact_2422_accp__subset__induct,axiom,
% 5.45/5.69 ! [D3: product_prod_num_num > $o,R: product_prod_num_num > product_prod_num_num > $o,X: product_prod_num_num,P: product_prod_num_num > $o] :
% 5.45/5.69 ( ( ord_le2239182809043710856_num_o @ D3 @ ( accp_P3113834385874906142um_num @ R ) )
% 5.45/5.69 => ( ! [X3: product_prod_num_num,Z2: product_prod_num_num] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ( R @ Z2 @ X3 )
% 5.45/5.69 => ( D3 @ Z2 ) ) )
% 5.45/5.69 => ( ( D3 @ X )
% 5.45/5.69 => ( ! [X3: product_prod_num_num] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ! [Z5: product_prod_num_num] :
% 5.45/5.69 ( ( R @ Z5 @ X3 )
% 5.45/5.69 => ( P @ Z5 ) )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( P @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset_induct
% 5.45/5.69 thf(fact_2423_accp__subset__induct,axiom,
% 5.45/5.69 ! [D3: product_prod_nat_nat > $o,R: product_prod_nat_nat > product_prod_nat_nat > $o,X: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.69 ( ( ord_le704812498762024988_nat_o @ D3 @ ( accp_P4275260045618599050at_nat @ R ) )
% 5.45/5.69 => ( ! [X3: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ( R @ Z2 @ X3 )
% 5.45/5.69 => ( D3 @ Z2 ) ) )
% 5.45/5.69 => ( ( D3 @ X )
% 5.45/5.69 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ! [Z5: product_prod_nat_nat] :
% 5.45/5.69 ( ( R @ Z5 @ X3 )
% 5.45/5.69 => ( P @ Z5 ) )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( P @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset_induct
% 5.45/5.69 thf(fact_2424_accp__subset__induct,axiom,
% 5.45/5.69 ! [D3: product_prod_int_int > $o,R: product_prod_int_int > product_prod_int_int > $o,X: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.45/5.69 ( ( ord_le8369615600986905444_int_o @ D3 @ ( accp_P1096762738010456898nt_int @ R ) )
% 5.45/5.69 => ( ! [X3: product_prod_int_int,Z2: product_prod_int_int] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ( R @ Z2 @ X3 )
% 5.45/5.69 => ( D3 @ Z2 ) ) )
% 5.45/5.69 => ( ( D3 @ X )
% 5.45/5.69 => ( ! [X3: product_prod_int_int] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ! [Z5: product_prod_int_int] :
% 5.45/5.69 ( ( R @ Z5 @ X3 )
% 5.45/5.69 => ( P @ Z5 ) )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( P @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset_induct
% 5.45/5.69 thf(fact_2425_accp__subset__induct,axiom,
% 5.45/5.69 ! [D3: produc2732055786443039994et_nat > $o,R: produc2732055786443039994et_nat > produc2732055786443039994et_nat > $o,X: produc2732055786443039994et_nat,P: produc2732055786443039994et_nat > $o] :
% 5.45/5.69 ( ( ord_le1658592502415435381_nat_o @ D3 @ ( accp_P1862375125659990705et_nat @ R ) )
% 5.45/5.69 => ( ! [X3: produc2732055786443039994et_nat,Z2: produc2732055786443039994et_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ( R @ Z2 @ X3 )
% 5.45/5.69 => ( D3 @ Z2 ) ) )
% 5.45/5.69 => ( ( D3 @ X )
% 5.45/5.69 => ( ! [X3: produc2732055786443039994et_nat] :
% 5.45/5.69 ( ( D3 @ X3 )
% 5.45/5.69 => ( ! [Z5: produc2732055786443039994et_nat] :
% 5.45/5.69 ( ( R @ Z5 @ X3 )
% 5.45/5.69 => ( P @ Z5 ) )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( P @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % accp_subset_induct
% 5.45/5.69 thf(fact_2426_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( orderi2172309028950807442at_nat
% 5.45/5.69 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( ord_le7866589430770878221at_nat @ Y4 @ X4 )
% 5.45/5.69 @ bot_bo2099793752762293965at_nat ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2427_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( ordering_top_set_o
% 5.45/5.69 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_eq_set_o @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_o,Y4: set_o] : ( ord_less_set_o @ Y4 @ X4 )
% 5.45/5.69 @ bot_bot_set_o ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2428_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( ordering_top_set_nat
% 5.45/5.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 )
% 5.45/5.69 @ bot_bot_set_nat ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2429_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( ordering_top_assn
% 5.45/5.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 )
% 5.45/5.69 @ bot_bot_assn ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2430_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( ordering_top_set_int
% 5.45/5.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 )
% 5.45/5.69 @ bot_bot_set_int ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2431_bot_Oordering__top__axioms,axiom,
% 5.45/5.69 ( ordering_top_nat
% 5.45/5.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 5.45/5.69 @ bot_bot_nat ) ).
% 5.45/5.69
% 5.45/5.69 % bot.ordering_top_axioms
% 5.45/5.69 thf(fact_2432_mod__h__bot__iff_I1_J,axiom,
% 5.45/5.69 ! [B: $o,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( rep_assn @ ( pure_assn @ B ) @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) )
% 5.45/5.69 = B ) ).
% 5.45/5.69
% 5.45/5.69 % mod_h_bot_iff(1)
% 5.45/5.69 thf(fact_2433_hoare__triple__effect,axiom,
% 5.45/5.69 ! [P: assn,C: heap_Time_Heap_a,Q: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( hoare_hoare_triple_a @ P @ C @ Q )
% 5.45/5.69 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 => ? [H5: heap_e7401611519738050253t_unit,R2: a,T2: nat] :
% 5.45/5.69 ( ( heap_Time_effect_a @ C @ H @ H5 @ R2 @ T2 )
% 5.45/5.69 & ( rep_assn @ ( Q @ R2 ) @ ( produc7507926704131184380et_nat @ H5 @ ( hoare_new_addrs @ H @ As @ H5 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % hoare_triple_effect
% 5.45/5.69 thf(fact_2434_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic5672175589177086241at_nat @ sup_su718114333110466843at_nat
% 5.45/5.69 @ ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le3000389064537975527at_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_Pr8693737435421807431at_nat,Y4: set_Pr8693737435421807431at_nat] : ( ord_le6428140832669894131at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2435_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic5174734335190411425at_nat @ sup_su3035147773818789531at_nat
% 5.45/5.69 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le8081472938463900775at_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_Pr8551490117392284871at_nat,Y4: set_Pr8551490117392284871at_nat] : ( ord_le7642048601412989811at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2436_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic6976360593897529633at_nat @ sup_su5525570899277871387at_nat
% 5.45/5.69 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le1268244103169919719at_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_Pr4329608150637261639at_nat,Y4: set_Pr4329608150637261639at_nat] : ( ord_le2604355607129572851at_nat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2437_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic3109210760196336428et_nat @ sup_sup_set_nat
% 5.45/5.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_eq_set_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_nat,Y4: set_nat] : ( ord_less_set_nat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2438_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic5623431474481994958t_assn @ sup_sup_assn
% 5.45/5.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_eq_assn @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: assn,Y4: assn] : ( ord_less_assn @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2439_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic8154731777541915528et_int @ sup_sup_set_int
% 5.45/5.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_eq_set_int @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: set_int,Y4: set_int] : ( ord_less_set_int @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2440_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic5374021519246970238et_rat @ sup_sup_rat
% 5.45/5.69 @ ^ [X4: rat,Y4: rat] : ( ord_less_eq_rat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: rat,Y4: rat] : ( ord_less_rat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2441_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic6009151579333465974et_nat @ sup_sup_nat
% 5.45/5.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2442_Sup__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 ( lattic6006661108824415698et_int @ sup_sup_int
% 5.45/5.69 @ ^ [X4: int,Y4: int] : ( ord_less_eq_int @ Y4 @ X4 )
% 5.45/5.69 @ ^ [X4: int,Y4: int] : ( ord_less_int @ Y4 @ X4 ) ) ).
% 5.45/5.69
% 5.45/5.69 % Sup_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2443_wand__assnI,axiom,
% 5.45/5.69 ! [H: heap_e7401611519738050253t_unit,As: set_nat,Q: assn,R: assn] :
% 5.45/5.69 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 => ( ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 5.45/5.69 ( ( ( inf_inf_set_nat @ As @ As6 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 => ( ( relH @ As @ H @ H5 )
% 5.45/5.69 => ( ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As ) )
% 5.45/5.69 => ( ( rep_assn @ Q @ ( produc7507926704131184380et_nat @ H5 @ As6 ) )
% 5.45/5.69 => ( rep_assn @ R @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As @ As6 ) ) ) ) ) ) )
% 5.45/5.69 => ( rep_assn @ ( wand_assn @ Q @ R ) @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_assnI
% 5.45/5.69 thf(fact_2444_pure__assn__eq__conv,axiom,
% 5.45/5.69 ! [P: $o,Q: $o] :
% 5.45/5.69 ( ( ( pure_assn @ P )
% 5.45/5.69 = ( pure_assn @ Q ) )
% 5.45/5.69 = ( P = Q ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_eq_conv
% 5.45/5.69 thf(fact_2445_merge__pure__star,axiom,
% 5.45/5.69 ! [A: $o,B: $o] :
% 5.45/5.69 ( ( times_times_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 5.45/5.69 = ( pure_assn
% 5.45/5.69 @ ( A
% 5.45/5.69 & B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % merge_pure_star
% 5.45/5.69 thf(fact_2446_merge__pure__or,axiom,
% 5.45/5.69 ! [A: $o,B: $o] :
% 5.45/5.69 ( ( sup_sup_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 5.45/5.69 = ( pure_assn
% 5.45/5.69 @ ( A
% 5.45/5.69 | B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % merge_pure_or
% 5.45/5.69 thf(fact_2447_pure__assn__eq__false__iff,axiom,
% 5.45/5.69 ! [P: $o] :
% 5.45/5.69 ( ( ( pure_assn @ P )
% 5.45/5.69 = bot_bot_assn )
% 5.45/5.69 = ~ P ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_eq_false_iff
% 5.45/5.69 thf(fact_2448_pure__false,axiom,
% 5.45/5.69 ( ( pure_assn @ $false )
% 5.45/5.69 = bot_bot_assn ) ).
% 5.45/5.69
% 5.45/5.69 % pure_false
% 5.45/5.69 thf(fact_2449_merge__pure__and,axiom,
% 5.45/5.69 ! [A: $o,B: $o] :
% 5.45/5.69 ( ( inf_inf_assn @ ( pure_assn @ A ) @ ( pure_assn @ B ) )
% 5.45/5.69 = ( pure_assn
% 5.45/5.69 @ ( A
% 5.45/5.69 & B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % merge_pure_and
% 5.45/5.69 thf(fact_2450_in__range__empty,axiom,
% 5.45/5.69 ! [H: heap_e7401611519738050253t_unit] : ( in_range @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range_empty
% 5.45/5.69 thf(fact_2451_mod__pure__star__dist,axiom,
% 5.45/5.69 ! [P: assn,B: $o,H: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( rep_assn @ ( times_times_assn @ P @ ( pure_assn @ B ) ) @ H )
% 5.45/5.69 = ( ( rep_assn @ P @ H )
% 5.45/5.69 & B ) ) ).
% 5.45/5.69
% 5.45/5.69 % mod_pure_star_dist
% 5.45/5.69 thf(fact_2452_in__range__dist__union,axiom,
% 5.45/5.69 ! [H: heap_e7401611519738050253t_unit,As: set_nat,As3: set_nat] :
% 5.45/5.69 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ ( sup_sup_set_nat @ As @ As3 ) ) )
% 5.45/5.69 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H @ As3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range_dist_union
% 5.45/5.69 thf(fact_2453_ordering__top_Oextremum__uniqueI,axiom,
% 5.45/5.69 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 5.45/5.69 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 5.45/5.69 => ( ( Less_eq @ Top @ A )
% 5.45/5.69 => ( A = Top ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % ordering_top.extremum_uniqueI
% 5.45/5.69 thf(fact_2454_ordering__top_Onot__eq__extremum,axiom,
% 5.45/5.69 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 5.45/5.69 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 5.45/5.69 => ( ( A != Top )
% 5.45/5.69 = ( Less @ A @ Top ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % ordering_top.not_eq_extremum
% 5.45/5.69 thf(fact_2455_ordering__top_Oextremum__unique,axiom,
% 5.45/5.69 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 5.45/5.69 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 5.45/5.69 => ( ( Less_eq @ Top @ A )
% 5.45/5.69 = ( A = Top ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % ordering_top.extremum_unique
% 5.45/5.69 thf(fact_2456_ordering__top_Oextremum__strict,axiom,
% 5.45/5.69 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 5.45/5.69 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 5.45/5.69 => ~ ( Less @ Top @ A ) ) ).
% 5.45/5.69
% 5.45/5.69 % ordering_top.extremum_strict
% 5.45/5.69 thf(fact_2457_ordering__top_Oextremum,axiom,
% 5.45/5.69 ! [Less_eq: nat > nat > $o,Less: nat > nat > $o,Top: nat,A: nat] :
% 5.45/5.69 ( ( ordering_top_nat @ Less_eq @ Less @ Top )
% 5.45/5.69 => ( Less_eq @ A @ Top ) ) ).
% 5.45/5.69
% 5.45/5.69 % ordering_top.extremum
% 5.45/5.69 thf(fact_2458_models__in__range,axiom,
% 5.45/5.69 ! [P: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( rep_assn @ P @ H )
% 5.45/5.69 => ( in_range @ H ) ) ).
% 5.45/5.69
% 5.45/5.69 % models_in_range
% 5.45/5.69 thf(fact_2459_relH__in__rangeI_I2_J,axiom,
% 5.45/5.69 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( relH @ As @ H @ H3 )
% 5.45/5.69 => ( in_range @ ( produc7507926704131184380et_nat @ H3 @ As ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % relH_in_rangeI(2)
% 5.45/5.69 thf(fact_2460_relH__in__rangeI_I1_J,axiom,
% 5.45/5.69 ! [As: set_nat,H: heap_e7401611519738050253t_unit,H3: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( relH @ As @ H @ H3 )
% 5.45/5.69 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % relH_in_rangeI(1)
% 5.45/5.69 thf(fact_2461_relH__refl,axiom,
% 5.45/5.69 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 => ( relH @ As @ H @ H ) ) ).
% 5.45/5.69
% 5.45/5.69 % relH_refl
% 5.45/5.69 thf(fact_2462_in__range__subset,axiom,
% 5.45/5.69 ! [As: set_nat,As3: set_nat,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( ord_less_eq_set_nat @ As @ As3 )
% 5.45/5.69 => ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As3 ) )
% 5.45/5.69 => ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range_subset
% 5.45/5.69 thf(fact_2463_effectI,axiom,
% 5.45/5.69 ! [C: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,R3: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat] :
% 5.45/5.69 ( ( ( heap_T875086893843062177t_unit @ C @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R3 @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( heap_T6553295506729943825t_unit @ C @ H @ H3 @ R3 @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % effectI
% 5.45/5.69 thf(fact_2464_effectI,axiom,
% 5.45/5.69 ! [C: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,R3: a,H3: heap_e7401611519738050253t_unit,N2: nat] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ C @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R3 @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( heap_Time_effect_a @ C @ H @ H3 @ R3 @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % effectI
% 5.45/5.69 thf(fact_2465_effect__def,axiom,
% 5.45/5.69 ( heap_T6553295506729943825t_unit
% 5.45/5.69 = ( ^ [C4: heap_T5738788834812785303t_unit,H6: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,R4: product_unit,N: nat] :
% 5.45/5.69 ( ( heap_T875086893843062177t_unit @ C4 @ H6 )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R4 @ ( produc584006145561248582it_nat @ H7 @ N ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % effect_def
% 5.45/5.69 thf(fact_2466_effect__def,axiom,
% 5.45/5.69 ( heap_Time_effect_a
% 5.45/5.69 = ( ^ [C4: heap_Time_Heap_a,H6: heap_e7401611519738050253t_unit,H7: heap_e7401611519738050253t_unit,R4: a,N: nat] :
% 5.45/5.69 ( ( heap_Time_execute_a @ C4 @ H6 )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R4 @ ( produc584006145561248582it_nat @ H7 @ N ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % effect_def
% 5.45/5.69 thf(fact_2467_in__range_Oelims_I3_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( in_range @ X )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ! [X3: nat] :
% 5.45/5.69 ( ( member_nat @ X3 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.elims(3)
% 5.45/5.69 thf(fact_2468_in__range_Oelims_I2_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( in_range @ X )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ~ ! [X7: nat] :
% 5.45/5.69 ( ( member_nat @ X7 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X7 @ ( lim_Product_unit @ H4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.elims(2)
% 5.45/5.69 thf(fact_2469_in__range_Oelims_I1_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( in_range @ X )
% 5.45/5.69 = Y )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( Y
% 5.45/5.69 = ( ~ ! [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.elims(1)
% 5.45/5.69 thf(fact_2470_in__range_Osimps,axiom,
% 5.45/5.69 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 = ( ! [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ As )
% 5.45/5.69 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.simps
% 5.45/5.69 thf(fact_2471_Heap__eqI,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,G: heap_Time_Heap_a] :
% 5.45/5.69 ( ! [H4: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( heap_Time_execute_a @ F @ H4 )
% 5.45/5.69 = ( heap_Time_execute_a @ G @ H4 ) )
% 5.45/5.69 => ( F = G ) ) ).
% 5.45/5.69
% 5.45/5.69 % Heap_eqI
% 5.45/5.69 thf(fact_2472_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic3109210760196336428et_nat @ inf_inf_set_nat @ ord_less_eq_set_nat @ ord_less_set_nat ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2473_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic5111740090977526247t_unit @ inf_inf_Product_unit @ ord_le3221252021190050221t_unit @ ord_le361264281704409273t_unit ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2474_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic6529551498584149819at_nat @ inf_in2572325071724192079at_nat @ ord_le3146513528884898305at_nat @ ord_le7866589430770878221at_nat ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2475_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic5623431474481994958t_assn @ inf_inf_assn @ ord_less_eq_assn @ ord_less_assn ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2476_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic8154731777541915528et_int @ inf_inf_set_int @ ord_less_eq_set_int @ ord_less_set_int ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2477_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic5374021519246970238et_rat @ inf_inf_rat @ ord_less_eq_rat @ ord_less_rat ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2478_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic6009151579333465974et_nat @ inf_inf_nat @ ord_less_eq_nat @ ord_less_nat ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2479_Inf__fin_Osemilattice__order__set__axioms,axiom,
% 5.45/5.69 lattic6006661108824415698et_int @ inf_inf_int @ ord_less_eq_int @ ord_less_int ).
% 5.45/5.69
% 5.45/5.69 % Inf_fin.semilattice_order_set_axioms
% 5.45/5.69 thf(fact_2480_the__default_Osimps_I1_J,axiom,
% 5.45/5.69 ! [Uu: produc3260487557148687353it_nat,X: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( the_de542837501814275618it_nat @ Uu @ ( some_P7913643980934408916it_nat @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_default.simps(1)
% 5.45/5.69 thf(fact_2481_the__default_Osimps_I1_J,axiom,
% 5.45/5.69 ! [Uu: num,X: num] :
% 5.45/5.69 ( ( the_default_num @ Uu @ ( some_num @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_default.simps(1)
% 5.45/5.69 thf(fact_2482_the__default_Osimps_I1_J,axiom,
% 5.45/5.69 ! [Uu: produc8664842809031399944it_nat,X: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( the_de2487931475039285041it_nat @ Uu @ ( some_P1914260805536162275it_nat @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_default.simps(1)
% 5.45/5.69 thf(fact_2483_wand__raw_Oelims_I3_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H5 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As6 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.elims(3)
% 5.45/5.69 thf(fact_2484_wand__raw_Oelims_I2_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As7 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H8 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As4 @ As7 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.elims(2)
% 5.45/5.69 thf(fact_2485_wand__raw_Oelims_I1_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 = Y )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( Y
% 5.45/5.69 = ( ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H7 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.elims(1)
% 5.45/5.69 thf(fact_2486_wand__raw_Osimps,axiom,
% 5.45/5.69 ! [P: produc3658429121746597890et_nat > $o,Q: produc3658429121746597890et_nat > $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( wand_raw @ P @ Q @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 = ( ( in_range @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As @ As8 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As @ H @ H7 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As ) )
% 5.45/5.69 & ( P @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 5.45/5.69 => ( Q @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As @ As8 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.simps
% 5.45/5.69 thf(fact_2487_in__measure,axiom,
% 5.45/5.69 ! [X: nat,Y: nat,F: nat > nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( measure_nat @ F ) )
% 5.45/5.69 = ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_measure
% 5.45/5.69 thf(fact_2488_wand__raw_Opelims_I3_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) )
% 5.45/5.69 => ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H5: heap_e7401611519738050253t_unit,As6: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As6 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H5 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H5 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H5 @ As6 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H5 @ ( sup_sup_set_nat @ As4 @ As6 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.pelims(3)
% 5.45/5.69 thf(fact_2489_wand__raw_Opelims_I2_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) )
% 5.45/5.69 => ~ ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H8: heap_e7401611519738050253t_unit,As7: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As7 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H8 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H8 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H8 @ As7 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H8 @ ( sup_sup_set_nat @ As4 @ As7 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.pelims(2)
% 5.45/5.69 thf(fact_2490_wand__raw_Opelims_I1_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat > $o,Xa: produc3658429121746597890et_nat > $o,Xb: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( wand_raw @ X @ Xa @ Xb )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ Xb ) ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xb
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( ( in_range @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 & ! [H7: heap_e7401611519738050253t_unit,As8: set_nat] :
% 5.45/5.69 ( ( ( ( inf_inf_set_nat @ As4 @ As8 )
% 5.45/5.69 = bot_bot_set_nat )
% 5.45/5.69 & ( relH @ As4 @ H4 @ H7 )
% 5.45/5.69 & ( in_range @ ( produc7507926704131184380et_nat @ H7 @ As4 ) )
% 5.45/5.69 & ( X @ ( produc7507926704131184380et_nat @ H7 @ As8 ) ) )
% 5.45/5.69 => ( Xa @ ( produc7507926704131184380et_nat @ H7 @ ( sup_sup_set_nat @ As4 @ As8 ) ) ) ) ) )
% 5.45/5.69 => ~ ( accp_P1862375125659990705et_nat @ wand_raw_rel @ ( produc2245416461498447860et_nat @ X @ ( produc5001842942810119800et_nat @ Xa @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_raw.pelims(1)
% 5.45/5.69 thf(fact_2491_in__range_Opelims_I3_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( in_range @ X )
% 5.45/5.69 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ! [X3: nat] :
% 5.45/5.69 ( ( member_nat @ X3 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X3 @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.pelims(3)
% 5.45/5.69 thf(fact_2492_in__range_Opelims_I2_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( in_range @ X )
% 5.45/5.69 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ~ ! [X7: nat] :
% 5.45/5.69 ( ( member_nat @ X7 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X7 @ ( lim_Product_unit @ H4 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.pelims(2)
% 5.45/5.69 thf(fact_2493_in__range_Opelims_I1_J,axiom,
% 5.45/5.69 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( in_range @ X )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P5801069581201407417et_nat @ in_range_rel @ X )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( ! [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ As4 )
% 5.45/5.69 => ( ord_less_nat @ X4 @ ( lim_Product_unit @ H4 ) ) ) ) )
% 5.45/5.69 => ~ ( accp_P5801069581201407417et_nat @ in_range_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % in_range.pelims(1)
% 5.45/5.69 thf(fact_2494_wand__assn__def,axiom,
% 5.45/5.69 ( wand_assn
% 5.45/5.69 = ( ^ [P4: assn,Q3: assn] : ( abs_assn @ ( wand_raw @ ( rep_assn @ P4 ) @ ( rep_assn @ Q3 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % wand_assn_def
% 5.45/5.69 thf(fact_2495_sup__option__def,axiom,
% 5.45/5.69 ( sup_su1419176701018045153at_nat
% 5.45/5.69 = ( ^ [X4: option2158460348403737357at_nat,Y4: option2158460348403737357at_nat] :
% 5.45/5.69 ( case_o7467001542679133189at_nat @ Y4
% 5.45/5.69 @ ^ [X8: set_Pr8693737435421807431at_nat] :
% 5.45/5.69 ( case_o7467001542679133189at_nat @ X4
% 5.45/5.69 @ ^ [Z6: set_Pr8693737435421807431at_nat] : ( some_s579751585967276588at_nat @ ( sup_su718114333110466843at_nat @ X8 @ Z6 ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_option_def
% 5.45/5.69 thf(fact_2496_sup__option__def,axiom,
% 5.45/5.69 ( sup_su5873096292857799009at_nat
% 5.45/5.69 = ( ^ [X4: option2498585697089621389at_nat,Y4: option2498585697089621389at_nat] :
% 5.45/5.69 ( case_o8757249484648823045at_nat @ Y4
% 5.45/5.69 @ ^ [X8: set_Pr8551490117392284871at_nat] :
% 5.45/5.69 ( case_o8757249484648823045at_nat @ X4
% 5.45/5.69 @ ^ [Z6: set_Pr8551490117392284871at_nat] : ( some_s287724117700012716at_nat @ ( sup_su3035147773818789531at_nat @ X8 @ Z6 ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_option_def
% 5.45/5.69 thf(fact_2497_sup__option__def,axiom,
% 5.45/5.69 ( sup_su2273273666271716065at_nat
% 5.45/5.69 = ( ^ [X4: option1583680563626158861at_nat,Y4: option1583680563626158861at_nat] :
% 5.45/5.69 ( case_o9080059180780454917at_nat @ Y4
% 5.45/5.69 @ ^ [X8: set_Pr4329608150637261639at_nat] :
% 5.45/5.69 ( case_o9080059180780454917at_nat @ X4
% 5.45/5.69 @ ^ [Z6: set_Pr4329608150637261639at_nat] : ( some_s5890477192898017836at_nat @ ( sup_su5525570899277871387at_nat @ X8 @ Z6 ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_option_def
% 5.45/5.69 thf(fact_2498_sup__option__def,axiom,
% 5.45/5.69 ( sup_su3598758113090618626et_nat
% 5.45/5.69 = ( ^ [X4: option_set_nat,Y4: option_set_nat] :
% 5.45/5.69 ( case_o4054078431260844265et_nat @ Y4
% 5.45/5.69 @ ^ [X8: set_nat] :
% 5.45/5.69 ( case_o4054078431260844265et_nat @ X4
% 5.45/5.69 @ ^ [Z6: set_nat] : ( some_set_nat @ ( sup_sup_set_nat @ X8 @ Z6 ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_option_def
% 5.45/5.69 thf(fact_2499_sup__option__def,axiom,
% 5.45/5.69 ( sup_sup_option_nat
% 5.45/5.69 = ( ^ [X4: option_nat,Y4: option_nat] :
% 5.45/5.69 ( case_o7429725398727453821at_nat @ Y4
% 5.45/5.69 @ ^ [X8: nat] :
% 5.45/5.69 ( case_o7429725398727453821at_nat @ X4
% 5.45/5.69 @ ^ [Z6: nat] : ( some_nat @ ( sup_sup_nat @ X8 @ Z6 ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_option_def
% 5.45/5.69 thf(fact_2500_dflt__None__set__def,axiom,
% 5.45/5.69 ( dflt_N6592383573632408824at_nat
% 5.45/5.69 = ( ^ [S5: set_Pr1261947904930325089at_nat] : ( if_opt7704869406773131885at_nat @ ( S5 = bot_bo2099793752762293965at_nat ) @ none_s625347054029921090at_nat @ ( some_s147305329494351046at_nat @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % dflt_None_set_def
% 5.45/5.69 thf(fact_2501_dflt__None__set__def,axiom,
% 5.45/5.69 ( dflt_None_set_o
% 5.45/5.69 = ( ^ [S5: set_o] : ( if_option_set_o @ ( S5 = bot_bot_set_o ) @ none_set_o @ ( some_set_o @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % dflt_None_set_def
% 5.45/5.69 thf(fact_2502_dflt__None__set__def,axiom,
% 5.45/5.69 ( dflt_None_set_nat
% 5.45/5.69 = ( ^ [S5: set_nat] : ( if_option_set_nat @ ( S5 = bot_bot_set_nat ) @ none_set_nat @ ( some_set_nat @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % dflt_None_set_def
% 5.45/5.69 thf(fact_2503_dflt__None__set__def,axiom,
% 5.45/5.69 ( dflt_None_set_int
% 5.45/5.69 = ( ^ [S5: set_int] : ( if_option_set_int @ ( S5 = bot_bot_set_int ) @ none_set_int @ ( some_set_int @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % dflt_None_set_def
% 5.45/5.69 thf(fact_2504_times__assn__def,axiom,
% 5.45/5.69 ( times_times_assn
% 5.45/5.69 = ( ^ [P4: assn,Q3: assn] : ( abs_assn @ ( times_assn_raw @ ( rep_assn @ P4 ) @ ( rep_assn @ Q3 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % times_assn_def
% 5.45/5.69 thf(fact_2505_Set_Ois__empty__def,axiom,
% 5.45/5.69 ( is_emp1662574758705540307at_nat
% 5.45/5.69 = ( ^ [A6: set_Pr1261947904930325089at_nat] : ( A6 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Set.is_empty_def
% 5.45/5.69 thf(fact_2506_Set_Ois__empty__def,axiom,
% 5.45/5.69 ( is_empty_o
% 5.45/5.69 = ( ^ [A6: set_o] : ( A6 = bot_bot_set_o ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Set.is_empty_def
% 5.45/5.69 thf(fact_2507_Set_Ois__empty__def,axiom,
% 5.45/5.69 ( is_empty_nat
% 5.45/5.69 = ( ^ [A6: set_nat] : ( A6 = bot_bot_set_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Set.is_empty_def
% 5.45/5.69 thf(fact_2508_Set_Ois__empty__def,axiom,
% 5.45/5.69 ( is_empty_int
% 5.45/5.69 = ( ^ [A6: set_int] : ( A6 = bot_bot_set_int ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Set.is_empty_def
% 5.45/5.69 thf(fact_2509_hoare__triple__success,axiom,
% 5.45/5.69 ! [P: assn,C: heap_Time_Heap_a,Q: a > assn,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( hoare_hoare_triple_a @ P @ C @ Q )
% 5.45/5.69 => ( ( rep_assn @ P @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 => ( heap_Time_success_a @ C @ H ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % hoare_triple_success
% 5.45/5.69 thf(fact_2510_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.45/5.69 ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_le3146513528884898305at_nat @ B3
% 5.45/5.69 @ ( collec3392354462482085612at_nat
% 5.45/5.69 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2511_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_o,A3: set_o,P: $o > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_o @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_less_eq_set_o @ B3
% 5.45/5.69 @ ( collect_o
% 5.45/5.69 @ ^ [X4: $o] :
% 5.45/5.69 ( ( member_o @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: $o] :
% 5.45/5.69 ( ( member_o @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2512_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.45/5.69 ( ( ord_le2843351958646193337nt_int @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_le2843351958646193337nt_int @ B3
% 5.45/5.69 @ ( collec213857154873943460nt_int
% 5.45/5.69 @ ^ [X4: product_prod_int_int] :
% 5.45/5.69 ( ( member5262025264175285858nt_int @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: product_prod_int_int] :
% 5.45/5.69 ( ( member5262025264175285858nt_int @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2513_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_list_nat,A3: set_list_nat,P: list_nat > $o] :
% 5.45/5.69 ( ( ord_le6045566169113846134st_nat @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_le6045566169113846134st_nat @ B3
% 5.45/5.69 @ ( collect_list_nat
% 5.45/5.69 @ ^ [X4: list_nat] :
% 5.45/5.69 ( ( member_list_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: list_nat] :
% 5.45/5.69 ( ( member_list_nat @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2514_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_set_nat,A3: set_set_nat,P: set_nat > $o] :
% 5.45/5.69 ( ( ord_le6893508408891458716et_nat @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_le6893508408891458716et_nat @ B3
% 5.45/5.69 @ ( collect_set_nat
% 5.45/5.69 @ ^ [X4: set_nat] :
% 5.45/5.69 ( ( member_set_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: set_nat] :
% 5.45/5.69 ( ( member_set_nat @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2515_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_nat,A3: set_nat,P: nat > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_less_eq_set_nat @ B3
% 5.45/5.69 @ ( collect_nat
% 5.45/5.69 @ ^ [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2516_subset__Collect__iff,axiom,
% 5.45/5.69 ! [B3: set_int,A3: set_int,P: int > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.69 => ( ( ord_less_eq_set_int @ B3
% 5.45/5.69 @ ( collect_int
% 5.45/5.69 @ ^ [X4: int] :
% 5.45/5.69 ( ( member_int @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) )
% 5.45/5.69 = ( ! [X4: int] :
% 5.45/5.69 ( ( member_int @ X4 @ B3 )
% 5.45/5.69 => ( P @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_Collect_iff
% 5.45/5.69 thf(fact_2517_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,Q: product_prod_nat_nat > $o,P: product_prod_nat_nat > $o] :
% 5.45/5.69 ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_le3146513528884898305at_nat
% 5.45/5.69 @ ( collec3392354462482085612at_nat
% 5.45/5.69 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collec3392354462482085612at_nat
% 5.45/5.69 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2518_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_o,A3: set_o,Q: $o > $o,P: $o > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_o @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: $o] :
% 5.45/5.69 ( ( member_o @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_less_eq_set_o
% 5.45/5.69 @ ( collect_o
% 5.45/5.69 @ ^ [X4: $o] :
% 5.45/5.69 ( ( member_o @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collect_o
% 5.45/5.69 @ ^ [X4: $o] :
% 5.45/5.69 ( ( member_o @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2519_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_Pr958786334691620121nt_int,A3: set_Pr958786334691620121nt_int,Q: product_prod_int_int > $o,P: product_prod_int_int > $o] :
% 5.45/5.69 ( ( ord_le2843351958646193337nt_int @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: product_prod_int_int] :
% 5.45/5.69 ( ( member5262025264175285858nt_int @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_le2843351958646193337nt_int
% 5.45/5.69 @ ( collec213857154873943460nt_int
% 5.45/5.69 @ ^ [X4: product_prod_int_int] :
% 5.45/5.69 ( ( member5262025264175285858nt_int @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collec213857154873943460nt_int
% 5.45/5.69 @ ^ [X4: product_prod_int_int] :
% 5.45/5.69 ( ( member5262025264175285858nt_int @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2520_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_list_nat,A3: set_list_nat,Q: list_nat > $o,P: list_nat > $o] :
% 5.45/5.69 ( ( ord_le6045566169113846134st_nat @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: list_nat] :
% 5.45/5.69 ( ( member_list_nat @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_le6045566169113846134st_nat
% 5.45/5.69 @ ( collect_list_nat
% 5.45/5.69 @ ^ [X4: list_nat] :
% 5.45/5.69 ( ( member_list_nat @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collect_list_nat
% 5.45/5.69 @ ^ [X4: list_nat] :
% 5.45/5.69 ( ( member_list_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2521_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_set_nat,A3: set_set_nat,Q: set_nat > $o,P: set_nat > $o] :
% 5.45/5.69 ( ( ord_le6893508408891458716et_nat @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: set_nat] :
% 5.45/5.69 ( ( member_set_nat @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_le6893508408891458716et_nat
% 5.45/5.69 @ ( collect_set_nat
% 5.45/5.69 @ ^ [X4: set_nat] :
% 5.45/5.69 ( ( member_set_nat @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collect_set_nat
% 5.45/5.69 @ ^ [X4: set_nat] :
% 5.45/5.69 ( ( member_set_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2522_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_nat,A3: set_nat,Q: nat > $o,P: nat > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: nat] :
% 5.45/5.69 ( ( member_nat @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_less_eq_set_nat
% 5.45/5.69 @ ( collect_nat
% 5.45/5.69 @ ^ [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collect_nat
% 5.45/5.69 @ ^ [X4: nat] :
% 5.45/5.69 ( ( member_nat @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2523_subset__CollectI,axiom,
% 5.45/5.69 ! [B3: set_int,A3: set_int,Q: int > $o,P: int > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.69 => ( ! [X3: int] :
% 5.45/5.69 ( ( member_int @ X3 @ B3 )
% 5.45/5.69 => ( ( Q @ X3 )
% 5.45/5.69 => ( P @ X3 ) ) )
% 5.45/5.69 => ( ord_less_eq_set_int
% 5.45/5.69 @ ( collect_int
% 5.45/5.69 @ ^ [X4: int] :
% 5.45/5.69 ( ( member_int @ X4 @ B3 )
% 5.45/5.69 & ( Q @ X4 ) ) )
% 5.45/5.69 @ ( collect_int
% 5.45/5.69 @ ^ [X4: int] :
% 5.45/5.69 ( ( member_int @ X4 @ A3 )
% 5.45/5.69 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % subset_CollectI
% 5.45/5.69 thf(fact_2524_conj__subset__def,axiom,
% 5.45/5.69 ! [A3: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.69 ( ( ord_le2843351958646193337nt_int @ A3
% 5.45/5.69 @ ( collec213857154873943460nt_int
% 5.45/5.69 @ ^ [X4: product_prod_int_int] :
% 5.45/5.69 ( ( P @ X4 )
% 5.45/5.69 & ( Q @ X4 ) ) ) )
% 5.45/5.69 = ( ( ord_le2843351958646193337nt_int @ A3 @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.69 & ( ord_le2843351958646193337nt_int @ A3 @ ( collec213857154873943460nt_int @ Q ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % conj_subset_def
% 5.45/5.69 thf(fact_2525_conj__subset__def,axiom,
% 5.45/5.69 ! [A3: set_list_nat,P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.69 ( ( ord_le6045566169113846134st_nat @ A3
% 5.45/5.69 @ ( collect_list_nat
% 5.45/5.69 @ ^ [X4: list_nat] :
% 5.45/5.69 ( ( P @ X4 )
% 5.45/5.69 & ( Q @ X4 ) ) ) )
% 5.45/5.69 = ( ( ord_le6045566169113846134st_nat @ A3 @ ( collect_list_nat @ P ) )
% 5.45/5.69 & ( ord_le6045566169113846134st_nat @ A3 @ ( collect_list_nat @ Q ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % conj_subset_def
% 5.45/5.69 thf(fact_2526_conj__subset__def,axiom,
% 5.45/5.69 ! [A3: set_set_nat,P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.69 ( ( ord_le6893508408891458716et_nat @ A3
% 5.45/5.69 @ ( collect_set_nat
% 5.45/5.69 @ ^ [X4: set_nat] :
% 5.45/5.69 ( ( P @ X4 )
% 5.45/5.69 & ( Q @ X4 ) ) ) )
% 5.45/5.69 = ( ( ord_le6893508408891458716et_nat @ A3 @ ( collect_set_nat @ P ) )
% 5.45/5.69 & ( ord_le6893508408891458716et_nat @ A3 @ ( collect_set_nat @ Q ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % conj_subset_def
% 5.45/5.69 thf(fact_2527_conj__subset__def,axiom,
% 5.45/5.69 ! [A3: set_nat,P: nat > $o,Q: nat > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_nat @ A3
% 5.45/5.69 @ ( collect_nat
% 5.45/5.69 @ ^ [X4: nat] :
% 5.45/5.69 ( ( P @ X4 )
% 5.45/5.69 & ( Q @ X4 ) ) ) )
% 5.45/5.69 = ( ( ord_less_eq_set_nat @ A3 @ ( collect_nat @ P ) )
% 5.45/5.69 & ( ord_less_eq_set_nat @ A3 @ ( collect_nat @ Q ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % conj_subset_def
% 5.45/5.69 thf(fact_2528_conj__subset__def,axiom,
% 5.45/5.69 ! [A3: set_int,P: int > $o,Q: int > $o] :
% 5.45/5.69 ( ( ord_less_eq_set_int @ A3
% 5.45/5.69 @ ( collect_int
% 5.45/5.69 @ ^ [X4: int] :
% 5.45/5.69 ( ( P @ X4 )
% 5.45/5.69 & ( Q @ X4 ) ) ) )
% 5.45/5.69 = ( ( ord_less_eq_set_int @ A3 @ ( collect_int @ P ) )
% 5.45/5.69 & ( ord_less_eq_set_int @ A3 @ ( collect_int @ Q ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % conj_subset_def
% 5.45/5.69 thf(fact_2529_not__None__eq,axiom,
% 5.45/5.69 ! [X: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( X != none_P2651198173097904984it_nat )
% 5.45/5.69 = ( ? [Y4: produc3260487557148687353it_nat] :
% 5.45/5.69 ( X
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ Y4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_None_eq
% 5.45/5.69 thf(fact_2530_not__None__eq,axiom,
% 5.45/5.69 ! [X: option_num] :
% 5.45/5.69 ( ( X != none_num )
% 5.45/5.69 = ( ? [Y4: num] :
% 5.45/5.69 ( X
% 5.45/5.69 = ( some_num @ Y4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_None_eq
% 5.45/5.69 thf(fact_2531_not__None__eq,axiom,
% 5.45/5.69 ! [X: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( X != none_P9117596204409417319it_nat )
% 5.45/5.69 = ( ? [Y4: produc8664842809031399944it_nat] :
% 5.45/5.69 ( X
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ Y4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_None_eq
% 5.45/5.69 thf(fact_2532_not__Some__eq,axiom,
% 5.45/5.69 ! [X: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ! [Y4: produc3260487557148687353it_nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ Y4 ) ) )
% 5.45/5.69 = ( X = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq
% 5.45/5.69 thf(fact_2533_not__Some__eq,axiom,
% 5.45/5.69 ! [X: option_num] :
% 5.45/5.69 ( ( ! [Y4: num] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( some_num @ Y4 ) ) )
% 5.45/5.69 = ( X = none_num ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq
% 5.45/5.69 thf(fact_2534_not__Some__eq,axiom,
% 5.45/5.69 ! [X: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ! [Y4: produc8664842809031399944it_nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ Y4 ) ) )
% 5.45/5.69 = ( X = none_P9117596204409417319it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq
% 5.45/5.69 thf(fact_2535_Rep__assn__inverse,axiom,
% 5.45/5.69 ! [X: assn] :
% 5.45/5.69 ( ( abs_assn @ ( rep_assn @ X ) )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % Rep_assn_inverse
% 5.45/5.69 thf(fact_2536_less__eq__option__None__code,axiom,
% 5.45/5.69 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_None_code
% 5.45/5.69 thf(fact_2537_less__option__None,axiom,
% 5.45/5.69 ! [X: option_num] :
% 5.45/5.69 ~ ( ord_less_option_num @ X @ none_num ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_None
% 5.45/5.69 thf(fact_2538_less__eq__option__Some__None,axiom,
% 5.45/5.69 ! [X: num] :
% 5.45/5.69 ~ ( ord_le6622620407824499402on_num @ ( some_num @ X ) @ none_num ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_Some_None
% 5.45/5.69 thf(fact_2539_less__option__None__Some__code,axiom,
% 5.45/5.69 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_None_Some_code
% 5.45/5.69 thf(fact_2540_the__dflt__None__empty,axiom,
% 5.45/5.69 ( ( dflt_N6592383573632408824at_nat @ bot_bo2099793752762293965at_nat )
% 5.45/5.69 = none_s625347054029921090at_nat ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_empty
% 5.45/5.69 thf(fact_2541_the__dflt__None__empty,axiom,
% 5.45/5.69 ( ( dflt_None_set_o @ bot_bot_set_o )
% 5.45/5.69 = none_set_o ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_empty
% 5.45/5.69 thf(fact_2542_the__dflt__None__empty,axiom,
% 5.45/5.69 ( ( dflt_None_set_nat @ bot_bot_set_nat )
% 5.45/5.69 = none_set_nat ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_empty
% 5.45/5.69 thf(fact_2543_the__dflt__None__empty,axiom,
% 5.45/5.69 ( ( dflt_None_set_int @ bot_bot_set_int )
% 5.45/5.69 = none_set_int ) ).
% 5.45/5.69
% 5.45/5.69 % the_dflt_None_empty
% 5.45/5.69 thf(fact_2544_option_Osimps_I4_J,axiom,
% 5.45/5.69 ! [F1: int,F22: num > int] :
% 5.45/5.69 ( ( case_option_int_num @ F1 @ F22 @ none_num )
% 5.45/5.69 = F1 ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(4)
% 5.45/5.69 thf(fact_2545_option_Osimps_I4_J,axiom,
% 5.45/5.69 ! [F1: option_num,F22: num > option_num] :
% 5.45/5.69 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ none_num )
% 5.45/5.69 = F1 ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(4)
% 5.45/5.69 thf(fact_2546_option_Osimps_I4_J,axiom,
% 5.45/5.69 ! [F1: num,F22: num > num] :
% 5.45/5.69 ( ( case_option_num_num @ F1 @ F22 @ none_num )
% 5.45/5.69 = F1 ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(4)
% 5.45/5.69 thf(fact_2547_bot__option__def,axiom,
% 5.45/5.69 bot_bot_option_num = none_num ).
% 5.45/5.69
% 5.45/5.69 % bot_option_def
% 5.45/5.69 thf(fact_2548_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: int > int,F1: int,F22: num > int,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_int_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2549_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: int > option_num,F1: int,F22: num > int,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2550_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: int > num,F1: int,F22: num > int,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_int_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_num_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2551_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: option_num > int,F1: option_num,F22: num > option_num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_int_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2552_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: option_num > option_num,F1: option_num,F22: num > option_num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2553_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: option_num > num,F1: option_num,F22: num > option_num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_o6005452278849405969um_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_num_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2554_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: num > int,F1: num,F22: num > num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_int_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2555_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: num > option_num,F1: num,F22: num > num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_o6005452278849405969um_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2556_option_Ocase__distrib,axiom,
% 5.45/5.69 ! [H: num > num,F1: num,F22: num > num,Option: option_num] :
% 5.45/5.69 ( ( H @ ( case_option_num_num @ F1 @ F22 @ Option ) )
% 5.45/5.69 = ( case_option_num_num @ ( H @ F1 )
% 5.45/5.69 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.case_distrib
% 5.45/5.69 thf(fact_2557_option_Odistinct_I1_J,axiom,
% 5.45/5.69 ! [X2: produc3260487557148687353it_nat] :
% 5.45/5.69 ( none_P2651198173097904984it_nat
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.distinct(1)
% 5.45/5.69 thf(fact_2558_option_Odistinct_I1_J,axiom,
% 5.45/5.69 ! [X2: num] :
% 5.45/5.69 ( none_num
% 5.45/5.69 != ( some_num @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.distinct(1)
% 5.45/5.69 thf(fact_2559_option_Odistinct_I1_J,axiom,
% 5.45/5.69 ! [X2: produc8664842809031399944it_nat] :
% 5.45/5.69 ( none_P9117596204409417319it_nat
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.distinct(1)
% 5.45/5.69 thf(fact_2560_option_OdiscI,axiom,
% 5.45/5.69 ! [Option: option3562590408128118217it_nat,X2: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( Option
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ X2 ) )
% 5.45/5.69 => ( Option != none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.discI
% 5.45/5.69 thf(fact_2561_option_OdiscI,axiom,
% 5.45/5.69 ! [Option: option_num,X2: num] :
% 5.45/5.69 ( ( Option
% 5.45/5.69 = ( some_num @ X2 ) )
% 5.45/5.69 => ( Option != none_num ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.discI
% 5.45/5.69 thf(fact_2562_option_OdiscI,axiom,
% 5.45/5.69 ! [Option: option8956607266484857688it_nat,X2: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( Option
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ X2 ) )
% 5.45/5.69 => ( Option != none_P9117596204409417319it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.discI
% 5.45/5.69 thf(fact_2563_option_Oexhaust,axiom,
% 5.45/5.69 ! [Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( Y != none_P2651198173097904984it_nat )
% 5.45/5.69 => ~ ! [X22: produc3260487557148687353it_nat] :
% 5.45/5.69 ( Y
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ X22 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.exhaust
% 5.45/5.69 thf(fact_2564_option_Oexhaust,axiom,
% 5.45/5.69 ! [Y: option_num] :
% 5.45/5.69 ( ( Y != none_num )
% 5.45/5.69 => ~ ! [X22: num] :
% 5.45/5.69 ( Y
% 5.45/5.69 != ( some_num @ X22 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.exhaust
% 5.45/5.69 thf(fact_2565_option_Oexhaust,axiom,
% 5.45/5.69 ! [Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( Y != none_P9117596204409417319it_nat )
% 5.45/5.69 => ~ ! [X22: produc8664842809031399944it_nat] :
% 5.45/5.69 ( Y
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ X22 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.exhaust
% 5.45/5.69 thf(fact_2566_split__option__ex,axiom,
% 5.45/5.69 ( ( ^ [P5: option3562590408128118217it_nat > $o] :
% 5.45/5.69 ? [X5: option3562590408128118217it_nat] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option3562590408128118217it_nat > $o] :
% 5.45/5.69 ( ( P4 @ none_P2651198173097904984it_nat )
% 5.45/5.69 | ? [X4: produc3260487557148687353it_nat] : ( P4 @ ( some_P7913643980934408916it_nat @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_ex
% 5.45/5.69 thf(fact_2567_split__option__ex,axiom,
% 5.45/5.69 ( ( ^ [P5: option_num > $o] :
% 5.45/5.69 ? [X5: option_num] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option_num > $o] :
% 5.45/5.69 ( ( P4 @ none_num )
% 5.45/5.69 | ? [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_ex
% 5.45/5.69 thf(fact_2568_split__option__ex,axiom,
% 5.45/5.69 ( ( ^ [P5: option8956607266484857688it_nat > $o] :
% 5.45/5.69 ? [X5: option8956607266484857688it_nat] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option8956607266484857688it_nat > $o] :
% 5.45/5.69 ( ( P4 @ none_P9117596204409417319it_nat )
% 5.45/5.69 | ? [X4: produc8664842809031399944it_nat] : ( P4 @ ( some_P1914260805536162275it_nat @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_ex
% 5.45/5.69 thf(fact_2569_split__option__all,axiom,
% 5.45/5.69 ( ( ^ [P5: option3562590408128118217it_nat > $o] :
% 5.45/5.69 ! [X5: option3562590408128118217it_nat] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option3562590408128118217it_nat > $o] :
% 5.45/5.69 ( ( P4 @ none_P2651198173097904984it_nat )
% 5.45/5.69 & ! [X4: produc3260487557148687353it_nat] : ( P4 @ ( some_P7913643980934408916it_nat @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_all
% 5.45/5.69 thf(fact_2570_split__option__all,axiom,
% 5.45/5.69 ( ( ^ [P5: option_num > $o] :
% 5.45/5.69 ! [X5: option_num] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option_num > $o] :
% 5.45/5.69 ( ( P4 @ none_num )
% 5.45/5.69 & ! [X4: num] : ( P4 @ ( some_num @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_all
% 5.45/5.69 thf(fact_2571_split__option__all,axiom,
% 5.45/5.69 ( ( ^ [P5: option8956607266484857688it_nat > $o] :
% 5.45/5.69 ! [X5: option8956607266484857688it_nat] : ( P5 @ X5 ) )
% 5.45/5.69 = ( ^ [P4: option8956607266484857688it_nat > $o] :
% 5.45/5.69 ( ( P4 @ none_P9117596204409417319it_nat )
% 5.45/5.69 & ! [X4: produc8664842809031399944it_nat] : ( P4 @ ( some_P1914260805536162275it_nat @ X4 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % split_option_all
% 5.45/5.69 thf(fact_2572_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option3562590408128118217it_nat,P: option3562590408128118217it_nat > option3562590408128118217it_nat > $o,Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ( X = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc3260487557148687353it_nat,B4: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2573_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option3562590408128118217it_nat,P: option3562590408128118217it_nat > option_num > $o,Y: option_num] :
% 5.45/5.69 ( ( ( X = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc3260487557148687353it_nat,B4: num] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_num @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2574_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option3562590408128118217it_nat,P: option3562590408128118217it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ( X = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc3260487557148687353it_nat,B4: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2575_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option_num,P: option_num > option3562590408128118217it_nat > $o,Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ( X = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: num,B4: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_num @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2576_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.45/5.69 ( ( ( X = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: num,B4: num] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_num @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_num @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2577_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option_num,P: option_num > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ( X = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: num,B4: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_num @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2578_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option3562590408128118217it_nat > $o,Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ( X = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc8664842809031399944it_nat,B4: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2579_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option_num > $o,Y: option_num] :
% 5.45/5.69 ( ( ( X = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_num )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc8664842809031399944it_nat,B4: num] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_num @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2580_combine__options__cases,axiom,
% 5.45/5.69 ! [X: option8956607266484857688it_nat,P: option8956607266484857688it_nat > option8956607266484857688it_nat > $o,Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ( X = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ( ( Y = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( P @ X @ Y ) )
% 5.45/5.69 => ( ! [A4: produc8664842809031399944it_nat,B4: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ A4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ B4 ) )
% 5.45/5.69 => ( P @ X @ Y ) ) )
% 5.45/5.69 => ( P @ X @ Y ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % combine_options_cases
% 5.45/5.69 thf(fact_2581_less__eq__option__None,axiom,
% 5.45/5.69 ! [X: option_num] : ( ord_le6622620407824499402on_num @ none_num @ X ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_None
% 5.45/5.69 thf(fact_2582_less__eq__option__None__is__None,axiom,
% 5.45/5.69 ! [X: option_num] :
% 5.45/5.69 ( ( ord_le6622620407824499402on_num @ X @ none_num )
% 5.45/5.69 => ( X = none_num ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_None_is_None
% 5.45/5.69 thf(fact_2583_Abs__assn__eqI_I1_J,axiom,
% 5.45/5.69 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 5.45/5.69 ( ! [H4: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( P @ H4 )
% 5.45/5.69 = ( rep_assn @ Pr @ H4 ) )
% 5.45/5.69 => ( ( abs_assn @ P )
% 5.45/5.69 = Pr ) ) ).
% 5.45/5.69
% 5.45/5.69 % Abs_assn_eqI(1)
% 5.45/5.69 thf(fact_2584_Abs__assn__eqI_I2_J,axiom,
% 5.45/5.69 ! [P: produc3658429121746597890et_nat > $o,Pr: assn] :
% 5.45/5.69 ( ! [H4: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( P @ H4 )
% 5.45/5.69 = ( rep_assn @ Pr @ H4 ) )
% 5.45/5.69 => ( Pr
% 5.45/5.69 = ( abs_assn @ P ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Abs_assn_eqI(2)
% 5.45/5.69 thf(fact_2585_option_Osimps_I5_J,axiom,
% 5.45/5.69 ! [F1: int,F22: num > int,X2: num] :
% 5.45/5.69 ( ( case_option_int_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 5.45/5.69 = ( F22 @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(5)
% 5.45/5.69 thf(fact_2586_option_Osimps_I5_J,axiom,
% 5.45/5.69 ! [F1: option_num,F22: num > option_num,X2: num] :
% 5.45/5.69 ( ( case_o6005452278849405969um_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 5.45/5.69 = ( F22 @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(5)
% 5.45/5.69 thf(fact_2587_option_Osimps_I5_J,axiom,
% 5.45/5.69 ! [F1: num,F22: num > num,X2: num] :
% 5.45/5.69 ( ( case_option_num_num @ F1 @ F22 @ ( some_num @ X2 ) )
% 5.45/5.69 = ( F22 @ X2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.simps(5)
% 5.45/5.69 thf(fact_2588_the__default_Osimps_I2_J,axiom,
% 5.45/5.69 ! [X: num] :
% 5.45/5.69 ( ( the_default_num @ X @ none_num )
% 5.45/5.69 = X ) ).
% 5.45/5.69
% 5.45/5.69 % the_default.simps(2)
% 5.45/5.69 thf(fact_2589_inf__option__def,axiom,
% 5.45/5.69 ( inf_in7812914138253463912et_nat
% 5.45/5.69 = ( ^ [X4: option_set_nat,Y4: option_set_nat] :
% 5.45/5.69 ( case_o4054078431260844265et_nat @ none_set_nat
% 5.45/5.69 @ ^ [Z6: set_nat] :
% 5.45/5.69 ( case_o4054078431260844265et_nat @ none_set_nat
% 5.45/5.69 @ ^ [Aa: set_nat] : ( some_set_nat @ ( inf_inf_set_nat @ Z6 @ Aa ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_option_def
% 5.45/5.69 thf(fact_2590_inf__option__def,axiom,
% 5.45/5.69 ( inf_inf_option_assn
% 5.45/5.69 = ( ^ [X4: option_assn,Y4: option_assn] :
% 5.45/5.69 ( case_o4484465799723439917n_assn @ none_assn
% 5.45/5.69 @ ^ [Z6: assn] :
% 5.45/5.69 ( case_o4484465799723439917n_assn @ none_assn
% 5.45/5.69 @ ^ [Aa: assn] : ( some_assn @ ( inf_inf_assn @ Z6 @ Aa ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_option_def
% 5.45/5.69 thf(fact_2591_inf__option__def,axiom,
% 5.45/5.69 ( inf_inf_option_nat
% 5.45/5.69 = ( ^ [X4: option_nat,Y4: option_nat] :
% 5.45/5.69 ( case_o7429725398727453821at_nat @ none_nat
% 5.45/5.69 @ ^ [Z6: nat] :
% 5.45/5.69 ( case_o7429725398727453821at_nat @ none_nat
% 5.45/5.69 @ ^ [Aa: nat] : ( some_nat @ ( inf_inf_nat @ Z6 @ Aa ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_option_def
% 5.45/5.69 thf(fact_2592_inf__option__def,axiom,
% 5.45/5.69 ( inf_in5800606384722953409t_unit
% 5.45/5.69 = ( ^ [X4: option_Product_unit,Y4: option_Product_unit] :
% 5.45/5.69 ( case_o2985186191577459077t_unit @ none_Product_unit
% 5.45/5.69 @ ^ [Z6: product_unit] :
% 5.45/5.69 ( case_o2985186191577459077t_unit @ none_Product_unit
% 5.45/5.69 @ ^ [Aa: product_unit] : ( some_Product_unit @ ( inf_inf_Product_unit @ Z6 @ Aa ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_option_def
% 5.45/5.69 thf(fact_2593_inf__option__def,axiom,
% 5.45/5.69 ( inf_in777885744494410645at_nat
% 5.45/5.69 = ( ^ [X4: option8963830502488799655at_nat,Y4: option8963830502488799655at_nat] :
% 5.45/5.69 ( case_o311359030874850053at_nat @ none_s625347054029921090at_nat
% 5.45/5.69 @ ^ [Z6: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( case_o311359030874850053at_nat @ none_s625347054029921090at_nat
% 5.45/5.69 @ ^ [Aa: set_Pr1261947904930325089at_nat] : ( some_s147305329494351046at_nat @ ( inf_in2572325071724192079at_nat @ Z6 @ Aa ) )
% 5.45/5.69 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_option_def
% 5.45/5.69 thf(fact_2594_bot__assn__def,axiom,
% 5.45/5.69 ( bot_bot_assn
% 5.45/5.69 = ( abs_assn
% 5.45/5.69 @ ^ [Uu2: produc3658429121746597890et_nat] : $false ) ) ).
% 5.45/5.69
% 5.45/5.69 % bot_assn_def
% 5.45/5.69 thf(fact_2595_less__option__None__is__Some,axiom,
% 5.45/5.69 ! [X: option_num] :
% 5.45/5.69 ( ( ord_less_option_num @ none_num @ X )
% 5.45/5.69 => ? [Z2: num] :
% 5.45/5.69 ( X
% 5.45/5.69 = ( some_num @ Z2 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_None_is_Some
% 5.45/5.69 thf(fact_2596_less__option__None__Some,axiom,
% 5.45/5.69 ! [X: num] : ( ord_less_option_num @ none_num @ ( some_num @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_None_Some
% 5.45/5.69 thf(fact_2597_sup__assn__def,axiom,
% 5.45/5.69 ( sup_sup_assn
% 5.45/5.69 = ( ^ [P4: assn,Q3: assn] :
% 5.45/5.69 ( abs_assn
% 5.45/5.69 @ ^ [H6: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( rep_assn @ P4 @ H6 )
% 5.45/5.69 | ( rep_assn @ Q3 @ H6 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % sup_assn_def
% 5.45/5.69 thf(fact_2598_inf__assn__def,axiom,
% 5.45/5.69 ( inf_inf_assn
% 5.45/5.69 = ( ^ [P4: assn,Q3: assn] :
% 5.45/5.69 ( abs_assn
% 5.45/5.69 @ ^ [H6: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( rep_assn @ P4 @ H6 )
% 5.45/5.69 & ( rep_assn @ Q3 @ H6 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % inf_assn_def
% 5.45/5.69 thf(fact_2599_successE,axiom,
% 5.45/5.69 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( heap_T584514906347983379t_unit @ F @ H )
% 5.45/5.69 => ~ ! [R2: product_unit,H5: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ H5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % successE
% 5.45/5.69 thf(fact_2600_successE,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( heap_Time_success_a @ F @ H )
% 5.45/5.69 => ~ ! [R2: a,H5: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ H5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % successE
% 5.45/5.69 thf(fact_2601_rel__of__empty,axiom,
% 5.45/5.69 ! [P: product_prod_nat_nat > $o] :
% 5.45/5.69 ( ( rel_of_nat_nat
% 5.45/5.69 @ ^ [X4: nat] : none_nat
% 5.45/5.69 @ P )
% 5.45/5.69 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.69
% 5.45/5.69 % rel_of_empty
% 5.45/5.69 thf(fact_2602_set__to__map__empty,axiom,
% 5.45/5.69 ( ( set_to_map_nat_nat @ bot_bo2099793752762293965at_nat )
% 5.45/5.69 = ( ^ [X4: nat] : none_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_empty
% 5.45/5.69 thf(fact_2603_map__to__set__empty,axiom,
% 5.45/5.69 ( ( map_to_set_nat_nat
% 5.45/5.69 @ ^ [X4: nat] : none_nat )
% 5.45/5.69 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.69
% 5.45/5.69 % map_to_set_empty
% 5.45/5.69 thf(fact_2604_disjE__realizer2,axiom,
% 5.45/5.69 ! [P: $o,Q: num > $o,X: option_num,R: int > $o,F: int,G: num > int] :
% 5.45/5.69 ( ( case_option_o_num @ P @ Q @ X )
% 5.45/5.69 => ( ( P
% 5.45/5.69 => ( R @ F ) )
% 5.45/5.69 => ( ! [Q5: num] :
% 5.45/5.69 ( ( Q @ Q5 )
% 5.45/5.69 => ( R @ ( G @ Q5 ) ) )
% 5.45/5.69 => ( R @ ( case_option_int_num @ F @ G @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % disjE_realizer2
% 5.45/5.69 thf(fact_2605_disjE__realizer2,axiom,
% 5.45/5.69 ! [P: $o,Q: num > $o,X: option_num,R: option_num > $o,F: option_num,G: num > option_num] :
% 5.45/5.69 ( ( case_option_o_num @ P @ Q @ X )
% 5.45/5.69 => ( ( P
% 5.45/5.69 => ( R @ F ) )
% 5.45/5.69 => ( ! [Q5: num] :
% 5.45/5.69 ( ( Q @ Q5 )
% 5.45/5.69 => ( R @ ( G @ Q5 ) ) )
% 5.45/5.69 => ( R @ ( case_o6005452278849405969um_num @ F @ G @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % disjE_realizer2
% 5.45/5.69 thf(fact_2606_disjE__realizer2,axiom,
% 5.45/5.69 ! [P: $o,Q: num > $o,X: option_num,R: num > $o,F: num,G: num > num] :
% 5.45/5.69 ( ( case_option_o_num @ P @ Q @ X )
% 5.45/5.69 => ( ( P
% 5.45/5.69 => ( R @ F ) )
% 5.45/5.69 => ( ! [Q5: num] :
% 5.45/5.69 ( ( Q @ Q5 )
% 5.45/5.69 => ( R @ ( G @ Q5 ) ) )
% 5.45/5.69 => ( R @ ( case_option_num_num @ F @ G @ X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % disjE_realizer2
% 5.45/5.69 thf(fact_2607_pure__assn__def,axiom,
% 5.45/5.69 ( pure_assn
% 5.45/5.69 = ( ^ [B5: $o] : ( abs_assn @ ( pure_a825153325127701367it_nat @ B5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_def
% 5.45/5.69 thf(fact_2608_set__to__map__empty__iff_I2_J,axiom,
% 5.45/5.69 ! [S: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( ( ^ [X4: nat] : none_nat )
% 5.45/5.69 = ( set_to_map_nat_nat @ S ) )
% 5.45/5.69 = ( S = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_empty_iff(2)
% 5.45/5.69 thf(fact_2609_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option5190343406534369742et_nat] :
% 5.45/5.69 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3658429121746597890et_nat] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P750831030444334937et_nat @ ( produc5001842942810119800et_nat @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P4972525538344268765et_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2610_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option2860828798490689354et_nat] :
% 5.45/5.69 ( ( ! [X4: produc3658429121746597890et_nat > $o,Y4: produc3925858234332021118et_nat] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P1630309045189364437et_nat @ ( produc2245416461498447860et_nat @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P199884684680593241et_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2611_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option7541221861074943443nt_int] :
% 5.45/5.69 ( ( ! [X4: produc8551481072490612790e_term > option6357759511663192854e_term,Y4: product_prod_int_int] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P2355398578364412894nt_int @ ( produc5700946648718959541nt_int @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P1286213070022356066nt_int ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2612_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option4256020574406277085nt_int] :
% 5.45/5.69 ( ( ! [X4: int > option6357759511663192854e_term,Y4: product_prod_int_int] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P7455497367792166888nt_int @ ( produc4305682042979456191nt_int @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P3773570700014501484nt_int ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2613_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ! [X4: a,Y4: produc6653097349344004940it_nat] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2614_not__Some__eq2,axiom,
% 5.45/5.69 ! [V: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ! [X4: product_unit,Y4: produc6653097349344004940it_nat] :
% 5.45/5.69 ( V
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X4 @ Y4 ) ) ) )
% 5.45/5.69 = ( V = none_P9117596204409417319it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % not_Some_eq2
% 5.45/5.69 thf(fact_2615_execute__bind_I2_J,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,G: a > heap_Time_Heap_a] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 5.45/5.69 = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind(2)
% 5.45/5.69 thf(fact_2616_option_Odisc__eq__case_I2_J,axiom,
% 5.45/5.69 ! [Option: option_num] :
% 5.45/5.69 ( ( Option != none_num )
% 5.45/5.69 = ( case_option_o_num @ $false
% 5.45/5.69 @ ^ [Uu2: num] : $true
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.disc_eq_case(2)
% 5.45/5.69 thf(fact_2617_option_Odisc__eq__case_I1_J,axiom,
% 5.45/5.69 ! [Option: option_num] :
% 5.45/5.69 ( ( Option = none_num )
% 5.45/5.69 = ( case_option_o_num @ $true
% 5.45/5.69 @ ^ [Uu2: num] : $false
% 5.45/5.69 @ Option ) ) ).
% 5.45/5.69
% 5.45/5.69 % option.disc_eq_case(1)
% 5.45/5.69 thf(fact_2618_success__def,axiom,
% 5.45/5.69 ( heap_Time_success_a
% 5.45/5.69 = ( ^ [F3: heap_Time_Heap_a,H6: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( heap_Time_execute_a @ F3 @ H6 )
% 5.45/5.69 != none_P2651198173097904984it_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % success_def
% 5.45/5.69 thf(fact_2619_successI,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 != none_P2651198173097904984it_nat )
% 5.45/5.69 => ( heap_Time_success_a @ F @ H ) ) ).
% 5.45/5.69
% 5.45/5.69 % successI
% 5.45/5.69 thf(fact_2620_case__optionE,axiom,
% 5.45/5.69 ! [P: $o,Q: produc3260487557148687353it_nat > $o,X: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( case_o3267218206291580230it_nat @ P @ Q @ X )
% 5.45/5.69 => ( ( ( X = none_P2651198173097904984it_nat )
% 5.45/5.69 => ~ P )
% 5.45/5.69 => ~ ! [Y3: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ Y3 ) )
% 5.45/5.69 => ~ ( Q @ Y3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % case_optionE
% 5.45/5.69 thf(fact_2621_case__optionE,axiom,
% 5.45/5.69 ! [P: $o,Q: num > $o,X: option_num] :
% 5.45/5.69 ( ( case_option_o_num @ P @ Q @ X )
% 5.45/5.69 => ( ( ( X = none_num )
% 5.45/5.69 => ~ P )
% 5.45/5.69 => ~ ! [Y3: num] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_num @ Y3 ) )
% 5.45/5.69 => ~ ( Q @ Y3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % case_optionE
% 5.45/5.69 thf(fact_2622_case__optionE,axiom,
% 5.45/5.69 ! [P: $o,Q: produc8664842809031399944it_nat > $o,X: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( case_o2686588417244861013it_nat @ P @ Q @ X )
% 5.45/5.69 => ( ( ( X = none_P9117596204409417319it_nat )
% 5.45/5.69 => ~ P )
% 5.45/5.69 => ~ ! [Y3: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( X
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ Y3 ) )
% 5.45/5.69 => ~ ( Q @ Y3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % case_optionE
% 5.45/5.69 thf(fact_2623_map__to__set__empty__iff_I1_J,axiom,
% 5.45/5.69 ! [M: nat > option_nat] :
% 5.45/5.69 ( ( ( map_to_set_nat_nat @ M )
% 5.45/5.69 = bot_bo2099793752762293965at_nat )
% 5.45/5.69 = ( M
% 5.45/5.69 = ( ^ [X4: nat] : none_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % map_to_set_empty_iff(1)
% 5.45/5.69 thf(fact_2624_map__to__set__empty__iff_I2_J,axiom,
% 5.45/5.69 ! [M: nat > option_nat] :
% 5.45/5.69 ( ( bot_bo2099793752762293965at_nat
% 5.45/5.69 = ( map_to_set_nat_nat @ M ) )
% 5.45/5.69 = ( M
% 5.45/5.69 = ( ^ [X4: nat] : none_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % map_to_set_empty_iff(2)
% 5.45/5.69 thf(fact_2625_less__eq__option__def,axiom,
% 5.45/5.69 ( ord_le353528952715127954et_int
% 5.45/5.69 = ( ^ [X4: option_set_int,Y4: option_set_int] :
% 5.45/5.69 ( case_o223999843215110191et_int @ $true
% 5.45/5.69 @ ^ [Z6: set_int] : ( case_o223999843215110191et_int @ $false @ ( ord_less_eq_set_int @ Z6 ) @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_def
% 5.45/5.69 thf(fact_2626_less__eq__option__def,axiom,
% 5.45/5.69 ( ord_le2406147912482264968on_rat
% 5.45/5.69 = ( ^ [X4: option_rat,Y4: option_rat] :
% 5.45/5.69 ( case_option_o_rat @ $true
% 5.45/5.69 @ ^ [Z6: rat] : ( case_option_o_rat @ $false @ ( ord_less_eq_rat @ Z6 ) @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_def
% 5.45/5.69 thf(fact_2627_less__eq__option__def,axiom,
% 5.45/5.69 ( ord_le6622620407824499402on_num
% 5.45/5.69 = ( ^ [X4: option_num,Y4: option_num] :
% 5.45/5.69 ( case_option_o_num @ $true
% 5.45/5.69 @ ^ [Z6: num] : ( case_option_o_num @ $false @ ( ord_less_eq_num @ Z6 ) @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_def
% 5.45/5.69 thf(fact_2628_less__eq__option__def,axiom,
% 5.45/5.69 ( ord_le5914376470875661696on_nat
% 5.45/5.69 = ( ^ [X4: option_nat,Y4: option_nat] :
% 5.45/5.69 ( case_option_o_nat @ $true
% 5.45/5.69 @ ^ [Z6: nat] : ( case_option_o_nat @ $false @ ( ord_less_eq_nat @ Z6 ) @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_def
% 5.45/5.69 thf(fact_2629_less__eq__option__def,axiom,
% 5.45/5.69 ( ord_le1736525451366464988on_int
% 5.45/5.69 = ( ^ [X4: option_int,Y4: option_int] :
% 5.45/5.69 ( case_option_o_int @ $true
% 5.45/5.69 @ ^ [Z6: int] : ( case_option_o_int @ $false @ ( ord_less_eq_int @ Z6 ) @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_eq_option_def
% 5.45/5.69 thf(fact_2630_less__option__def,axiom,
% 5.45/5.69 ( ord_less_option_assn
% 5.45/5.69 = ( ^ [X4: option_assn] :
% 5.45/5.69 ( case_option_o_assn @ $false
% 5.45/5.69 @ ^ [Y4: assn] :
% 5.45/5.69 ( case_option_o_assn @ $true
% 5.45/5.69 @ ^ [Z6: assn] : ( ord_less_assn @ Z6 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_def
% 5.45/5.69 thf(fact_2631_less__option__def,axiom,
% 5.45/5.69 ( ord_less_option_rat
% 5.45/5.69 = ( ^ [X4: option_rat] :
% 5.45/5.69 ( case_option_o_rat @ $false
% 5.45/5.69 @ ^ [Y4: rat] :
% 5.45/5.69 ( case_option_o_rat @ $true
% 5.45/5.69 @ ^ [Z6: rat] : ( ord_less_rat @ Z6 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_def
% 5.45/5.69 thf(fact_2632_less__option__def,axiom,
% 5.45/5.69 ( ord_less_option_num
% 5.45/5.69 = ( ^ [X4: option_num] :
% 5.45/5.69 ( case_option_o_num @ $false
% 5.45/5.69 @ ^ [Y4: num] :
% 5.45/5.69 ( case_option_o_num @ $true
% 5.45/5.69 @ ^ [Z6: num] : ( ord_less_num @ Z6 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_def
% 5.45/5.69 thf(fact_2633_less__option__def,axiom,
% 5.45/5.69 ( ord_less_option_nat
% 5.45/5.69 = ( ^ [X4: option_nat] :
% 5.45/5.69 ( case_option_o_nat @ $false
% 5.45/5.69 @ ^ [Y4: nat] :
% 5.45/5.69 ( case_option_o_nat @ $true
% 5.45/5.69 @ ^ [Z6: nat] : ( ord_less_nat @ Z6 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_def
% 5.45/5.69 thf(fact_2634_less__option__def,axiom,
% 5.45/5.69 ( ord_less_option_int
% 5.45/5.69 = ( ^ [X4: option_int] :
% 5.45/5.69 ( case_option_o_int @ $false
% 5.45/5.69 @ ^ [Y4: int] :
% 5.45/5.69 ( case_option_o_int @ $true
% 5.45/5.69 @ ^ [Z6: int] : ( ord_less_int @ Z6 @ Y4 )
% 5.45/5.69 @ X4 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_option_def
% 5.45/5.69 thf(fact_2635_Heap__cases,axiom,
% 5.45/5.69 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ! [X3: product_unit,H5: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X3 @ H5 ) ) )
% 5.45/5.69 => ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 = none_P9117596204409417319it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % Heap_cases
% 5.45/5.69 thf(fact_2636_Heap__cases,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.69 ( ! [X3: a,H5: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X3 @ H5 ) ) )
% 5.45/5.69 => ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % Heap_cases
% 5.45/5.69 thf(fact_2637_timeFrame_Ocases,axiom,
% 5.45/5.69 ! [X: produc4453839368661128058it_nat] :
% 5.45/5.69 ( ! [N5: nat,R2: a,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( produc4111269673004989362it_nat @ N5 @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) ) )
% 5.45/5.69 => ~ ! [N5: nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( produc4111269673004989362it_nat @ N5 @ none_P2651198173097904984it_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.cases
% 5.45/5.69 thf(fact_2638_timeFrame_Ocases,axiom,
% 5.45/5.69 ! [X: produc3911288613690379145it_nat] :
% 5.45/5.69 ( ! [N5: nat,R2: product_unit,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( produc638857205735767105it_nat @ N5 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) ) )
% 5.45/5.69 => ~ ! [N5: nat] :
% 5.45/5.69 ( X
% 5.45/5.69 != ( produc638857205735767105it_nat @ N5 @ none_P9117596204409417319it_nat ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.cases
% 5.45/5.69 thf(fact_2639_set__to__map__empty__iff_I1_J,axiom,
% 5.45/5.69 ! [S: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( ( set_to_map_nat_nat @ S )
% 5.45/5.69 = ( ^ [X4: nat] : none_nat ) )
% 5.45/5.69 = ( S = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_empty_iff(1)
% 5.45/5.69 thf(fact_2640_pure__assn__raw_Oelims_I3_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.elims(3)
% 5.45/5.69 thf(fact_2641_pure__assn__raw_Oelims_I2_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ~ ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.elims(2)
% 5.45/5.69 thf(fact_2642_pure__assn__raw_Oelims_I1_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( Y
% 5.45/5.69 = ( ~ ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.elims(1)
% 5.45/5.69 thf(fact_2643_pure__assn__raw_Osimps,axiom,
% 5.45/5.69 ! [B: $o,H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.69 ( ( pure_a825153325127701367it_nat @ B @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.69 = ( ( As = bot_bot_set_nat )
% 5.45/5.69 & B ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.simps
% 5.45/5.69 thf(fact_2644_pure__assn__raw_Opelims_I1_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.69 ( ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) )
% 5.45/5.69 => ~ ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.pelims(1)
% 5.45/5.69 thf(fact_2645_pure__assn__raw_Opelims_I2_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) )
% 5.45/5.69 => ~ ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.pelims(2)
% 5.45/5.69 thf(fact_2646_pure__assn__raw_Opelims_I3_J,axiom,
% 5.45/5.69 ! [X: $o,Xa: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ~ ( pure_a825153325127701367it_nat @ X @ Xa )
% 5.45/5.69 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ Xa ) )
% 5.45/5.69 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.69 => ( ( accp_P8458817951426537472et_nat @ pure_a6022498039421069578it_nat @ ( produc3762353314782720579et_nat @ X @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) )
% 5.45/5.69 => ( ( As4 = bot_bot_set_nat )
% 5.45/5.69 & X ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % pure_assn_raw.pelims(3)
% 5.45/5.69 thf(fact_2647_execute__bind_I1_J,axiom,
% 5.45/5.69 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_a] :
% 5.45/5.69 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ H )
% 5.45/5.69 = ( heap_T7616092557645711335rame_a @ N2 @ ( heap_Time_execute_a @ ( G @ X ) @ H3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind(1)
% 5.45/5.69 thf(fact_2648_execute__bind_I1_J,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H3: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_a] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 5.45/5.69 = ( heap_T7616092557645711335rame_a @ N2 @ ( heap_Time_execute_a @ ( G @ X ) @ H3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind(1)
% 5.45/5.69 thf(fact_2649_execute__bind__eq__SomeI,axiom,
% 5.45/5.69 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_T5738788834812785303t_unit,Y: product_unit,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H3 )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 5.45/5.69 => ( ( heap_T875086893843062177t_unit @ ( heap_T2633723481742716231t_unit @ F @ G ) @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind_eq_SomeI
% 5.45/5.69 thf(fact_2650_execute__bind__eq__SomeI,axiom,
% 5.45/5.69 ! [F: heap_T5738788834812785303t_unit,H: heap_e7401611519738050253t_unit,X: product_unit,H3: heap_e7401611519738050253t_unit,N2: nat,G: product_unit > heap_Time_Heap_a,Y: a,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( ( heap_T875086893843062177t_unit @ F @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( ( heap_Time_execute_a @ ( G @ X ) @ H3 )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_T757603679106148408unit_a @ F @ G ) @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind_eq_SomeI
% 5.45/5.69 thf(fact_2651_execute__bind__eq__SomeI,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H3: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_T5738788834812785303t_unit,Y: product_unit,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( ( heap_T875086893843062177t_unit @ ( G @ X ) @ H3 )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 5.45/5.69 => ( ( heap_T875086893843062177t_unit @ ( heap_T8685611227969916822t_unit @ F @ G ) @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind_eq_SomeI
% 5.45/5.69 thf(fact_2652_execute__bind__eq__SomeI,axiom,
% 5.45/5.69 ! [F: heap_Time_Heap_a,H: heap_e7401611519738050253t_unit,X: a,H3: heap_e7401611519738050253t_unit,N2: nat,G: a > heap_Time_Heap_a,Y: a,H9: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( ( heap_Time_execute_a @ F @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H3 @ N2 ) ) ) )
% 5.45/5.69 => ( ( ( heap_Time_execute_a @ ( G @ X ) @ H3 )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ N6 ) ) ) )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ Y @ ( produc584006145561248582it_nat @ H9 @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_bind_eq_SomeI
% 5.45/5.69 thf(fact_2653_set__to__map__def,axiom,
% 5.45/5.69 ( set_to_map_nat_nat
% 5.45/5.69 = ( ^ [S5: set_Pr1261947904930325089at_nat,K3: nat] :
% 5.45/5.69 ( eps_Opt_nat
% 5.45/5.69 @ ^ [V2: nat] : ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2654_set__to__map__def,axiom,
% 5.45/5.69 ( set_to6040779677306527128et_nat
% 5.45/5.69 = ( ^ [S5: set_Pr3286484037609594932et_nat,K3: produc3658429121746597890et_nat > $o] :
% 5.45/5.69 ( eps_Op2013419657081471078et_nat
% 5.45/5.69 @ ^ [V2: produc3658429121746597890et_nat] : ( member1996754912294343701et_nat @ ( produc5001842942810119800et_nat @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2655_set__to__map__def,axiom,
% 5.45/5.69 ( set_to2047380710992656148et_nat
% 5.45/5.69 = ( ^ [S5: set_Pr8536935166611901872et_nat,K3: produc3658429121746597890et_nat > $o] :
% 5.45/5.69 ( eps_Op6423059015816587746et_nat
% 5.45/5.69 @ ^ [V2: produc3925858234332021118et_nat] : ( member6124377750444531601et_nat @ ( produc2245416461498447860et_nat @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2656_set__to__map__def,axiom,
% 5.45/5.69 ( set_to6585427216324510421nt_int
% 5.45/5.69 = ( ^ [S5: set_Pr9222295170931077689nt_int,K3: produc8551481072490612790e_term > option6357759511663192854e_term] :
% 5.45/5.69 ( eps_Op2446201859369042517nt_int
% 5.45/5.69 @ ^ [V2: product_prod_int_int] : ( member7618704894036264090nt_int @ ( produc5700946648718959541nt_int @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2657_set__to__map__def,axiom,
% 5.45/5.69 ( set_to1653371902132773855nt_int
% 5.45/5.69 = ( ^ [S5: set_Pr1872883991513573699nt_int,K3: int > option6357759511663192854e_term] :
% 5.45/5.69 ( eps_Op2446201859369042517nt_int
% 5.45/5.69 @ ^ [V2: product_prod_int_int] : ( member7034335876925520548nt_int @ ( produc4305682042979456191nt_int @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2658_set__to__map__def,axiom,
% 5.45/5.69 ( set_to2008915276733485075it_nat
% 5.45/5.69 = ( ^ [S5: set_Pr7098220151150636591it_nat,K3: a] :
% 5.45/5.69 ( eps_Op8301357815426737072it_nat
% 5.45/5.69 @ ^ [V2: produc6653097349344004940it_nat] : ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ K3 @ V2 ) @ S5 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % set_to_map_def
% 5.45/5.69 thf(fact_2659_execute__guard_I2_J,axiom,
% 5.45/5.69 ! [P: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( P @ H )
% 5.45/5.69 => ( ( heap_T875086893843062177t_unit @ ( heap_T8440541562793052209t_unit @ P @ F ) @ H )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( F @ H ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_guard(2)
% 5.45/5.69 thf(fact_2660_execute__guard_I2_J,axiom,
% 5.45/5.69 ! [P: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( P @ H )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_Time_guard_a @ P @ F ) @ H )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( F @ H ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_guard(2)
% 5.45/5.69 thf(fact_2661_mlex__leq,axiom,
% 5.45/5.69 ! [F: nat > nat,X: nat,Y: nat,R: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ ( F @ X ) @ ( F @ Y ) )
% 5.45/5.69 => ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R )
% 5.45/5.69 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % mlex_leq
% 5.45/5.69 thf(fact_2662_curryI,axiom,
% 5.45/5.69 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 5.45/5.69 => ( produc6216949301066131538_nat_o @ F @ A @ B ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryI
% 5.45/5.69 thf(fact_2663_curryI,axiom,
% 5.45/5.69 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 5.45/5.69 ( ( F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 5.45/5.69 => ( produc5101573711933517782_nat_o @ F @ A @ B ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryI
% 5.45/5.69 thf(fact_2664_curryI,axiom,
% 5.45/5.69 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 5.45/5.69 => ( produc730925184835016917_int_o @ F @ A @ B ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryI
% 5.45/5.69 thf(fact_2665_curryI,axiom,
% 5.45/5.69 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 5.45/5.69 => ( produc9098658269643458507_int_o @ F @ A @ B ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryI
% 5.45/5.69 thf(fact_2666_curryI,axiom,
% 5.45/5.69 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( F @ ( produc9178034014595674355it_nat @ A @ B ) )
% 5.45/5.69 => ( produc3709033845735585303_nat_o @ F @ A @ B ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryI
% 5.45/5.69 thf(fact_2667_nat__add__left__cancel__less,axiom,
% 5.45/5.69 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.45/5.69 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % nat_add_left_cancel_less
% 5.45/5.69 thf(fact_2668_nat__add__left__cancel__le,axiom,
% 5.45/5.69 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.45/5.69 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % nat_add_left_cancel_le
% 5.45/5.69 thf(fact_2669_some__opt__sym__eq__trivial,axiom,
% 5.45/5.69 ! [X: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( eps_Op1741419982095519837it_nat
% 5.45/5.69 @ ( ^ [Y5: produc3260487557148687353it_nat,Z3: produc3260487557148687353it_nat] : ( Y5 = Z3 )
% 5.45/5.69 @ X ) )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_sym_eq_trivial
% 5.45/5.69 thf(fact_2670_some__opt__sym__eq__trivial,axiom,
% 5.45/5.69 ! [X: num] :
% 5.45/5.69 ( ( eps_Opt_num
% 5.45/5.69 @ ( ^ [Y5: num,Z3: num] : ( Y5 = Z3 )
% 5.45/5.69 @ X ) )
% 5.45/5.69 = ( some_num @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_sym_eq_trivial
% 5.45/5.69 thf(fact_2671_some__opt__sym__eq__trivial,axiom,
% 5.45/5.69 ! [X: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( eps_Op3393321821070424684it_nat
% 5.45/5.69 @ ( ^ [Y5: produc8664842809031399944it_nat,Z3: produc8664842809031399944it_nat] : ( Y5 = Z3 )
% 5.45/5.69 @ X ) )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_sym_eq_trivial
% 5.45/5.69 thf(fact_2672_some__opt__eq__trivial,axiom,
% 5.45/5.69 ! [X: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( eps_Op1741419982095519837it_nat
% 5.45/5.69 @ ^ [Y4: produc3260487557148687353it_nat] : ( Y4 = X ) )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_eq_trivial
% 5.45/5.69 thf(fact_2673_some__opt__eq__trivial,axiom,
% 5.45/5.69 ! [X: num] :
% 5.45/5.69 ( ( eps_Opt_num
% 5.45/5.69 @ ^ [Y4: num] : ( Y4 = X ) )
% 5.45/5.69 = ( some_num @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_eq_trivial
% 5.45/5.69 thf(fact_2674_some__opt__eq__trivial,axiom,
% 5.45/5.69 ! [X: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( eps_Op3393321821070424684it_nat
% 5.45/5.69 @ ^ [Y4: produc8664842809031399944it_nat] : ( Y4 = X ) )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_eq_trivial
% 5.45/5.69 thf(fact_2675_some__opt__false__trivial,axiom,
% 5.45/5.69 ( ( eps_Opt_num
% 5.45/5.69 @ ^ [Uu2: num] : $false )
% 5.45/5.69 = none_num ) ).
% 5.45/5.69
% 5.45/5.69 % some_opt_false_trivial
% 5.45/5.69 thf(fact_2676_add__lessD1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.69 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.45/5.69 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_lessD1
% 5.45/5.69 thf(fact_2677_add__less__mono,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.69 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.69 => ( ( ord_less_nat @ K @ L )
% 5.45/5.69 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_less_mono
% 5.45/5.69 thf(fact_2678_not__add__less1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat] :
% 5.45/5.69 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.45/5.69
% 5.45/5.69 % not_add_less1
% 5.45/5.69 thf(fact_2679_not__add__less2,axiom,
% 5.45/5.69 ! [J: nat,I2: nat] :
% 5.45/5.69 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.45/5.69
% 5.45/5.69 % not_add_less2
% 5.45/5.69 thf(fact_2680_add__less__mono1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.69 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_less_mono1
% 5.45/5.69 thf(fact_2681_trans__less__add1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,M: nat] :
% 5.45/5.69 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % trans_less_add1
% 5.45/5.69 thf(fact_2682_trans__less__add2,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,M: nat] :
% 5.45/5.69 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % trans_less_add2
% 5.45/5.69 thf(fact_2683_less__add__eq__less,axiom,
% 5.45/5.69 ! [K: nat,L: nat,M: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_nat @ K @ L )
% 5.45/5.69 => ( ( ( plus_plus_nat @ M @ L )
% 5.45/5.69 = ( plus_plus_nat @ K @ N2 ) )
% 5.45/5.69 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % less_add_eq_less
% 5.45/5.69 thf(fact_2684_add__leE,axiom,
% 5.45/5.69 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.45/5.69 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.69 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_leE
% 5.45/5.69 thf(fact_2685_le__add1,axiom,
% 5.45/5.69 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 5.45/5.69
% 5.45/5.69 % le_add1
% 5.45/5.69 thf(fact_2686_le__add2,axiom,
% 5.45/5.69 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % le_add2
% 5.45/5.69 thf(fact_2687_add__leD1,axiom,
% 5.45/5.69 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.45/5.69 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_leD1
% 5.45/5.69 thf(fact_2688_add__leD2,axiom,
% 5.45/5.69 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.45/5.69 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_leD2
% 5.45/5.69 thf(fact_2689_le__Suc__ex,axiom,
% 5.45/5.69 ! [K: nat,L: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ K @ L )
% 5.45/5.69 => ? [N5: nat] :
% 5.45/5.69 ( L
% 5.45/5.69 = ( plus_plus_nat @ K @ N5 ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % le_Suc_ex
% 5.45/5.69 thf(fact_2690_add__le__mono,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.69 => ( ( ord_less_eq_nat @ K @ L )
% 5.45/5.69 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_le_mono
% 5.45/5.69 thf(fact_2691_add__le__mono1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % add_le_mono1
% 5.45/5.69 thf(fact_2692_trans__le__add1,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,M: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % trans_le_add1
% 5.45/5.69 thf(fact_2693_trans__le__add2,axiom,
% 5.45/5.69 ! [I2: nat,J: nat,M: nat] :
% 5.45/5.69 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.69 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % trans_le_add2
% 5.45/5.69 thf(fact_2694_nat__le__iff__add,axiom,
% 5.45/5.69 ( ord_less_eq_nat
% 5.45/5.69 = ( ^ [M3: nat,N: nat] :
% 5.45/5.69 ? [K3: nat] :
% 5.45/5.69 ( N
% 5.45/5.69 = ( plus_plus_nat @ M3 @ K3 ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % nat_le_iff_add
% 5.45/5.69 thf(fact_2695_curryE,axiom,
% 5.45/5.69 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryE
% 5.45/5.69 thf(fact_2696_curryE,axiom,
% 5.45/5.69 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 5.45/5.69 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryE
% 5.45/5.69 thf(fact_2697_curryE,axiom,
% 5.45/5.69 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryE
% 5.45/5.69 thf(fact_2698_curryE,axiom,
% 5.45/5.69 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryE
% 5.45/5.69 thf(fact_2699_curryE,axiom,
% 5.45/5.69 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryE
% 5.45/5.69 thf(fact_2700_curryD,axiom,
% 5.45/5.69 ! [F: produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.45/5.69 ( ( produc6216949301066131538_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryD
% 5.45/5.69 thf(fact_2701_curryD,axiom,
% 5.45/5.69 ! [F: produc2732055786443039994et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 5.45/5.69 ( ( produc5101573711933517782_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryD
% 5.45/5.69 thf(fact_2702_curryD,axiom,
% 5.45/5.69 ! [F: produc2285326912895808259nt_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( produc730925184835016917_int_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryD
% 5.45/5.69 thf(fact_2703_curryD,axiom,
% 5.45/5.69 ! [F: produc7773217078559923341nt_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.45/5.69 ( ( produc9098658269643458507_int_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryD
% 5.45/5.69 thf(fact_2704_curryD,axiom,
% 5.45/5.69 ! [F: produc3260487557148687353it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 5.45/5.69 ( ( produc3709033845735585303_nat_o @ F @ A @ B )
% 5.45/5.69 => ( F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % curryD
% 5.45/5.69 thf(fact_2705_timeFrame_Osimps_I1_J,axiom,
% 5.45/5.69 ! [N2: nat,R3: a,H: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( heap_T7616092557645711335rame_a @ N2 @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R3 @ ( produc584006145561248582it_nat @ H @ N6 ) ) ) )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R3 @ ( produc584006145561248582it_nat @ H @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.simps(1)
% 5.45/5.69 thf(fact_2706_timeFrame_Osimps_I1_J,axiom,
% 5.45/5.69 ! [N2: nat,R3: product_unit,H: heap_e7401611519738050253t_unit,N6: nat] :
% 5.45/5.69 ( ( heap_T3616969660504097270t_unit @ N2 @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R3 @ ( produc584006145561248582it_nat @ H @ N6 ) ) ) )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R3 @ ( produc584006145561248582it_nat @ H @ ( plus_plus_nat @ N2 @ N6 ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.simps(1)
% 5.45/5.69 thf(fact_2707_timeFrame_Oelims,axiom,
% 5.45/5.69 ! [X: nat,Xa: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ( heap_T7616092557645711335rame_a @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ! [R2: a,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) )
% 5.45/5.69 => ( Y
% 5.45/5.69 != ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ ( plus_plus_nat @ X @ N4 ) ) ) ) ) )
% 5.45/5.69 => ~ ( ( Xa = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( Y != none_P2651198173097904984it_nat ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.elims
% 5.45/5.69 thf(fact_2708_timeFrame_Oelims,axiom,
% 5.45/5.69 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ! [R2: product_unit,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) )
% 5.45/5.69 => ( Y
% 5.45/5.69 != ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ ( plus_plus_nat @ X @ N4 ) ) ) ) ) )
% 5.45/5.69 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 5.45/5.69 => ( Y != none_P9117596204409417319it_nat ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.elims
% 5.45/5.69 thf(fact_2709_mono__nat__linear__lb,axiom,
% 5.45/5.69 ! [F: nat > nat,M: nat,K: nat] :
% 5.45/5.69 ( ! [M5: nat,N5: nat] :
% 5.45/5.69 ( ( ord_less_nat @ M5 @ N5 )
% 5.45/5.69 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N5 ) ) )
% 5.45/5.69 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % mono_nat_linear_lb
% 5.45/5.69 thf(fact_2710_Eps__Opt__eq__Some,axiom,
% 5.45/5.69 ! [P: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ! [X9: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( P @ X )
% 5.45/5.69 => ( ( P @ X9 )
% 5.45/5.69 => ( X9 = X ) ) )
% 5.45/5.69 => ( ( ( eps_Op1741419982095519837it_nat @ P )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ X ) )
% 5.45/5.69 = ( P @ X ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some
% 5.45/5.69 thf(fact_2711_Eps__Opt__eq__Some,axiom,
% 5.45/5.69 ! [P: num > $o,X: num] :
% 5.45/5.69 ( ! [X9: num] :
% 5.45/5.69 ( ( P @ X )
% 5.45/5.69 => ( ( P @ X9 )
% 5.45/5.69 => ( X9 = X ) ) )
% 5.45/5.69 => ( ( ( eps_Opt_num @ P )
% 5.45/5.69 = ( some_num @ X ) )
% 5.45/5.69 = ( P @ X ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some
% 5.45/5.69 thf(fact_2712_Eps__Opt__eq__Some,axiom,
% 5.45/5.69 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ! [X9: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( P @ X )
% 5.45/5.69 => ( ( P @ X9 )
% 5.45/5.69 => ( X9 = X ) ) )
% 5.45/5.69 => ( ( ( eps_Op3393321821070424684it_nat @ P )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ X ) )
% 5.45/5.69 = ( P @ X ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some
% 5.45/5.69 thf(fact_2713_Eps__Opt__eq__Some__implies,axiom,
% 5.45/5.69 ! [P: produc3260487557148687353it_nat > $o,X: produc3260487557148687353it_nat] :
% 5.45/5.69 ( ( ( eps_Op1741419982095519837it_nat @ P )
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ X ) )
% 5.45/5.69 => ( P @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some_implies
% 5.45/5.69 thf(fact_2714_Eps__Opt__eq__Some__implies,axiom,
% 5.45/5.69 ! [P: num > $o,X: num] :
% 5.45/5.69 ( ( ( eps_Opt_num @ P )
% 5.45/5.69 = ( some_num @ X ) )
% 5.45/5.69 => ( P @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some_implies
% 5.45/5.69 thf(fact_2715_Eps__Opt__eq__Some__implies,axiom,
% 5.45/5.69 ! [P: produc8664842809031399944it_nat > $o,X: produc8664842809031399944it_nat] :
% 5.45/5.69 ( ( ( eps_Op3393321821070424684it_nat @ P )
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ X ) )
% 5.45/5.69 => ( P @ X ) ) ).
% 5.45/5.69
% 5.45/5.69 % Eps_Opt_eq_Some_implies
% 5.45/5.69 thf(fact_2716_execute__guard_I1_J,axiom,
% 5.45/5.69 ! [P: heap_e7401611519738050253t_unit > $o,H: heap_e7401611519738050253t_unit,F: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 5.45/5.69 ( ~ ( P @ H )
% 5.45/5.69 => ( ( heap_Time_execute_a @ ( heap_Time_guard_a @ P @ F ) @ H )
% 5.45/5.69 = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.69
% 5.45/5.69 % execute_guard(1)
% 5.45/5.69 thf(fact_2717_mlex__less,axiom,
% 5.45/5.69 ! [F: nat > nat,X: nat,Y: nat,R: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 5.45/5.69 => ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % mlex_less
% 5.45/5.69 thf(fact_2718_mlex__iff,axiom,
% 5.45/5.69 ! [X: nat,Y: nat,F: nat > nat,R: set_Pr1261947904930325089at_nat] :
% 5.45/5.69 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( mlex_prod_nat @ F @ R ) )
% 5.45/5.69 = ( ( ord_less_nat @ ( F @ X ) @ ( F @ Y ) )
% 5.45/5.69 | ( ( ( F @ X )
% 5.45/5.69 = ( F @ Y ) )
% 5.45/5.69 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ R ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % mlex_iff
% 5.45/5.69 thf(fact_2719_timeFrame_Opelims,axiom,
% 5.45/5.69 ! [X: nat,Xa: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 5.45/5.69 ( ( ( heap_T7616092557645711335rame_a @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ Xa ) )
% 5.45/5.69 => ( ! [R2: a,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ ( plus_plus_nat @ X @ N4 ) ) ) ) )
% 5.45/5.69 => ~ ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) ) ) ) )
% 5.45/5.69 => ~ ( ( Xa = none_P2651198173097904984it_nat )
% 5.45/5.69 => ( ( Y = none_P2651198173097904984it_nat )
% 5.45/5.69 => ~ ( accp_P6263092265436569219it_nat @ heap_T8132184524487034138_rel_a @ ( produc4111269673004989362it_nat @ X @ none_P2651198173097904984it_nat ) ) ) ) ) ) ) ).
% 5.45/5.69
% 5.45/5.69 % timeFrame.pelims
% 5.45/5.69 thf(fact_2720_timeFrame_Opelims,axiom,
% 5.45/5.69 ! [X: nat,Xa: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 5.45/5.69 ( ( ( heap_T3616969660504097270t_unit @ X @ Xa )
% 5.45/5.69 = Y )
% 5.45/5.69 => ( ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ Xa ) )
% 5.45/5.69 => ( ! [R2: product_unit,H4: heap_e7401611519738050253t_unit,N4: nat] :
% 5.45/5.69 ( ( Xa
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) )
% 5.45/5.69 => ( ( Y
% 5.45/5.69 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ ( plus_plus_nat @ X @ N4 ) ) ) ) )
% 5.45/5.70 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ R2 @ ( produc584006145561248582it_nat @ H4 @ N4 ) ) ) ) ) ) )
% 5.45/5.70 => ~ ( ( Xa = none_P9117596204409417319it_nat )
% 5.45/5.70 => ( ( Y = none_P9117596204409417319it_nat )
% 5.45/5.70 => ~ ( accp_P414730952086964626it_nat @ heap_T996182799752388649t_unit @ ( produc638857205735767105it_nat @ X @ none_P9117596204409417319it_nat ) ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % timeFrame.pelims
% 5.45/5.70 thf(fact_2721_add__less__cancel__left,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.45/5.70 = ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_left
% 5.45/5.70 thf(fact_2722_add__less__cancel__left,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.45/5.70 = ( ord_less_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_left
% 5.45/5.70 thf(fact_2723_add__less__cancel__left,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.45/5.70 = ( ord_less_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_left
% 5.45/5.70 thf(fact_2724_add__less__cancel__right,axiom,
% 5.45/5.70 ! [A: rat,C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 = ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_right
% 5.45/5.70 thf(fact_2725_add__less__cancel__right,axiom,
% 5.45/5.70 ! [A: nat,C: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.70 = ( ord_less_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_right
% 5.45/5.70 thf(fact_2726_add__less__cancel__right,axiom,
% 5.45/5.70 ! [A: int,C: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 = ( ord_less_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_cancel_right
% 5.45/5.70 thf(fact_2727_add__le__cancel__left,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.45/5.70 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_left
% 5.45/5.70 thf(fact_2728_add__le__cancel__left,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.45/5.70 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_left
% 5.45/5.70 thf(fact_2729_add__le__cancel__left,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.45/5.70 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_left
% 5.45/5.70 thf(fact_2730_add__le__cancel__right,axiom,
% 5.45/5.70 ! [A: rat,C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_right
% 5.45/5.70 thf(fact_2731_add__le__cancel__right,axiom,
% 5.45/5.70 ! [A: nat,C: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.70 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_right
% 5.45/5.70 thf(fact_2732_add__le__cancel__right,axiom,
% 5.45/5.70 ! [A: int,C: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_cancel_right
% 5.45/5.70 thf(fact_2733_add__mono__thms__linordered__field_I4_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.45/5.70 & ( ord_less_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(4)
% 5.45/5.70 thf(fact_2734_add__mono__thms__linordered__field_I4_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 & ( ord_less_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(4)
% 5.45/5.70 thf(fact_2735_add__mono__thms__linordered__field_I4_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.45/5.70 & ( ord_less_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(4)
% 5.45/5.70 thf(fact_2736_add__mono__thms__linordered__field_I3_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_rat @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(3)
% 5.45/5.70 thf(fact_2737_add__mono__thms__linordered__field_I3_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_nat @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(3)
% 5.45/5.70 thf(fact_2738_add__mono__thms__linordered__field_I3_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_int @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(3)
% 5.45/5.70 thf(fact_2739_add__le__less__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.70 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_less_mono
% 5.45/5.70 thf(fact_2740_add__le__less__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_less_mono
% 5.45/5.70 thf(fact_2741_add__le__less__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.70 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_less_mono
% 5.45/5.70 thf(fact_2742_add__less__le__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_le_mono
% 5.45/5.70 thf(fact_2743_add__less__le__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_le_mono
% 5.45/5.70 thf(fact_2744_add__less__le__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_int @ C @ D2 )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_le_mono
% 5.45/5.70 thf(fact_2745_crossproduct__noteq,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.70 ( ( ( A != B )
% 5.45/5.70 & ( C != D2 ) )
% 5.45/5.70 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) )
% 5.45/5.70 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ D2 ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_noteq
% 5.45/5.70 thf(fact_2746_crossproduct__noteq,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.70 ( ( ( A != B )
% 5.45/5.70 & ( C != D2 ) )
% 5.45/5.70 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) )
% 5.45/5.70 != ( plus_plus_rat @ ( times_times_rat @ A @ D2 ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_noteq
% 5.45/5.70 thf(fact_2747_crossproduct__noteq,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.70 ( ( ( A != B )
% 5.45/5.70 & ( C != D2 ) )
% 5.45/5.70 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) )
% 5.45/5.70 != ( plus_plus_nat @ ( times_times_nat @ A @ D2 ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_noteq
% 5.45/5.70 thf(fact_2748_crossproduct__noteq,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.70 ( ( ( A != B )
% 5.45/5.70 & ( C != D2 ) )
% 5.45/5.70 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) )
% 5.45/5.70 != ( plus_plus_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_noteq
% 5.45/5.70 thf(fact_2749_mult__le__mono2,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_mono2
% 5.45/5.70 thf(fact_2750_mult__le__mono1,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_mono1
% 5.45/5.70 thf(fact_2751_mult__le__mono,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 => ( ( ord_less_eq_nat @ K @ L )
% 5.45/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_mono
% 5.45/5.70 thf(fact_2752_le__square,axiom,
% 5.45/5.70 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_square
% 5.45/5.70 thf(fact_2753_le__cube,axiom,
% 5.45/5.70 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_cube
% 5.45/5.70 thf(fact_2754_add__mult__distrib,axiom,
% 5.45/5.70 ! [M: nat,N2: nat,K: nat] :
% 5.45/5.70 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mult_distrib
% 5.45/5.70 thf(fact_2755_add__mult__distrib2,axiom,
% 5.45/5.70 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.70 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mult_distrib2
% 5.45/5.70 thf(fact_2756_mlex__bound,axiom,
% 5.45/5.70 ! [A: nat,A3: nat,B: nat,N7: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ A3 )
% 5.45/5.70 => ( ( ord_less_nat @ B @ N7 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( times_times_nat @ A3 @ N7 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mlex_bound
% 5.45/5.70 thf(fact_2757_mlex__fst__decrI,axiom,
% 5.45/5.70 ! [A: nat,A2: nat,B: nat,N7: nat,B2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ A2 )
% 5.45/5.70 => ( ( ord_less_nat @ B @ N7 )
% 5.45/5.70 => ( ( ord_less_nat @ B2 @ N7 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mlex_fst_decrI
% 5.45/5.70 thf(fact_2758_mlex__snd__decrI,axiom,
% 5.45/5.70 ! [A: nat,A2: nat,B: nat,B2: nat,N7: nat] :
% 5.45/5.70 ( ( A = A2 )
% 5.45/5.70 => ( ( ord_less_nat @ B @ B2 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mlex_snd_decrI
% 5.45/5.70 thf(fact_2759_mlex__leI,axiom,
% 5.45/5.70 ! [A: nat,A2: nat,B: nat,B2: nat,N7: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ A2 )
% 5.45/5.70 => ( ( ord_less_eq_nat @ B @ B2 )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ A @ N7 ) @ B ) @ ( plus_plus_nat @ ( times_times_nat @ A2 @ N7 ) @ B2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mlex_leI
% 5.45/5.70 thf(fact_2760_mult_Oassoc,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.70 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult.assoc
% 5.45/5.70 thf(fact_2761_mult_Oassoc,axiom,
% 5.45/5.70 ! [A: assn,B: assn,C: assn] :
% 5.45/5.70 ( ( times_times_assn @ ( times_times_assn @ A @ B ) @ C )
% 5.45/5.70 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult.assoc
% 5.45/5.70 thf(fact_2762_mult_Oassoc,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.45/5.70 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult.assoc
% 5.45/5.70 thf(fact_2763_mult_Oassoc,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.70 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult.assoc
% 5.45/5.70 thf(fact_2764_mult_Oassoc,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.70 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult.assoc
% 5.45/5.70 thf(fact_2765_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.45/5.70 ( times_3573771949741848930nteger
% 5.45/5.70 = ( ^ [A5: code_integer,B5: code_integer] : ( times_3573771949741848930nteger @ B5 @ A5 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.commute
% 5.45/5.70 thf(fact_2766_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.45/5.70 ( times_times_assn
% 5.45/5.70 = ( ^ [A5: assn,B5: assn] : ( times_times_assn @ B5 @ A5 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.commute
% 5.45/5.70 thf(fact_2767_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.45/5.70 ( times_times_rat
% 5.45/5.70 = ( ^ [A5: rat,B5: rat] : ( times_times_rat @ B5 @ A5 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.commute
% 5.45/5.70 thf(fact_2768_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.45/5.70 ( times_times_nat
% 5.45/5.70 = ( ^ [A5: nat,B5: nat] : ( times_times_nat @ B5 @ A5 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.commute
% 5.45/5.70 thf(fact_2769_ab__semigroup__mult__class_Omult_Ocommute,axiom,
% 5.45/5.70 ( times_times_int
% 5.45/5.70 = ( ^ [A5: int,B5: int] : ( times_times_int @ B5 @ A5 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.commute
% 5.45/5.70 thf(fact_2770_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.45/5.70 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ B @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.45/5.70 = ( times_3573771949741848930nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.left_commute
% 5.45/5.70 thf(fact_2771_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.45/5.70 ! [B: assn,A: assn,C: assn] :
% 5.45/5.70 ( ( times_times_assn @ B @ ( times_times_assn @ A @ C ) )
% 5.45/5.70 = ( times_times_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.left_commute
% 5.45/5.70 thf(fact_2772_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.45/5.70 ! [B: rat,A: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.45/5.70 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.left_commute
% 5.45/5.70 thf(fact_2773_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.45/5.70 ! [B: nat,A: nat,C: nat] :
% 5.45/5.70 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.45/5.70 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.left_commute
% 5.45/5.70 thf(fact_2774_ab__semigroup__mult__class_Omult_Oleft__commute,axiom,
% 5.45/5.70 ! [B: int,A: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.45/5.70 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ab_semigroup_mult_class.mult.left_commute
% 5.45/5.70 thf(fact_2775_add__le__imp__le__right,axiom,
% 5.45/5.70 ! [A: rat,C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_right
% 5.45/5.70 thf(fact_2776_add__le__imp__le__right,axiom,
% 5.45/5.70 ! [A: nat,C: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.70 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_right
% 5.45/5.70 thf(fact_2777_add__le__imp__le__right,axiom,
% 5.45/5.70 ! [A: int,C: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_right
% 5.45/5.70 thf(fact_2778_add__le__imp__le__left,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.45/5.70 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_left
% 5.45/5.70 thf(fact_2779_add__le__imp__le__left,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.45/5.70 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_left
% 5.45/5.70 thf(fact_2780_add__le__imp__le__left,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.45/5.70 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_imp_le_left
% 5.45/5.70 thf(fact_2781_le__iff__add,axiom,
% 5.45/5.70 ( ord_less_eq_nat
% 5.45/5.70 = ( ^ [A5: nat,B5: nat] :
% 5.45/5.70 ? [C4: nat] :
% 5.45/5.70 ( B5
% 5.45/5.70 = ( plus_plus_nat @ A5 @ C4 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_iff_add
% 5.45/5.70 thf(fact_2782_add__right__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_right_mono
% 5.45/5.70 thf(fact_2783_add__right__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_right_mono
% 5.45/5.70 thf(fact_2784_add__right__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_right_mono
% 5.45/5.70 thf(fact_2785_less__eqE,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ~ ! [C2: nat] :
% 5.45/5.70 ( B
% 5.45/5.70 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_eqE
% 5.45/5.70 thf(fact_2786_add__left__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_left_mono
% 5.45/5.70 thf(fact_2787_add__left__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_left_mono
% 5.45/5.70 thf(fact_2788_add__left__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_left_mono
% 5.45/5.70 thf(fact_2789_add__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono
% 5.45/5.70 thf(fact_2790_add__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono
% 5.45/5.70 thf(fact_2791_add__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.70 => ( ( ord_less_eq_int @ C @ D2 )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono
% 5.45/5.70 thf(fact_2792_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(1)
% 5.45/5.70 thf(fact_2793_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(1)
% 5.45/5.70 thf(fact_2794_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.45/5.70 & ( ord_less_eq_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(1)
% 5.45/5.70 thf(fact_2795_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_eq_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(2)
% 5.45/5.70 thf(fact_2796_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_eq_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(2)
% 5.45/5.70 thf(fact_2797_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_eq_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(2)
% 5.45/5.70 thf(fact_2798_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(3)
% 5.45/5.70 thf(fact_2799_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(3)
% 5.45/5.70 thf(fact_2800_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_semiring(3)
% 5.45/5.70 thf(fact_2801_add__less__imp__less__right,axiom,
% 5.45/5.70 ! [A: rat,C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 => ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_right
% 5.45/5.70 thf(fact_2802_add__less__imp__less__right,axiom,
% 5.45/5.70 ! [A: nat,C: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.70 => ( ord_less_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_right
% 5.45/5.70 thf(fact_2803_add__less__imp__less__right,axiom,
% 5.45/5.70 ! [A: int,C: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 => ( ord_less_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_right
% 5.45/5.70 thf(fact_2804_add__less__imp__less__left,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.45/5.70 => ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_left
% 5.45/5.70 thf(fact_2805_add__less__imp__less__left,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.45/5.70 => ( ord_less_nat @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_left
% 5.45/5.70 thf(fact_2806_add__less__imp__less__left,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.45/5.70 => ( ord_less_int @ A @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_imp_less_left
% 5.45/5.70 thf(fact_2807_add__strict__right__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ B )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_right_mono
% 5.45/5.70 thf(fact_2808_add__strict__right__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ B )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_right_mono
% 5.45/5.70 thf(fact_2809_add__strict__right__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ B )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_right_mono
% 5.45/5.70 thf(fact_2810_add__strict__left__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ B )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_left_mono
% 5.45/5.70 thf(fact_2811_add__strict__left__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ B )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_left_mono
% 5.45/5.70 thf(fact_2812_add__strict__left__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ B )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_left_mono
% 5.45/5.70 thf(fact_2813_add__strict__mono,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ B )
% 5.45/5.70 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_mono
% 5.45/5.70 thf(fact_2814_add__strict__mono,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ B )
% 5.45/5.70 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_mono
% 5.45/5.70 thf(fact_2815_add__strict__mono,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ B )
% 5.45/5.70 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_strict_mono
% 5.45/5.70 thf(fact_2816_add__mono__thms__linordered__field_I1_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_rat @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(1)
% 5.45/5.70 thf(fact_2817_add__mono__thms__linordered__field_I1_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_nat @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(1)
% 5.45/5.70 thf(fact_2818_add__mono__thms__linordered__field_I1_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_int @ I2 @ J )
% 5.45/5.70 & ( K = L ) )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(1)
% 5.45/5.70 thf(fact_2819_add__mono__thms__linordered__field_I2_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(2)
% 5.45/5.70 thf(fact_2820_add__mono__thms__linordered__field_I2_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(2)
% 5.45/5.70 thf(fact_2821_add__mono__thms__linordered__field_I2_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( I2 = J )
% 5.45/5.70 & ( ord_less_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(2)
% 5.45/5.70 thf(fact_2822_add__mono__thms__linordered__field_I5_J,axiom,
% 5.45/5.70 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.45/5.70 ( ( ( ord_less_rat @ I2 @ J )
% 5.45/5.70 & ( ord_less_rat @ K @ L ) )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(5)
% 5.45/5.70 thf(fact_2823_add__mono__thms__linordered__field_I5_J,axiom,
% 5.45/5.70 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.45/5.70 ( ( ( ord_less_nat @ I2 @ J )
% 5.45/5.70 & ( ord_less_nat @ K @ L ) )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(5)
% 5.45/5.70 thf(fact_2824_add__mono__thms__linordered__field_I5_J,axiom,
% 5.45/5.70 ! [I2: int,J: int,K: int,L: int] :
% 5.45/5.70 ( ( ( ord_less_int @ I2 @ J )
% 5.45/5.70 & ( ord_less_int @ K @ L ) )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono_thms_linordered_field(5)
% 5.45/5.70 thf(fact_2825_crossproduct__eq,axiom,
% 5.45/5.70 ! [W2: code_integer,Y: code_integer,X: code_integer,Z: code_integer] :
% 5.45/5.70 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Y ) @ ( times_3573771949741848930nteger @ X @ Z ) )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ W2 @ Z ) @ ( times_3573771949741848930nteger @ X @ Y ) ) )
% 5.45/5.70 = ( ( W2 = X )
% 5.45/5.70 | ( Y = Z ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_eq
% 5.45/5.70 thf(fact_2826_crossproduct__eq,axiom,
% 5.45/5.70 ! [W2: rat,Y: rat,X: rat,Z: rat] :
% 5.45/5.70 ( ( ( plus_plus_rat @ ( times_times_rat @ W2 @ Y ) @ ( times_times_rat @ X @ Z ) )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ W2 @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 5.45/5.70 = ( ( W2 = X )
% 5.45/5.70 | ( Y = Z ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_eq
% 5.45/5.70 thf(fact_2827_crossproduct__eq,axiom,
% 5.45/5.70 ! [W2: nat,Y: nat,X: nat,Z: nat] :
% 5.45/5.70 ( ( ( plus_plus_nat @ ( times_times_nat @ W2 @ Y ) @ ( times_times_nat @ X @ Z ) )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ W2 @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 5.45/5.70 = ( ( W2 = X )
% 5.45/5.70 | ( Y = Z ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_eq
% 5.45/5.70 thf(fact_2828_crossproduct__eq,axiom,
% 5.45/5.70 ! [W2: int,Y: int,X: int,Z: int] :
% 5.45/5.70 ( ( ( plus_plus_int @ ( times_times_int @ W2 @ Y ) @ ( times_times_int @ X @ Z ) )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ W2 @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 5.45/5.70 = ( ( W2 = X )
% 5.45/5.70 | ( Y = Z ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % crossproduct_eq
% 5.45/5.70 thf(fact_2829_ring__class_Oring__distribs_I2_J,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(2)
% 5.45/5.70 thf(fact_2830_ring__class_Oring__distribs_I2_J,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(2)
% 5.45/5.70 thf(fact_2831_ring__class_Oring__distribs_I2_J,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(2)
% 5.45/5.70 thf(fact_2832_ring__class_Oring__distribs_I1_J,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(1)
% 5.45/5.70 thf(fact_2833_ring__class_Oring__distribs_I1_J,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(1)
% 5.45/5.70 thf(fact_2834_ring__class_Oring__distribs_I1_J,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ring_class.ring_distribs(1)
% 5.45/5.70 thf(fact_2835_comm__semiring__class_Odistrib,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % comm_semiring_class.distrib
% 5.45/5.70 thf(fact_2836_comm__semiring__class_Odistrib,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % comm_semiring_class.distrib
% 5.45/5.70 thf(fact_2837_comm__semiring__class_Odistrib,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % comm_semiring_class.distrib
% 5.45/5.70 thf(fact_2838_comm__semiring__class_Odistrib,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % comm_semiring_class.distrib
% 5.45/5.70 thf(fact_2839_distrib__left,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_left
% 5.45/5.70 thf(fact_2840_distrib__left,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_left
% 5.45/5.70 thf(fact_2841_distrib__left,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_left
% 5.45/5.70 thf(fact_2842_distrib__left,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_left
% 5.45/5.70 thf(fact_2843_distrib__right,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_right
% 5.45/5.70 thf(fact_2844_distrib__right,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_right
% 5.45/5.70 thf(fact_2845_distrib__right,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_right
% 5.45/5.70 thf(fact_2846_distrib__right,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % distrib_right
% 5.45/5.70 thf(fact_2847_combine__common__factor,axiom,
% 5.45/5.70 ! [A: code_integer,E: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ C ) )
% 5.45/5.70 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ E ) @ C ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_common_factor
% 5.45/5.70 thf(fact_2848_combine__common__factor,axiom,
% 5.45/5.70 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.45/5.70 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_common_factor
% 5.45/5.70 thf(fact_2849_combine__common__factor,axiom,
% 5.45/5.70 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.45/5.70 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_common_factor
% 5.45/5.70 thf(fact_2850_combine__common__factor,axiom,
% 5.45/5.70 ! [A: int,E: int,B: int,C: int] :
% 5.45/5.70 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.45/5.70 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_common_factor
% 5.45/5.70 thf(fact_2851_execute__raise,axiom,
% 5.45/5.70 ! [S2: list_char] :
% 5.45/5.70 ( ( heap_Time_execute_a @ ( heap_Time_raise_a @ S2 ) )
% 5.45/5.70 = ( ^ [Uu2: heap_e7401611519738050253t_unit] : none_P2651198173097904984it_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % execute_raise
% 5.45/5.70 thf(fact_2852_guard__def,axiom,
% 5.45/5.70 ( heap_Time_guard_a
% 5.45/5.70 = ( ^ [P4: heap_e7401611519738050253t_unit > $o,F3: heap_e7401611519738050253t_unit > produc3260487557148687353it_nat] :
% 5.45/5.70 ( heap_Time_Heap_a2
% 5.45/5.70 @ ^ [H6: heap_e7401611519738050253t_unit] : ( if_opt6883606601682554499it_nat @ ( P4 @ H6 ) @ ( some_P7913643980934408916it_nat @ ( F3 @ H6 ) ) @ none_P2651198173097904984it_nat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % guard_def
% 5.45/5.70 thf(fact_2853_guard__def,axiom,
% 5.45/5.70 ( heap_T8440541562793052209t_unit
% 5.45/5.70 = ( ^ [P4: heap_e7401611519738050253t_unit > $o,F3: heap_e7401611519738050253t_unit > produc8664842809031399944it_nat] :
% 5.45/5.70 ( heap_T6183433275982383450t_unit
% 5.45/5.70 @ ^ [H6: heap_e7401611519738050253t_unit] : ( if_opt1729522071442692626it_nat @ ( P4 @ H6 ) @ ( some_P1914260805536162275it_nat @ ( F3 @ H6 ) ) @ none_P9117596204409417319it_nat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % guard_def
% 5.45/5.70 thf(fact_2854_execute__assert_I2_J,axiom,
% 5.45/5.70 ! [P: a > $o,X: a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.70 ( ~ ( P @ X )
% 5.45/5.70 => ( ( heap_Time_execute_a @ ( heap_Time_assert_a @ P @ X ) @ H )
% 5.45/5.70 = none_P2651198173097904984it_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % execute_assert(2)
% 5.45/5.70 thf(fact_2855_ent__pure__post__iff,axiom,
% 5.45/5.70 ! [P: assn,Q: assn,B: $o] :
% 5.45/5.70 ( ( entails @ P @ ( times_times_assn @ Q @ ( pure_assn @ B ) ) )
% 5.45/5.70 = ( ! [H6: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( rep_assn @ P @ H6 )
% 5.45/5.70 => B )
% 5.45/5.70 & ( entails @ P @ Q ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_pure_post_iff
% 5.45/5.70 thf(fact_2856_Heap__execute,axiom,
% 5.45/5.70 ! [F: heap_Time_Heap_a] :
% 5.45/5.70 ( ( heap_Time_Heap_a2 @ ( heap_Time_execute_a @ F ) )
% 5.45/5.70 = F ) ).
% 5.45/5.70
% 5.45/5.70 % Heap_execute
% 5.45/5.70 thf(fact_2857_Heap__execute,axiom,
% 5.45/5.70 ! [F: heap_T5738788834812785303t_unit] :
% 5.45/5.70 ( ( heap_T6183433275982383450t_unit @ ( heap_T875086893843062177t_unit @ F ) )
% 5.45/5.70 = F ) ).
% 5.45/5.70
% 5.45/5.70 % Heap_execute
% 5.45/5.70 thf(fact_2858_ent__pure__pre__iff,axiom,
% 5.45/5.70 ! [P: assn,B: $o,Q: assn] :
% 5.45/5.70 ( ( entails @ ( times_times_assn @ P @ ( pure_assn @ B ) ) @ Q )
% 5.45/5.70 = ( B
% 5.45/5.70 => ( entails @ P @ Q ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_pure_pre_iff
% 5.45/5.70 thf(fact_2859_ent__false__iff,axiom,
% 5.45/5.70 ! [P: assn] :
% 5.45/5.70 ( ( entails @ P @ bot_bot_assn )
% 5.45/5.70 = ( ! [H6: produc3658429121746597890et_nat] :
% 5.45/5.70 ~ ( rep_assn @ P @ H6 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_false_iff
% 5.45/5.70 thf(fact_2860_ent__trans,axiom,
% 5.45/5.70 ! [P: assn,Q: assn,R: assn] :
% 5.45/5.70 ( ( entails @ P @ Q )
% 5.45/5.70 => ( ( entails @ Q @ R )
% 5.45/5.70 => ( entails @ P @ R ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_trans
% 5.45/5.70 thf(fact_2861_ent__refl,axiom,
% 5.45/5.70 ! [P: assn] : ( entails @ P @ P ) ).
% 5.45/5.70
% 5.45/5.70 % ent_refl
% 5.45/5.70 thf(fact_2862_ent__iffI,axiom,
% 5.45/5.70 ! [A3: assn,B3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ B3 )
% 5.45/5.70 => ( ( entails @ B3 @ A3 )
% 5.45/5.70 => ( A3 = B3 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_iffI
% 5.45/5.70 thf(fact_2863_raise__def,axiom,
% 5.45/5.70 ( heap_T2927564422264180874t_unit
% 5.45/5.70 = ( ^ [S6: list_char] :
% 5.45/5.70 ( heap_T6183433275982383450t_unit
% 5.45/5.70 @ ^ [Uu2: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % raise_def
% 5.45/5.70 thf(fact_2864_entails__def,axiom,
% 5.45/5.70 ( entails
% 5.45/5.70 = ( ^ [P4: assn,Q3: assn] :
% 5.45/5.70 ! [H6: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( rep_assn @ P4 @ H6 )
% 5.45/5.70 => ( rep_assn @ Q3 @ H6 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % entails_def
% 5.45/5.70 thf(fact_2865_entailsI,axiom,
% 5.45/5.70 ! [P: assn,Q: assn] :
% 5.45/5.70 ( ! [H4: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( rep_assn @ P @ H4 )
% 5.45/5.70 => ( rep_assn @ Q @ H4 ) )
% 5.45/5.70 => ( entails @ P @ Q ) ) ).
% 5.45/5.70
% 5.45/5.70 % entailsI
% 5.45/5.70 thf(fact_2866_entailsD,axiom,
% 5.45/5.70 ! [P: assn,Q: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( entails @ P @ Q )
% 5.45/5.70 => ( ( rep_assn @ P @ H )
% 5.45/5.70 => ( rep_assn @ Q @ H ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % entailsD
% 5.45/5.70 thf(fact_2867_ent__fwd,axiom,
% 5.45/5.70 ! [P: assn,H: produc3658429121746597890et_nat,Q: assn] :
% 5.45/5.70 ( ( rep_assn @ P @ H )
% 5.45/5.70 => ( ( entails @ P @ Q )
% 5.45/5.70 => ( rep_assn @ Q @ H ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_fwd
% 5.45/5.70 thf(fact_2868_ent__star__mono,axiom,
% 5.45/5.70 ! [P: assn,P6: assn,Q: assn,Q4: assn] :
% 5.45/5.70 ( ( entails @ P @ P6 )
% 5.45/5.70 => ( ( entails @ Q @ Q4 )
% 5.45/5.70 => ( entails @ ( times_times_assn @ P @ Q ) @ ( times_times_assn @ P6 @ Q4 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_star_mono
% 5.45/5.70 thf(fact_2869_ent__disjE,axiom,
% 5.45/5.70 ! [A3: assn,C3: assn,B3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ C3 )
% 5.45/5.70 => ( ( entails @ B3 @ C3 )
% 5.45/5.70 => ( entails @ ( sup_sup_assn @ A3 @ B3 ) @ C3 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjE
% 5.45/5.70 thf(fact_2870_ent__disjI1,axiom,
% 5.45/5.70 ! [P: assn,Q: assn,R: assn] :
% 5.45/5.70 ( ( entails @ ( sup_sup_assn @ P @ Q ) @ R )
% 5.45/5.70 => ( entails @ P @ R ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI1
% 5.45/5.70 thf(fact_2871_ent__disjI2,axiom,
% 5.45/5.70 ! [P: assn,Q: assn,R: assn] :
% 5.45/5.70 ( ( entails @ ( sup_sup_assn @ P @ Q ) @ R )
% 5.45/5.70 => ( entails @ Q @ R ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI2
% 5.45/5.70 thf(fact_2872_ent__disjI1_H,axiom,
% 5.45/5.70 ! [A3: assn,B3: assn,C3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ B3 )
% 5.45/5.70 => ( entails @ A3 @ ( sup_sup_assn @ B3 @ C3 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI1'
% 5.45/5.70 thf(fact_2873_ent__disjI2_H,axiom,
% 5.45/5.70 ! [A3: assn,C3: assn,B3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ C3 )
% 5.45/5.70 => ( entails @ A3 @ ( sup_sup_assn @ B3 @ C3 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI2'
% 5.45/5.70 thf(fact_2874_ent__disjI1__direct,axiom,
% 5.45/5.70 ! [A3: assn,B3: assn] : ( entails @ A3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI1_direct
% 5.45/5.70 thf(fact_2875_ent__disjI2__direct,axiom,
% 5.45/5.70 ! [B3: assn,A3: assn] : ( entails @ B3 @ ( sup_sup_assn @ A3 @ B3 ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_disjI2_direct
% 5.45/5.70 thf(fact_2876_execute_Osimps,axiom,
% 5.45/5.70 ! [F: heap_e7401611519738050253t_unit > option3562590408128118217it_nat] :
% 5.45/5.70 ( ( heap_Time_execute_a @ ( heap_Time_Heap_a2 @ F ) )
% 5.45/5.70 = F ) ).
% 5.45/5.70
% 5.45/5.70 % execute.simps
% 5.45/5.70 thf(fact_2877_execute_Osimps,axiom,
% 5.45/5.70 ! [F: heap_e7401611519738050253t_unit > option8956607266484857688it_nat] :
% 5.45/5.70 ( ( heap_T875086893843062177t_unit @ ( heap_T6183433275982383450t_unit @ F ) )
% 5.45/5.70 = F ) ).
% 5.45/5.70
% 5.45/5.70 % execute.simps
% 5.45/5.70 thf(fact_2878_ent__false,axiom,
% 5.45/5.70 ! [P: assn] : ( entails @ bot_bot_assn @ P ) ).
% 5.45/5.70
% 5.45/5.70 % ent_false
% 5.45/5.70 thf(fact_2879_ent__conjI,axiom,
% 5.45/5.70 ! [A3: assn,B3: assn,C3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ B3 )
% 5.45/5.70 => ( ( entails @ A3 @ C3 )
% 5.45/5.70 => ( entails @ A3 @ ( inf_inf_assn @ B3 @ C3 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_conjI
% 5.45/5.70 thf(fact_2880_ent__conjE1,axiom,
% 5.45/5.70 ! [A3: assn,C3: assn,B3: assn] :
% 5.45/5.70 ( ( entails @ A3 @ C3 )
% 5.45/5.70 => ( entails @ ( inf_inf_assn @ A3 @ B3 ) @ C3 ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_conjE1
% 5.45/5.70 thf(fact_2881_ent__conjE2,axiom,
% 5.45/5.70 ! [B3: assn,C3: assn,A3: assn] :
% 5.45/5.70 ( ( entails @ B3 @ C3 )
% 5.45/5.70 => ( entails @ ( inf_inf_assn @ A3 @ B3 ) @ C3 ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_conjE2
% 5.45/5.70 thf(fact_2882_ent__wandI,axiom,
% 5.45/5.70 ! [Q: assn,P: assn,R: assn] :
% 5.45/5.70 ( ( entails @ ( times_times_assn @ Q @ P ) @ R )
% 5.45/5.70 => ( entails @ P @ ( wand_assn @ Q @ R ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_wandI
% 5.45/5.70 thf(fact_2883_ent__mp,axiom,
% 5.45/5.70 ! [P: assn,Q: assn] : ( entails @ ( times_times_assn @ P @ ( wand_assn @ P @ Q ) ) @ Q ) ).
% 5.45/5.70
% 5.45/5.70 % ent_mp
% 5.45/5.70 thf(fact_2884_linorder__neqE__linordered__idom,axiom,
% 5.45/5.70 ! [X: rat,Y: rat] :
% 5.45/5.70 ( ( X != Y )
% 5.45/5.70 => ( ~ ( ord_less_rat @ X @ Y )
% 5.45/5.70 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % linorder_neqE_linordered_idom
% 5.45/5.70 thf(fact_2885_linorder__neqE__linordered__idom,axiom,
% 5.45/5.70 ! [X: int,Y: int] :
% 5.45/5.70 ( ( X != Y )
% 5.45/5.70 => ( ~ ( ord_less_int @ X @ Y )
% 5.45/5.70 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % linorder_neqE_linordered_idom
% 5.45/5.70 thf(fact_2886_execute__assert_I1_J,axiom,
% 5.45/5.70 ! [P: product_unit > $o,X: product_unit,H: heap_e7401611519738050253t_unit] :
% 5.45/5.70 ( ( P @ X )
% 5.45/5.70 => ( ( heap_T875086893843062177t_unit @ ( heap_T4208721593536448476t_unit @ P @ X ) @ H )
% 5.45/5.70 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % execute_assert(1)
% 5.45/5.70 thf(fact_2887_execute__assert_I1_J,axiom,
% 5.45/5.70 ! [P: a > $o,X: a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.70 ( ( P @ X )
% 5.45/5.70 => ( ( heap_Time_execute_a @ ( heap_Time_assert_a @ P @ X ) @ H )
% 5.45/5.70 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ X @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % execute_assert(1)
% 5.45/5.70 thf(fact_2888_Heap__lub__empty,axiom,
% 5.45/5.70 ( ( heap_T4436805183663264329t_unit @ bot_bo8105976889876132193t_unit )
% 5.45/5.70 = ( heap_T6183433275982383450t_unit
% 5.45/5.70 @ ^ [X4: heap_e7401611519738050253t_unit] : none_P9117596204409417319it_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % Heap_lub_empty
% 5.45/5.70 thf(fact_2889_ent__pure__post__iff__sng,axiom,
% 5.45/5.70 ! [P: assn,B: $o] :
% 5.45/5.70 ( ( entails @ P @ ( pure_assn @ B ) )
% 5.45/5.70 = ( ! [H6: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( rep_assn @ P @ H6 )
% 5.45/5.70 => B )
% 5.45/5.70 & ( entails @ P @ one_one_assn ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_pure_post_iff_sng
% 5.45/5.70 thf(fact_2890_pairself_Opelims,axiom,
% 5.45/5.70 ! [X: int > option6357759511663192854e_term,Xa: product_prod_int_int,Y: produc6576344331059438605e_term] :
% 5.45/5.70 ( ( ( pairse3534876335208825186e_term @ X @ Xa )
% 5.45/5.70 = Y )
% 5.45/5.70 => ( ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ Xa ) )
% 5.45/5.70 => ~ ! [A4: int,B4: int] :
% 5.45/5.70 ( ( Xa
% 5.45/5.70 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.45/5.70 => ( ( Y
% 5.45/5.70 = ( produc5950683997804057413e_term @ ( X @ A4 ) @ ( X @ B4 ) ) )
% 5.45/5.70 => ~ ( accp_P8928870874622223812nt_int @ pairse6848479906795794847e_term @ ( produc4305682042979456191nt_int @ X @ ( product_Pair_int_int @ A4 @ B4 ) ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % pairself.pelims
% 5.45/5.70 thf(fact_2891_one__assn__raw_Osimps,axiom,
% 5.45/5.70 ! [H: heap_e7401611519738050253t_unit,As: set_nat] :
% 5.45/5.70 ( ( one_assn_raw @ ( produc7507926704131184380et_nat @ H @ As ) )
% 5.45/5.70 = ( As = bot_bot_set_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % one_assn_raw.simps
% 5.45/5.70 thf(fact_2892_one__assn__raw_Oelims_I1_J,axiom,
% 5.45/5.70 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.70 ( ( ( one_assn_raw @ X )
% 5.45/5.70 = Y )
% 5.45/5.70 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.70 ( ( X
% 5.45/5.70 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.70 => ( Y
% 5.45/5.70 = ( As4 != bot_bot_set_nat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % one_assn_raw.elims(1)
% 5.45/5.70 thf(fact_2893_one__assn__raw_Oelims_I2_J,axiom,
% 5.45/5.70 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ( one_assn_raw @ X )
% 5.45/5.70 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.70 ( ( X
% 5.45/5.70 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.70 => ( As4 != bot_bot_set_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % one_assn_raw.elims(2)
% 5.45/5.70 thf(fact_2894_one__assn__raw_Oelims_I3_J,axiom,
% 5.45/5.70 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.70 ( ~ ( one_assn_raw @ X )
% 5.45/5.70 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.70 ( ( X
% 5.45/5.70 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.70 => ( As4 = bot_bot_set_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % one_assn_raw.elims(3)
% 5.45/5.70 thf(fact_2895_mult__le__cancel2,axiom,
% 5.45/5.70 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.45/5.70 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.70 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel2
% 5.45/5.70 thf(fact_2896_combine__options__def,axiom,
% 5.45/5.70 ( combin5819755802923621690it_nat
% 5.45/5.70 = ( ^ [F3: produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat,X4: option3562590408128118217it_nat,Y4: option3562590408128118217it_nat] :
% 5.45/5.70 ( case_o6061097939050036047it_nat @ Y4
% 5.45/5.70 @ ^ [Z6: produc3260487557148687353it_nat] :
% 5.45/5.70 ( case_o6061097939050036047it_nat @ ( some_P7913643980934408916it_nat @ Z6 )
% 5.45/5.70 @ ^ [Aa: produc3260487557148687353it_nat] : ( some_P7913643980934408916it_nat @ ( F3 @ Z6 @ Aa ) )
% 5.45/5.70 @ Y4 )
% 5.45/5.70 @ X4 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_def
% 5.45/5.70 thf(fact_2897_combine__options__def,axiom,
% 5.45/5.70 ( combin4318129983670048329it_nat
% 5.45/5.70 = ( ^ [F3: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,X4: option8956607266484857688it_nat,Y4: option8956607266484857688it_nat] :
% 5.45/5.70 ( case_o2963978774867076333it_nat @ Y4
% 5.45/5.70 @ ^ [Z6: produc8664842809031399944it_nat] :
% 5.45/5.70 ( case_o2963978774867076333it_nat @ ( some_P1914260805536162275it_nat @ Z6 )
% 5.45/5.70 @ ^ [Aa: produc8664842809031399944it_nat] : ( some_P1914260805536162275it_nat @ ( F3 @ Z6 @ Aa ) )
% 5.45/5.70 @ Y4 )
% 5.45/5.70 @ X4 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_def
% 5.45/5.70 thf(fact_2898_combine__options__def,axiom,
% 5.45/5.70 ( combine_options_num
% 5.45/5.70 = ( ^ [F3: num > num > num,X4: option_num,Y4: option_num] :
% 5.45/5.70 ( case_o6005452278849405969um_num @ Y4
% 5.45/5.70 @ ^ [Z6: num] :
% 5.45/5.70 ( case_o6005452278849405969um_num @ ( some_num @ Z6 )
% 5.45/5.70 @ ^ [Aa: num] : ( some_num @ ( F3 @ Z6 @ Aa ) )
% 5.45/5.70 @ Y4 )
% 5.45/5.70 @ X4 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_def
% 5.45/5.70 thf(fact_2899_le__zero__eq,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.45/5.70 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_zero_eq
% 5.45/5.70 thf(fact_2900_not__gr__zero,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.70 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % not_gr_zero
% 5.45/5.70 thf(fact_2901_mult__zero__left,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.70 = zero_z3403309356797280102nteger ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_left
% 5.45/5.70 thf(fact_2902_mult__zero__left,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.45/5.70 = zero_zero_rat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_left
% 5.45/5.70 thf(fact_2903_mult__zero__left,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.45/5.70 = zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_left
% 5.45/5.70 thf(fact_2904_mult__zero__left,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ zero_zero_int @ A )
% 5.45/5.70 = zero_zero_int ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_left
% 5.45/5.70 thf(fact_2905_mult__zero__right,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.70 = zero_z3403309356797280102nteger ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_right
% 5.45/5.70 thf(fact_2906_mult__zero__right,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.45/5.70 = zero_zero_rat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_right
% 5.45/5.70 thf(fact_2907_mult__zero__right,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.45/5.70 = zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_right
% 5.45/5.70 thf(fact_2908_mult__zero__right,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ A @ zero_zero_int )
% 5.45/5.70 = zero_zero_int ) ).
% 5.45/5.70
% 5.45/5.70 % mult_zero_right
% 5.45/5.70 thf(fact_2909_mult__eq__0__iff,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.70 = zero_z3403309356797280102nteger )
% 5.45/5.70 = ( ( A = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_eq_0_iff
% 5.45/5.70 thf(fact_2910_mult__eq__0__iff,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ A @ B )
% 5.45/5.70 = zero_zero_rat )
% 5.45/5.70 = ( ( A = zero_zero_rat )
% 5.45/5.70 | ( B = zero_zero_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_eq_0_iff
% 5.45/5.70 thf(fact_2911_mult__eq__0__iff,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ A @ B )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 = ( ( A = zero_zero_nat )
% 5.45/5.70 | ( B = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_eq_0_iff
% 5.45/5.70 thf(fact_2912_mult__eq__0__iff,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ( times_times_int @ A @ B )
% 5.45/5.70 = zero_zero_int )
% 5.45/5.70 = ( ( A = zero_zero_int )
% 5.45/5.70 | ( B = zero_zero_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_eq_0_iff
% 5.45/5.70 thf(fact_2913_mult__cancel__left,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ C @ A )
% 5.45/5.70 = ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left
% 5.45/5.70 thf(fact_2914_mult__cancel__left,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ C @ A )
% 5.45/5.70 = ( times_times_rat @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left
% 5.45/5.70 thf(fact_2915_mult__cancel__left,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ C @ A )
% 5.45/5.70 = ( times_times_nat @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_zero_nat )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left
% 5.45/5.70 thf(fact_2916_mult__cancel__left,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ( times_times_int @ C @ A )
% 5.45/5.70 = ( times_times_int @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left
% 5.45/5.70 thf(fact_2917_mult__cancel__right,axiom,
% 5.45/5.70 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ A @ C )
% 5.45/5.70 = ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right
% 5.45/5.70 thf(fact_2918_mult__cancel__right,axiom,
% 5.45/5.70 ! [A: rat,C: rat,B: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ A @ C )
% 5.45/5.70 = ( times_times_rat @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right
% 5.45/5.70 thf(fact_2919_mult__cancel__right,axiom,
% 5.45/5.70 ! [A: nat,C: nat,B: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ A @ C )
% 5.45/5.70 = ( times_times_nat @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_zero_nat )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right
% 5.45/5.70 thf(fact_2920_mult__cancel__right,axiom,
% 5.45/5.70 ! [A: int,C: int,B: int] :
% 5.45/5.70 ( ( ( times_times_int @ A @ C )
% 5.45/5.70 = ( times_times_int @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right
% 5.45/5.70 thf(fact_2921_mult_Oright__neutral,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.right_neutral
% 5.45/5.70 thf(fact_2922_mult_Oright__neutral,axiom,
% 5.45/5.70 ! [A: assn] :
% 5.45/5.70 ( ( times_times_assn @ A @ one_one_assn )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.right_neutral
% 5.45/5.70 thf(fact_2923_mult_Oright__neutral,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ A @ one_one_rat )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.right_neutral
% 5.45/5.70 thf(fact_2924_mult_Oright__neutral,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ A @ one_one_nat )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.right_neutral
% 5.45/5.70 thf(fact_2925_mult_Oright__neutral,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ A @ one_one_int )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.right_neutral
% 5.45/5.70 thf(fact_2926_mult__1,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult_1
% 5.45/5.70 thf(fact_2927_mult__1,axiom,
% 5.45/5.70 ! [A: assn] :
% 5.45/5.70 ( ( times_times_assn @ one_one_assn @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult_1
% 5.45/5.70 thf(fact_2928_mult__1,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ one_one_rat @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult_1
% 5.45/5.70 thf(fact_2929_mult__1,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ one_one_nat @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult_1
% 5.45/5.70 thf(fact_2930_mult__1,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ one_one_int @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult_1
% 5.45/5.70 thf(fact_2931_less__nat__zero__code,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % less_nat_zero_code
% 5.45/5.70 thf(fact_2932_neq0__conv,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( N2 != zero_zero_nat )
% 5.45/5.70 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.70
% 5.45/5.70 % neq0_conv
% 5.45/5.70 thf(fact_2933_bot__nat__0_Onot__eq__extremum,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( A != zero_zero_nat )
% 5.45/5.70 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_0.not_eq_extremum
% 5.45/5.70 thf(fact_2934_le0,axiom,
% 5.45/5.70 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.45/5.70
% 5.45/5.70 % le0
% 5.45/5.70 thf(fact_2935_bot__nat__0_Oextremum,axiom,
% 5.45/5.70 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_0.extremum
% 5.45/5.70 thf(fact_2936_add__is__0,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ( plus_plus_nat @ M @ N2 )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 = ( ( M = zero_zero_nat )
% 5.45/5.70 & ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_is_0
% 5.45/5.70 thf(fact_2937_Nat_Oadd__0__right,axiom,
% 5.45/5.70 ! [M: nat] :
% 5.45/5.70 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.45/5.70 = M ) ).
% 5.45/5.70
% 5.45/5.70 % Nat.add_0_right
% 5.45/5.70 thf(fact_2938_mult__cancel2,axiom,
% 5.45/5.70 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ M @ K )
% 5.45/5.70 = ( times_times_nat @ N2 @ K ) )
% 5.45/5.70 = ( ( M = N2 )
% 5.45/5.70 | ( K = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel2
% 5.45/5.70 thf(fact_2939_mult__cancel1,axiom,
% 5.45/5.70 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ K @ M )
% 5.45/5.70 = ( times_times_nat @ K @ N2 ) )
% 5.45/5.70 = ( ( M = N2 )
% 5.45/5.70 | ( K = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel1
% 5.45/5.70 thf(fact_2940_mult__0__right,axiom,
% 5.45/5.70 ! [M: nat] :
% 5.45/5.70 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.45/5.70 = zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_0_right
% 5.45/5.70 thf(fact_2941_mult__is__0,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ M @ N2 )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 = ( ( M = zero_zero_nat )
% 5.45/5.70 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_is_0
% 5.45/5.70 thf(fact_2942_nat__mult__eq__1__iff,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ M @ N2 )
% 5.45/5.70 = one_one_nat )
% 5.45/5.70 = ( ( M = one_one_nat )
% 5.45/5.70 & ( N2 = one_one_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % nat_mult_eq_1_iff
% 5.45/5.70 thf(fact_2943_nat__1__eq__mult__iff,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( one_one_nat
% 5.45/5.70 = ( times_times_nat @ M @ N2 ) )
% 5.45/5.70 = ( ( M = one_one_nat )
% 5.45/5.70 & ( N2 = one_one_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % nat_1_eq_mult_iff
% 5.45/5.70 thf(fact_2944_combine__options__simps_I3_J,axiom,
% 5.45/5.70 ! [F: produc3260487557148687353it_nat > produc3260487557148687353it_nat > produc3260487557148687353it_nat,A: produc3260487557148687353it_nat,B: produc3260487557148687353it_nat] :
% 5.45/5.70 ( ( combin5819755802923621690it_nat @ F @ ( some_P7913643980934408916it_nat @ A ) @ ( some_P7913643980934408916it_nat @ B ) )
% 5.45/5.70 = ( some_P7913643980934408916it_nat @ ( F @ A @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_simps(3)
% 5.45/5.70 thf(fact_2945_combine__options__simps_I3_J,axiom,
% 5.45/5.70 ! [F: num > num > num,A: num,B: num] :
% 5.45/5.70 ( ( combine_options_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.45/5.70 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_simps(3)
% 5.45/5.70 thf(fact_2946_combine__options__simps_I3_J,axiom,
% 5.45/5.70 ! [F: produc8664842809031399944it_nat > produc8664842809031399944it_nat > produc8664842809031399944it_nat,A: produc8664842809031399944it_nat,B: produc8664842809031399944it_nat] :
% 5.45/5.70 ( ( combin4318129983670048329it_nat @ F @ ( some_P1914260805536162275it_nat @ A ) @ ( some_P1914260805536162275it_nat @ B ) )
% 5.45/5.70 = ( some_P1914260805536162275it_nat @ ( F @ A @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_simps(3)
% 5.45/5.70 thf(fact_2947_combine__options__simps_I2_J,axiom,
% 5.45/5.70 ! [F: num > num > num,X: option_num] :
% 5.45/5.70 ( ( combine_options_num @ F @ X @ none_num )
% 5.45/5.70 = X ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_simps(2)
% 5.45/5.70 thf(fact_2948_combine__options__simps_I1_J,axiom,
% 5.45/5.70 ! [F: num > num > num,Y: option_num] :
% 5.45/5.70 ( ( combine_options_num @ F @ none_num @ Y )
% 5.45/5.70 = Y ) ).
% 5.45/5.70
% 5.45/5.70 % combine_options_simps(1)
% 5.45/5.70 thf(fact_2949_pure__true,axiom,
% 5.45/5.70 ( ( pure_assn @ $true )
% 5.45/5.70 = one_one_assn ) ).
% 5.45/5.70
% 5.45/5.70 % pure_true
% 5.45/5.70 thf(fact_2950_pure__assn__eq__emp__iff,axiom,
% 5.45/5.70 ! [P: $o] :
% 5.45/5.70 ( ( ( pure_assn @ P )
% 5.45/5.70 = one_one_assn )
% 5.45/5.70 = P ) ).
% 5.45/5.70
% 5.45/5.70 % pure_assn_eq_emp_iff
% 5.45/5.70 thf(fact_2951_assn__basic__inequalities_I3_J,axiom,
% 5.45/5.70 bot_bot_assn != one_one_assn ).
% 5.45/5.70
% 5.45/5.70 % assn_basic_inequalities(3)
% 5.45/5.70 thf(fact_2952_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_le_double_add_iff_zero_le_single_add
% 5.45/5.70 thf(fact_2953_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.45/5.70 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_le_double_add_iff_zero_le_single_add
% 5.45/5.70 thf(fact_2954_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.45/5.70 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_le_double_add_iff_zero_le_single_add
% 5.45/5.70 thf(fact_2955_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_le_zero_iff_single_add_le_zero
% 5.45/5.70 thf(fact_2956_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.45/5.70 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_le_zero_iff_single_add_le_zero
% 5.45/5.70 thf(fact_2957_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.45/5.70 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_le_zero_iff_single_add_le_zero
% 5.45/5.70 thf(fact_2958_le__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel2
% 5.45/5.70 thf(fact_2959_le__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.45/5.70 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel2
% 5.45/5.70 thf(fact_2960_le__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.45/5.70 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel2
% 5.45/5.70 thf(fact_2961_le__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.45/5.70 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel2
% 5.45/5.70 thf(fact_2962_le__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel1
% 5.45/5.70 thf(fact_2963_le__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.45/5.70 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel1
% 5.45/5.70 thf(fact_2964_le__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.45/5.70 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel1
% 5.45/5.70 thf(fact_2965_le__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.45/5.70 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_add_same_cancel1
% 5.45/5.70 thf(fact_2966_add__le__same__cancel2,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel2
% 5.45/5.70 thf(fact_2967_add__le__same__cancel2,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel2
% 5.45/5.70 thf(fact_2968_add__le__same__cancel2,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel2
% 5.45/5.70 thf(fact_2969_add__le__same__cancel2,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel2
% 5.45/5.70 thf(fact_2970_add__le__same__cancel1,axiom,
% 5.45/5.70 ! [B: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.45/5.70 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel1
% 5.45/5.70 thf(fact_2971_add__le__same__cancel1,axiom,
% 5.45/5.70 ! [B: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel1
% 5.45/5.70 thf(fact_2972_add__le__same__cancel1,axiom,
% 5.45/5.70 ! [B: nat,A: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel1
% 5.45/5.70 thf(fact_2973_add__le__same__cancel1,axiom,
% 5.45/5.70 ! [B: int,A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_le_same_cancel1
% 5.45/5.70 thf(fact_2974_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ A ) )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_double_add_iff_zero_less_single_add
% 5.45/5.70 thf(fact_2975_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.45/5.70 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_double_add_iff_zero_less_single_add
% 5.45/5.70 thf(fact_2976_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.45/5.70 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_double_add_iff_zero_less_single_add
% 5.45/5.70 thf(fact_2977_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_less_zero_iff_single_add_less_zero
% 5.45/5.70 thf(fact_2978_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.45/5.70 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_less_zero_iff_single_add_less_zero
% 5.45/5.70 thf(fact_2979_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.45/5.70 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % double_add_less_zero_iff_single_add_less_zero
% 5.45/5.70 thf(fact_2980_less__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel2
% 5.45/5.70 thf(fact_2981_less__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.45/5.70 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel2
% 5.45/5.70 thf(fact_2982_less__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.45/5.70 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel2
% 5.45/5.70 thf(fact_2983_less__add__same__cancel2,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.45/5.70 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel2
% 5.45/5.70 thf(fact_2984_less__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel1
% 5.45/5.70 thf(fact_2985_less__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.45/5.70 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel1
% 5.45/5.70 thf(fact_2986_less__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.45/5.70 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel1
% 5.45/5.70 thf(fact_2987_less__add__same__cancel1,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.45/5.70 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_same_cancel1
% 5.45/5.70 thf(fact_2988_add__less__same__cancel2,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel2
% 5.45/5.70 thf(fact_2989_add__less__same__cancel2,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel2
% 5.45/5.70 thf(fact_2990_add__less__same__cancel2,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel2
% 5.45/5.70 thf(fact_2991_add__less__same__cancel2,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.45/5.70 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel2
% 5.45/5.70 thf(fact_2992_add__less__same__cancel1,axiom,
% 5.45/5.70 ! [B: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.45/5.70 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel1
% 5.45/5.70 thf(fact_2993_add__less__same__cancel1,axiom,
% 5.45/5.70 ! [B: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel1
% 5.45/5.70 thf(fact_2994_add__less__same__cancel1,axiom,
% 5.45/5.70 ! [B: nat,A: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel1
% 5.45/5.70 thf(fact_2995_add__less__same__cancel1,axiom,
% 5.45/5.70 ! [B: int,A: int] :
% 5.45/5.70 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.45/5.70 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_less_same_cancel1
% 5.45/5.70 thf(fact_2996_mult__cancel__left1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( B = one_one_Code_integer ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left1
% 5.45/5.70 thf(fact_2997_mult__cancel__left1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_times_rat @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( B = one_one_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left1
% 5.45/5.70 thf(fact_2998_mult__cancel__left1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_times_int @ C @ B ) )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( B = one_one_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left1
% 5.45/5.70 thf(fact_2999_mult__cancel__left2,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ C @ A )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( A = one_one_Code_integer ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left2
% 5.45/5.70 thf(fact_3000_mult__cancel__left2,axiom,
% 5.45/5.70 ! [C: rat,A: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ C @ A )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( A = one_one_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left2
% 5.45/5.70 thf(fact_3001_mult__cancel__left2,axiom,
% 5.45/5.70 ! [C: int,A: int] :
% 5.45/5.70 ( ( ( times_times_int @ C @ A )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( A = one_one_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_left2
% 5.45/5.70 thf(fact_3002_mult__cancel__right1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( B = one_one_Code_integer ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right1
% 5.45/5.70 thf(fact_3003_mult__cancel__right1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_times_rat @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( B = one_one_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right1
% 5.45/5.70 thf(fact_3004_mult__cancel__right1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( C
% 5.45/5.70 = ( times_times_int @ B @ C ) )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( B = one_one_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right1
% 5.45/5.70 thf(fact_3005_mult__cancel__right2,axiom,
% 5.45/5.70 ! [A: code_integer,C: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ A @ C )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( A = one_one_Code_integer ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right2
% 5.45/5.70 thf(fact_3006_mult__cancel__right2,axiom,
% 5.45/5.70 ! [A: rat,C: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ A @ C )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_zero_rat )
% 5.45/5.70 | ( A = one_one_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right2
% 5.45/5.70 thf(fact_3007_mult__cancel__right2,axiom,
% 5.45/5.70 ! [A: int,C: int] :
% 5.45/5.70 ( ( ( times_times_int @ A @ C )
% 5.45/5.70 = C )
% 5.45/5.70 = ( ( C = zero_zero_int )
% 5.45/5.70 | ( A = one_one_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_cancel_right2
% 5.45/5.70 thf(fact_3008_add__gr__0,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.70 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.70 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_gr_0
% 5.45/5.70 thf(fact_3009_mult__less__cancel2,axiom,
% 5.45/5.70 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.45/5.70 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.70 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel2
% 5.45/5.70 thf(fact_3010_nat__0__less__mult__iff,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.70 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.70 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % nat_0_less_mult_iff
% 5.45/5.70 thf(fact_3011_less__one,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ N2 @ one_one_nat )
% 5.45/5.70 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_one
% 5.45/5.70 thf(fact_3012_ent__pure__pre__iff__sng,axiom,
% 5.45/5.70 ! [B: $o,Q: assn] :
% 5.45/5.70 ( ( entails @ ( pure_assn @ B ) @ Q )
% 5.45/5.70 = ( B
% 5.45/5.70 => ( entails @ one_one_assn @ Q ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % ent_pure_pre_iff_sng
% 5.45/5.70 thf(fact_3013_zero__less__one__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one_class.zero_le_one
% 5.45/5.70 thf(fact_3014_zero__less__one__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one_class.zero_le_one
% 5.45/5.70 thf(fact_3015_zero__less__one__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one_class.zero_le_one
% 5.45/5.70 thf(fact_3016_zero__less__one__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one_class.zero_le_one
% 5.45/5.70 thf(fact_3017_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.45/5.70
% 5.45/5.70 % linordered_nonzero_semiring_class.zero_le_one
% 5.45/5.70 thf(fact_3018_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.45/5.70
% 5.45/5.70 % linordered_nonzero_semiring_class.zero_le_one
% 5.45/5.70 thf(fact_3019_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.45/5.70
% 5.45/5.70 % linordered_nonzero_semiring_class.zero_le_one
% 5.45/5.70 thf(fact_3020_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.45/5.70 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.45/5.70
% 5.45/5.70 % linordered_nonzero_semiring_class.zero_le_one
% 5.45/5.70 thf(fact_3021_not__one__le__zero,axiom,
% 5.45/5.70 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_le_zero
% 5.45/5.70 thf(fact_3022_not__one__le__zero,axiom,
% 5.45/5.70 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_le_zero
% 5.45/5.70 thf(fact_3023_not__one__le__zero,axiom,
% 5.45/5.70 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_le_zero
% 5.45/5.70 thf(fact_3024_not__one__le__zero,axiom,
% 5.45/5.70 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_le_zero
% 5.45/5.70 thf(fact_3025_zero__less__one,axiom,
% 5.45/5.70 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one
% 5.45/5.70 thf(fact_3026_zero__less__one,axiom,
% 5.45/5.70 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one
% 5.45/5.70 thf(fact_3027_zero__less__one,axiom,
% 5.45/5.70 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one
% 5.45/5.70 thf(fact_3028_zero__less__one,axiom,
% 5.45/5.70 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.45/5.70
% 5.45/5.70 % zero_less_one
% 5.45/5.70 thf(fact_3029_not__one__less__zero,axiom,
% 5.45/5.70 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_less_zero
% 5.45/5.70 thf(fact_3030_not__one__less__zero,axiom,
% 5.45/5.70 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_less_zero
% 5.45/5.70 thf(fact_3031_not__one__less__zero,axiom,
% 5.45/5.70 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_less_zero
% 5.45/5.70 thf(fact_3032_not__one__less__zero,axiom,
% 5.45/5.70 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.45/5.70
% 5.45/5.70 % not_one_less_zero
% 5.45/5.70 thf(fact_3033_bot__nat__def,axiom,
% 5.45/5.70 bot_bot_nat = zero_zero_nat ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_def
% 5.45/5.70 thf(fact_3034_nat__geq__1__eq__neqz,axiom,
% 5.45/5.70 ! [X: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ one_one_nat @ X )
% 5.45/5.70 = ( X != zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % nat_geq_1_eq_neqz
% 5.45/5.70 thf(fact_3035_mult__eq__self__implies__10,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( M
% 5.45/5.70 = ( times_times_nat @ M @ N2 ) )
% 5.45/5.70 => ( ( N2 = one_one_nat )
% 5.45/5.70 | ( M = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_eq_self_implies_10
% 5.45/5.70 thf(fact_3036_one__assn__def,axiom,
% 5.45/5.70 ( one_one_assn
% 5.45/5.70 = ( abs_assn @ one_assn_raw ) ) ).
% 5.45/5.70
% 5.45/5.70 % one_assn_def
% 5.45/5.70 thf(fact_3037_mult__left__le,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ C @ one_one_Code_integer )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ A ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le
% 5.45/5.70 thf(fact_3038_mult__left__le,axiom,
% 5.45/5.70 ! [C: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le
% 5.45/5.70 thf(fact_3039_mult__left__le,axiom,
% 5.45/5.70 ! [C: nat,A: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.45/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le
% 5.45/5.70 thf(fact_3040_mult__left__le,axiom,
% 5.45/5.70 ! [C: int,A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.70 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le
% 5.45/5.70 thf(fact_3041_mult__le__one,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_one
% 5.45/5.70 thf(fact_3042_mult__le__one,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.70 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_one
% 5.45/5.70 thf(fact_3043_mult__le__one,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.45/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.70 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.45/5.70 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_one
% 5.45/5.70 thf(fact_3044_mult__le__one,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.70 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.45/5.70 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_one
% 5.45/5.70 thf(fact_3045_mult__right__le__one__le,axiom,
% 5.45/5.70 ! [X: code_integer,Y: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Y ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_le_one_le
% 5.45/5.70 thf(fact_3046_mult__right__le__one__le,axiom,
% 5.45/5.70 ! [X: rat,Y: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.70 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_le_one_le
% 5.45/5.70 thf(fact_3047_mult__right__le__one__le,axiom,
% 5.45/5.70 ! [X: int,Y: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.70 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.45/5.70 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_le_one_le
% 5.45/5.70 thf(fact_3048_mult__left__le__one__le,axiom,
% 5.45/5.70 ! [X: code_integer,Y: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ Y @ one_one_Code_integer )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Y @ X ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le_one_le
% 5.45/5.70 thf(fact_3049_mult__left__le__one__le,axiom,
% 5.45/5.70 ! [X: rat,Y: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.70 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le_one_le
% 5.45/5.70 thf(fact_3050_mult__left__le__one__le,axiom,
% 5.45/5.70 ! [X: int,Y: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.70 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.45/5.70 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_le_one_le
% 5.45/5.70 thf(fact_3051_zero__less__two,axiom,
% 5.45/5.70 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_two
% 5.45/5.70 thf(fact_3052_zero__less__two,axiom,
% 5.45/5.70 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_two
% 5.45/5.70 thf(fact_3053_zero__less__two,axiom,
% 5.45/5.70 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_two
% 5.45/5.70 thf(fact_3054_zero__less__two,axiom,
% 5.45/5.70 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_two
% 5.45/5.70 thf(fact_3055_zero__le,axiom,
% 5.45/5.70 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.45/5.70
% 5.45/5.70 % zero_le
% 5.45/5.70 thf(fact_3056_comm__monoid__mult__class_Omult__1,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ one_one_Code_integer @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % comm_monoid_mult_class.mult_1
% 5.45/5.70 thf(fact_3057_comm__monoid__mult__class_Omult__1,axiom,
% 5.45/5.70 ! [A: assn] :
% 5.45/5.70 ( ( times_times_assn @ one_one_assn @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % comm_monoid_mult_class.mult_1
% 5.45/5.70 thf(fact_3058_comm__monoid__mult__class_Omult__1,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ one_one_rat @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % comm_monoid_mult_class.mult_1
% 5.45/5.70 thf(fact_3059_comm__monoid__mult__class_Omult__1,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ one_one_nat @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % comm_monoid_mult_class.mult_1
% 5.45/5.70 thf(fact_3060_comm__monoid__mult__class_Omult__1,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ one_one_int @ A )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % comm_monoid_mult_class.mult_1
% 5.45/5.70 thf(fact_3061_mult_Ocomm__neutral,axiom,
% 5.45/5.70 ! [A: code_integer] :
% 5.45/5.70 ( ( times_3573771949741848930nteger @ A @ one_one_Code_integer )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.comm_neutral
% 5.45/5.70 thf(fact_3062_mult_Ocomm__neutral,axiom,
% 5.45/5.70 ! [A: assn] :
% 5.45/5.70 ( ( times_times_assn @ A @ one_one_assn )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.comm_neutral
% 5.45/5.70 thf(fact_3063_mult_Ocomm__neutral,axiom,
% 5.45/5.70 ! [A: rat] :
% 5.45/5.70 ( ( times_times_rat @ A @ one_one_rat )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.comm_neutral
% 5.45/5.70 thf(fact_3064_mult_Ocomm__neutral,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( times_times_nat @ A @ one_one_nat )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.comm_neutral
% 5.45/5.70 thf(fact_3065_mult_Ocomm__neutral,axiom,
% 5.45/5.70 ! [A: int] :
% 5.45/5.70 ( ( times_times_int @ A @ one_one_int )
% 5.45/5.70 = A ) ).
% 5.45/5.70
% 5.45/5.70 % mult.comm_neutral
% 5.45/5.70 thf(fact_3066_zero__less__iff__neq__zero,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.70 = ( N2 != zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % zero_less_iff_neq_zero
% 5.45/5.70 thf(fact_3067_gr__implies__not__zero,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.70 => ( N2 != zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % gr_implies_not_zero
% 5.45/5.70 thf(fact_3068_not__less__zero,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % not_less_zero
% 5.45/5.70 thf(fact_3069_gr__zeroI,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( N2 != zero_zero_nat )
% 5.45/5.70 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.70
% 5.45/5.70 % gr_zeroI
% 5.45/5.70 thf(fact_3070_mult__not__zero,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.70 != zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.70 & ( B != zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_not_zero
% 5.45/5.70 thf(fact_3071_mult__not__zero,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ A @ B )
% 5.45/5.70 != zero_zero_rat )
% 5.45/5.70 => ( ( A != zero_zero_rat )
% 5.45/5.70 & ( B != zero_zero_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_not_zero
% 5.45/5.70 thf(fact_3072_mult__not__zero,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ A @ B )
% 5.45/5.70 != zero_zero_nat )
% 5.45/5.70 => ( ( A != zero_zero_nat )
% 5.45/5.70 & ( B != zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_not_zero
% 5.45/5.70 thf(fact_3073_mult__not__zero,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ( times_times_int @ A @ B )
% 5.45/5.70 != zero_zero_int )
% 5.45/5.70 => ( ( A != zero_zero_int )
% 5.45/5.70 & ( B != zero_zero_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_not_zero
% 5.45/5.70 thf(fact_3074_divisors__zero,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.70 = zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( A = zero_z3403309356797280102nteger )
% 5.45/5.70 | ( B = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % divisors_zero
% 5.45/5.70 thf(fact_3075_divisors__zero,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ( times_times_rat @ A @ B )
% 5.45/5.70 = zero_zero_rat )
% 5.45/5.70 => ( ( A = zero_zero_rat )
% 5.45/5.70 | ( B = zero_zero_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % divisors_zero
% 5.45/5.70 thf(fact_3076_divisors__zero,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ( times_times_nat @ A @ B )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 => ( ( A = zero_zero_nat )
% 5.45/5.70 | ( B = zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % divisors_zero
% 5.45/5.70 thf(fact_3077_divisors__zero,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ( times_times_int @ A @ B )
% 5.45/5.70 = zero_zero_int )
% 5.45/5.70 => ( ( A = zero_zero_int )
% 5.45/5.70 | ( B = zero_zero_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % divisors_zero
% 5.45/5.70 thf(fact_3078_no__zero__divisors,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.70 != zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % no_zero_divisors
% 5.45/5.70 thf(fact_3079_no__zero__divisors,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( A != zero_zero_rat )
% 5.45/5.70 => ( ( B != zero_zero_rat )
% 5.45/5.70 => ( ( times_times_rat @ A @ B )
% 5.45/5.70 != zero_zero_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % no_zero_divisors
% 5.45/5.70 thf(fact_3080_no__zero__divisors,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( A != zero_zero_nat )
% 5.45/5.70 => ( ( B != zero_zero_nat )
% 5.45/5.70 => ( ( times_times_nat @ A @ B )
% 5.45/5.70 != zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % no_zero_divisors
% 5.45/5.70 thf(fact_3081_no__zero__divisors,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( A != zero_zero_int )
% 5.45/5.70 => ( ( B != zero_zero_int )
% 5.45/5.70 => ( ( times_times_int @ A @ B )
% 5.45/5.70 != zero_zero_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % no_zero_divisors
% 5.45/5.70 thf(fact_3082_mult__left__cancel,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ( times_3573771949741848930nteger @ C @ A )
% 5.45/5.70 = ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_cancel
% 5.45/5.70 thf(fact_3083_mult__left__cancel,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( C != zero_zero_rat )
% 5.45/5.70 => ( ( ( times_times_rat @ C @ A )
% 5.45/5.70 = ( times_times_rat @ C @ B ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_cancel
% 5.45/5.70 thf(fact_3084_mult__left__cancel,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( C != zero_zero_nat )
% 5.45/5.70 => ( ( ( times_times_nat @ C @ A )
% 5.45/5.70 = ( times_times_nat @ C @ B ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_cancel
% 5.45/5.70 thf(fact_3085_mult__left__cancel,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( C != zero_zero_int )
% 5.45/5.70 => ( ( ( times_times_int @ C @ A )
% 5.45/5.70 = ( times_times_int @ C @ B ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_left_cancel
% 5.45/5.70 thf(fact_3086_mult__right__cancel,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ( times_3573771949741848930nteger @ A @ C )
% 5.45/5.70 = ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_cancel
% 5.45/5.70 thf(fact_3087_mult__right__cancel,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( C != zero_zero_rat )
% 5.45/5.70 => ( ( ( times_times_rat @ A @ C )
% 5.45/5.70 = ( times_times_rat @ B @ C ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_cancel
% 5.45/5.70 thf(fact_3088_mult__right__cancel,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( C != zero_zero_nat )
% 5.45/5.70 => ( ( ( times_times_nat @ A @ C )
% 5.45/5.70 = ( times_times_nat @ B @ C ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_cancel
% 5.45/5.70 thf(fact_3089_mult__right__cancel,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( C != zero_zero_int )
% 5.45/5.70 => ( ( ( times_times_int @ A @ C )
% 5.45/5.70 = ( times_times_int @ B @ C ) )
% 5.45/5.70 = ( A = B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_right_cancel
% 5.45/5.70 thf(fact_3090_infinite__descent0,axiom,
% 5.45/5.70 ! [P: nat > $o,N2: nat] :
% 5.45/5.70 ( ( P @ zero_zero_nat )
% 5.45/5.70 => ( ! [N5: nat] :
% 5.45/5.70 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.70 => ( ~ ( P @ N5 )
% 5.45/5.70 => ? [M4: nat] :
% 5.45/5.70 ( ( ord_less_nat @ M4 @ N5 )
% 5.45/5.70 & ~ ( P @ M4 ) ) ) )
% 5.45/5.70 => ( P @ N2 ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % infinite_descent0
% 5.45/5.70 thf(fact_3091_gr__implies__not0,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.70 => ( N2 != zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % gr_implies_not0
% 5.45/5.70 thf(fact_3092_less__zeroE,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % less_zeroE
% 5.45/5.70 thf(fact_3093_not__less0,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % not_less0
% 5.45/5.70 thf(fact_3094_not__gr0,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.70 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % not_gr0
% 5.45/5.70 thf(fact_3095_gr0I,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( N2 != zero_zero_nat )
% 5.45/5.70 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.70
% 5.45/5.70 % gr0I
% 5.45/5.70 thf(fact_3096_bot__nat__0_Oextremum__strict,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_0.extremum_strict
% 5.45/5.70 thf(fact_3097_nat__mult__1__right,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( times_times_nat @ N2 @ one_one_nat )
% 5.45/5.70 = N2 ) ).
% 5.45/5.70
% 5.45/5.70 % nat_mult_1_right
% 5.45/5.70 thf(fact_3098_nat__mult__1,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( times_times_nat @ one_one_nat @ N2 )
% 5.45/5.70 = N2 ) ).
% 5.45/5.70
% 5.45/5.70 % nat_mult_1
% 5.45/5.70 thf(fact_3099_le__0__eq,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.45/5.70 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % le_0_eq
% 5.45/5.70 thf(fact_3100_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.70 => ( A = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_0.extremum_uniqueI
% 5.45/5.70 thf(fact_3101_bot__nat__0_Oextremum__unique,axiom,
% 5.45/5.70 ! [A: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.70 = ( A = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % bot_nat_0.extremum_unique
% 5.45/5.70 thf(fact_3102_less__eq__nat_Osimps_I1_J,axiom,
% 5.45/5.70 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.45/5.70
% 5.45/5.70 % less_eq_nat.simps(1)
% 5.45/5.70 thf(fact_3103_plus__nat_Oadd__0,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 5.45/5.70 = N2 ) ).
% 5.45/5.70
% 5.45/5.70 % plus_nat.add_0
% 5.45/5.70 thf(fact_3104_add__eq__self__zero,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ( plus_plus_nat @ M @ N2 )
% 5.45/5.70 = M )
% 5.45/5.70 => ( N2 = zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_eq_self_zero
% 5.45/5.70 thf(fact_3105_mult__0,axiom,
% 5.45/5.70 ! [N2: nat] :
% 5.45/5.70 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 5.45/5.70 = zero_zero_nat ) ).
% 5.45/5.70
% 5.45/5.70 % mult_0
% 5.45/5.70 thf(fact_3106_assn__one__left,axiom,
% 5.45/5.70 ! [P: assn] :
% 5.45/5.70 ( ( times_times_assn @ one_one_assn @ P )
% 5.45/5.70 = P ) ).
% 5.45/5.70
% 5.45/5.70 % assn_one_left
% 5.45/5.70 thf(fact_3107_mult__le__cancel__left1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 5.45/5.70 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left1
% 5.45/5.70 thf(fact_3108_mult__le__cancel__left1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.45/5.70 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left1
% 5.45/5.70 thf(fact_3109_mult__le__cancel__left1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.45/5.70 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left1
% 5.45/5.70 thf(fact_3110_mult__le__cancel__left2,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 5.45/5.70 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left2
% 5.45/5.70 thf(fact_3111_mult__le__cancel__left2,axiom,
% 5.45/5.70 ! [C: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.45/5.70 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left2
% 5.45/5.70 thf(fact_3112_mult__le__cancel__left2,axiom,
% 5.45/5.70 ! [C: int,A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.45/5.70 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_left2
% 5.45/5.70 thf(fact_3113_mult__le__cancel__right1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ B ) )
% 5.45/5.70 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right1
% 5.45/5.70 thf(fact_3114_mult__le__cancel__right1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.45/5.70 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right1
% 5.45/5.70 thf(fact_3115_mult__le__cancel__right1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.45/5.70 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right1
% 5.45/5.70 thf(fact_3116_mult__le__cancel__right2,axiom,
% 5.45/5.70 ! [A: code_integer,C: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer ) )
% 5.45/5.70 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right2
% 5.45/5.70 thf(fact_3117_mult__le__cancel__right2,axiom,
% 5.45/5.70 ! [A: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.45/5.70 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right2
% 5.45/5.70 thf(fact_3118_mult__le__cancel__right2,axiom,
% 5.45/5.70 ! [A: int,C: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.45/5.70 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_le_cancel_right2
% 5.45/5.70 thf(fact_3119_mult__less__cancel__left1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 5.45/5.70 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left1
% 5.45/5.70 thf(fact_3120_mult__less__cancel__left1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.45/5.70 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left1
% 5.45/5.70 thf(fact_3121_mult__less__cancel__left1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.45/5.70 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_int @ one_one_int @ B ) )
% 5.45/5.70 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left1
% 5.45/5.70 thf(fact_3122_mult__less__cancel__left2,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 5.45/5.70 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left2
% 5.45/5.70 thf(fact_3123_mult__less__cancel__left2,axiom,
% 5.45/5.70 ! [C: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.45/5.70 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left2
% 5.45/5.70 thf(fact_3124_mult__less__cancel__left2,axiom,
% 5.45/5.70 ! [C: int,A: int] :
% 5.45/5.70 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.45/5.70 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_int @ A @ one_one_int ) )
% 5.45/5.70 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_left2
% 5.45/5.70 thf(fact_3125_mult__less__cancel__right1,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ C @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B ) )
% 5.45/5.70 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right1
% 5.45/5.70 thf(fact_3126_mult__less__cancel__right1,axiom,
% 5.45/5.70 ! [C: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.45/5.70 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right1
% 5.45/5.70 thf(fact_3127_mult__less__cancel__right1,axiom,
% 5.45/5.70 ! [C: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.45/5.70 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_int @ one_one_int @ B ) )
% 5.45/5.70 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right1
% 5.45/5.70 thf(fact_3128_mult__less__cancel__right2,axiom,
% 5.45/5.70 ! [A: code_integer,C: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer ) )
% 5.45/5.70 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right2
% 5.45/5.70 thf(fact_3129_mult__less__cancel__right2,axiom,
% 5.45/5.70 ! [A: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.45/5.70 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right2
% 5.45/5.70 thf(fact_3130_mult__less__cancel__right2,axiom,
% 5.45/5.70 ! [A: int,C: int] :
% 5.45/5.70 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.45/5.70 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ord_less_int @ A @ one_one_int ) )
% 5.45/5.70 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % mult_less_cancel_right2
% 5.45/5.70 thf(fact_3131_convex__bound__le,axiom,
% 5.45/5.70 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ X @ A )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ Y @ A )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 5.45/5.70 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 5.45/5.70 = one_one_Code_integer )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_le
% 5.45/5.70 thf(fact_3132_convex__bound__le,axiom,
% 5.45/5.70 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ X @ A )
% 5.45/5.70 => ( ( ord_less_eq_rat @ Y @ A )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.45/5.70 => ( ( ( plus_plus_rat @ U @ V )
% 5.45/5.70 = one_one_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_le
% 5.45/5.70 thf(fact_3133_convex__bound__le,axiom,
% 5.45/5.70 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ X @ A )
% 5.45/5.70 => ( ( ord_less_eq_int @ Y @ A )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.45/5.70 => ( ( ( plus_plus_int @ U @ V )
% 5.45/5.70 = one_one_int )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_le
% 5.45/5.70 thf(fact_3134_lambda__one,axiom,
% 5.45/5.70 ( ( ^ [X4: code_integer] : X4 )
% 5.45/5.70 = ( times_3573771949741848930nteger @ one_one_Code_integer ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_one
% 5.45/5.70 thf(fact_3135_lambda__one,axiom,
% 5.45/5.70 ( ( ^ [X4: assn] : X4 )
% 5.45/5.70 = ( times_times_assn @ one_one_assn ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_one
% 5.45/5.70 thf(fact_3136_lambda__one,axiom,
% 5.45/5.70 ( ( ^ [X4: rat] : X4 )
% 5.45/5.70 = ( times_times_rat @ one_one_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_one
% 5.45/5.70 thf(fact_3137_lambda__one,axiom,
% 5.45/5.70 ( ( ^ [X4: nat] : X4 )
% 5.45/5.70 = ( times_times_nat @ one_one_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_one
% 5.45/5.70 thf(fact_3138_lambda__one,axiom,
% 5.45/5.70 ( ( ^ [X4: int] : X4 )
% 5.45/5.70 = ( times_times_int @ one_one_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_one
% 5.45/5.70 thf(fact_3139_lambda__zero,axiom,
% 5.45/5.70 ( ( ^ [H6: code_integer] : zero_z3403309356797280102nteger )
% 5.45/5.70 = ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_zero
% 5.45/5.70 thf(fact_3140_lambda__zero,axiom,
% 5.45/5.70 ( ( ^ [H6: rat] : zero_zero_rat )
% 5.45/5.70 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_zero
% 5.45/5.70 thf(fact_3141_lambda__zero,axiom,
% 5.45/5.70 ( ( ^ [H6: nat] : zero_zero_nat )
% 5.45/5.70 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_zero
% 5.45/5.70 thf(fact_3142_lambda__zero,axiom,
% 5.45/5.70 ( ( ^ [H6: int] : zero_zero_int )
% 5.45/5.70 = ( times_times_int @ zero_zero_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % lambda_zero
% 5.45/5.70 thf(fact_3143_convex__bound__lt,axiom,
% 5.45/5.70 ! [X: code_integer,A: code_integer,Y: code_integer,U: code_integer,V: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ X @ A )
% 5.45/5.70 => ( ( ord_le6747313008572928689nteger @ Y @ A )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ V )
% 5.45/5.70 => ( ( ( plus_p5714425477246183910nteger @ U @ V )
% 5.45/5.70 = one_one_Code_integer )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ U @ X ) @ ( times_3573771949741848930nteger @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_lt
% 5.45/5.70 thf(fact_3144_convex__bound__lt,axiom,
% 5.45/5.70 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.45/5.70 ( ( ord_less_rat @ X @ A )
% 5.45/5.70 => ( ( ord_less_rat @ Y @ A )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.45/5.70 => ( ( ( plus_plus_rat @ U @ V )
% 5.45/5.70 = one_one_rat )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_lt
% 5.45/5.70 thf(fact_3145_convex__bound__lt,axiom,
% 5.45/5.70 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.45/5.70 ( ( ord_less_int @ X @ A )
% 5.45/5.70 => ( ( ord_less_int @ Y @ A )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.45/5.70 => ( ( ( plus_plus_int @ U @ V )
% 5.45/5.70 = one_one_int )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % convex_bound_lt
% 5.45/5.70 thf(fact_3146_add__mono1,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ B @ one_one_Code_integer ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono1
% 5.45/5.70 thf(fact_3147_add__mono1,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_rat @ A @ B )
% 5.45/5.70 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono1
% 5.45/5.70 thf(fact_3148_add__mono1,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_nat @ A @ B )
% 5.45/5.70 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono1
% 5.45/5.70 thf(fact_3149_add__mono1,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_int @ A @ B )
% 5.45/5.70 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_mono1
% 5.45/5.70 thf(fact_3150_less__add__one,axiom,
% 5.45/5.70 ! [A: code_integer] : ( ord_le6747313008572928689nteger @ A @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_one
% 5.45/5.70 thf(fact_3151_less__add__one,axiom,
% 5.45/5.70 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_one
% 5.45/5.70 thf(fact_3152_less__add__one,axiom,
% 5.45/5.70 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_one
% 5.45/5.70 thf(fact_3153_less__add__one,axiom,
% 5.45/5.70 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_add_one
% 5.45/5.70 thf(fact_3154_less__1__mult,axiom,
% 5.45/5.70 ! [M: code_integer,N2: code_integer] :
% 5.45/5.70 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ M )
% 5.45/5.70 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ N2 )
% 5.45/5.70 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ M @ N2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_1_mult
% 5.45/5.70 thf(fact_3155_less__1__mult,axiom,
% 5.45/5.70 ! [M: rat,N2: rat] :
% 5.45/5.70 ( ( ord_less_rat @ one_one_rat @ M )
% 5.45/5.70 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 5.45/5.70 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_1_mult
% 5.45/5.70 thf(fact_3156_less__1__mult,axiom,
% 5.45/5.70 ! [M: nat,N2: nat] :
% 5.45/5.70 ( ( ord_less_nat @ one_one_nat @ M )
% 5.45/5.70 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.45/5.70 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_1_mult
% 5.45/5.70 thf(fact_3157_less__1__mult,axiom,
% 5.45/5.70 ! [M: int,N2: int] :
% 5.45/5.70 ( ( ord_less_int @ one_one_int @ M )
% 5.45/5.70 => ( ( ord_less_int @ one_one_int @ N2 )
% 5.45/5.70 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % less_1_mult
% 5.45/5.70 thf(fact_3158_add__nonpos__eq__0__iff,axiom,
% 5.45/5.70 ! [X: code_integer,Y: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ X @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ Y @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 5.45/5.70 = zero_z3403309356797280102nteger )
% 5.45/5.70 = ( ( X = zero_z3403309356797280102nteger )
% 5.45/5.70 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_eq_0_iff
% 5.45/5.70 thf(fact_3159_add__nonpos__eq__0__iff,axiom,
% 5.45/5.70 ! [X: rat,Y: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.45/5.70 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.45/5.70 => ( ( ( plus_plus_rat @ X @ Y )
% 5.45/5.70 = zero_zero_rat )
% 5.45/5.70 = ( ( X = zero_zero_rat )
% 5.45/5.70 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_eq_0_iff
% 5.45/5.70 thf(fact_3160_add__nonpos__eq__0__iff,axiom,
% 5.45/5.70 ! [X: nat,Y: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.45/5.70 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.45/5.70 => ( ( ( plus_plus_nat @ X @ Y )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 = ( ( X = zero_zero_nat )
% 5.45/5.70 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_eq_0_iff
% 5.45/5.70 thf(fact_3161_add__nonpos__eq__0__iff,axiom,
% 5.45/5.70 ! [X: int,Y: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.45/5.70 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.45/5.70 => ( ( ( plus_plus_int @ X @ Y )
% 5.45/5.70 = zero_zero_int )
% 5.45/5.70 = ( ( X = zero_zero_int )
% 5.45/5.70 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_eq_0_iff
% 5.45/5.70 thf(fact_3162_add__nonneg__eq__0__iff,axiom,
% 5.45/5.70 ! [X: code_integer,Y: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.70 => ( ( ( plus_p5714425477246183910nteger @ X @ Y )
% 5.45/5.70 = zero_z3403309356797280102nteger )
% 5.45/5.70 = ( ( X = zero_z3403309356797280102nteger )
% 5.45/5.70 & ( Y = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_eq_0_iff
% 5.45/5.70 thf(fact_3163_add__nonneg__eq__0__iff,axiom,
% 5.45/5.70 ! [X: rat,Y: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.70 => ( ( ( plus_plus_rat @ X @ Y )
% 5.45/5.70 = zero_zero_rat )
% 5.45/5.70 = ( ( X = zero_zero_rat )
% 5.45/5.70 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_eq_0_iff
% 5.45/5.70 thf(fact_3164_add__nonneg__eq__0__iff,axiom,
% 5.45/5.70 ! [X: nat,Y: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.45/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.45/5.70 => ( ( ( plus_plus_nat @ X @ Y )
% 5.45/5.70 = zero_zero_nat )
% 5.45/5.70 = ( ( X = zero_zero_nat )
% 5.45/5.70 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_eq_0_iff
% 5.45/5.70 thf(fact_3165_add__nonneg__eq__0__iff,axiom,
% 5.45/5.70 ! [X: int,Y: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.70 => ( ( ( plus_plus_int @ X @ Y )
% 5.45/5.70 = zero_zero_int )
% 5.45/5.70 = ( ( X = zero_zero_int )
% 5.45/5.70 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_eq_0_iff
% 5.45/5.70 thf(fact_3166_add__nonpos__nonpos,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_nonpos
% 5.45/5.70 thf(fact_3167_add__nonpos__nonpos,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.70 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_nonpos
% 5.45/5.70 thf(fact_3168_add__nonpos__nonpos,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.70 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_nonpos
% 5.45/5.70 thf(fact_3169_add__nonpos__nonpos,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.70 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonpos_nonpos
% 5.45/5.70 thf(fact_3170_add__nonneg__nonneg,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_nonneg
% 5.45/5.70 thf(fact_3171_add__nonneg__nonneg,axiom,
% 5.45/5.70 ! [A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.70 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.70 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_nonneg
% 5.45/5.70 thf(fact_3172_add__nonneg__nonneg,axiom,
% 5.45/5.70 ! [A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.70 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.70 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_nonneg
% 5.45/5.70 thf(fact_3173_add__nonneg__nonneg,axiom,
% 5.45/5.70 ! [A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.70 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.70 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_nonneg_nonneg
% 5.45/5.70 thf(fact_3174_add__increasing2,axiom,
% 5.45/5.70 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing2
% 5.45/5.70 thf(fact_3175_add__increasing2,axiom,
% 5.45/5.70 ! [C: rat,B: rat,A: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.70 => ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.70 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing2
% 5.45/5.70 thf(fact_3176_add__increasing2,axiom,
% 5.45/5.70 ! [C: nat,B: nat,A: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.70 => ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.70 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing2
% 5.45/5.70 thf(fact_3177_add__increasing2,axiom,
% 5.45/5.70 ! [C: int,B: int,A: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.70 => ( ( ord_less_eq_int @ B @ A )
% 5.45/5.70 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing2
% 5.45/5.70 thf(fact_3178_add__decreasing2,axiom,
% 5.45/5.70 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_decreasing2
% 5.45/5.70 thf(fact_3179_add__decreasing2,axiom,
% 5.45/5.70 ! [C: rat,A: rat,B: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.70 => ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_decreasing2
% 5.45/5.70 thf(fact_3180_add__decreasing2,axiom,
% 5.45/5.70 ! [C: nat,A: nat,B: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.45/5.70 => ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.70 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_decreasing2
% 5.45/5.70 thf(fact_3181_add__decreasing2,axiom,
% 5.45/5.70 ! [C: int,A: int,B: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.70 => ( ( ord_less_eq_int @ A @ B )
% 5.45/5.70 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_decreasing2
% 5.45/5.70 thf(fact_3182_add__increasing,axiom,
% 5.45/5.70 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.70 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.70 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 5.45/5.70 => ( ord_le3102999989581377725nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing
% 5.45/5.70 thf(fact_3183_add__increasing,axiom,
% 5.45/5.70 ! [A: rat,B: rat,C: rat] :
% 5.45/5.70 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.70 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing
% 5.45/5.70 thf(fact_3184_add__increasing,axiom,
% 5.45/5.70 ! [A: nat,B: nat,C: nat] :
% 5.45/5.70 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.70 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.45/5.70
% 5.45/5.70 % add_increasing
% 5.45/5.70 thf(fact_3185_add__increasing,axiom,
% 5.45/5.70 ! [A: int,B: int,C: int] :
% 5.45/5.70 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.70 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.70 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_increasing
% 5.45/5.71 thf(fact_3186_add__decreasing,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ B )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A @ C ) @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_decreasing
% 5.45/5.71 thf(fact_3187_add__decreasing,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ B )
% 5.45/5.71 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_decreasing
% 5.45/5.71 thf(fact_3188_add__decreasing,axiom,
% 5.45/5.71 ! [A: nat,C: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_eq_nat @ C @ B )
% 5.45/5.71 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_decreasing
% 5.45/5.71 thf(fact_3189_add__decreasing,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ B )
% 5.45/5.71 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_decreasing
% 5.45/5.71 thf(fact_3190_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.45/5.71 thf(fact_3191_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.45/5.71 thf(fact_3192_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.45/5.71 thf(fact_3193_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.45/5.71 thf(fact_3194_zero__le__mult__iff,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 5.45/5.71 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_mult_iff
% 5.45/5.71 thf(fact_3195_zero__le__mult__iff,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.45/5.71 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_mult_iff
% 5.45/5.71 thf(fact_3196_zero__le__mult__iff,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.45/5.71 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_mult_iff
% 5.45/5.71 thf(fact_3197_mult__nonneg__nonpos2,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos2
% 5.45/5.71 thf(fact_3198_mult__nonneg__nonpos2,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos2
% 5.45/5.71 thf(fact_3199_mult__nonneg__nonpos2,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos2
% 5.45/5.71 thf(fact_3200_mult__nonneg__nonpos2,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos2
% 5.45/5.71 thf(fact_3201_mult__nonpos__nonneg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonneg
% 5.45/5.71 thf(fact_3202_mult__nonpos__nonneg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonneg
% 5.45/5.71 thf(fact_3203_mult__nonpos__nonneg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonneg
% 5.45/5.71 thf(fact_3204_mult__nonpos__nonneg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonneg
% 5.45/5.71 thf(fact_3205_mult__nonneg__nonpos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos
% 5.45/5.71 thf(fact_3206_mult__nonneg__nonpos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos
% 5.45/5.71 thf(fact_3207_mult__nonneg__nonpos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos
% 5.45/5.71 thf(fact_3208_mult__nonneg__nonpos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonpos
% 5.45/5.71 thf(fact_3209_mult__nonneg__nonneg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonneg
% 5.45/5.71 thf(fact_3210_mult__nonneg__nonneg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonneg
% 5.45/5.71 thf(fact_3211_mult__nonneg__nonneg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonneg
% 5.45/5.71 thf(fact_3212_mult__nonneg__nonneg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonneg_nonneg
% 5.45/5.71 thf(fact_3213_split__mult__neg__le,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 5.45/5.71 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_neg_le
% 5.45/5.71 thf(fact_3214_split__mult__neg__le,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.45/5.71 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_neg_le
% 5.45/5.71 thf(fact_3215_split__mult__neg__le,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.45/5.71 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.71 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_neg_le
% 5.45/5.71 thf(fact_3216_split__mult__neg__le,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.45/5.71 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_neg_le
% 5.45/5.71 thf(fact_3217_mult__le__0__iff,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 5.45/5.71 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) )
% 5.45/5.71 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_0_iff
% 5.45/5.71 thf(fact_3218_mult__le__0__iff,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.45/5.71 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.45/5.71 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_0_iff
% 5.45/5.71 thf(fact_3219_mult__le__0__iff,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.45/5.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.45/5.71 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_0_iff
% 5.45/5.71 thf(fact_3220_mult__right__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono
% 5.45/5.71 thf(fact_3221_mult__right__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono
% 5.45/5.71 thf(fact_3222_mult__right__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono
% 5.45/5.71 thf(fact_3223_mult__right__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono
% 5.45/5.71 thf(fact_3224_mult__right__mono__neg,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono_neg
% 5.45/5.71 thf(fact_3225_mult__right__mono__neg,axiom,
% 5.45/5.71 ! [B: rat,A: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono_neg
% 5.45/5.71 thf(fact_3226_mult__right__mono__neg,axiom,
% 5.45/5.71 ! [B: int,A: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_mono_neg
% 5.45/5.71 thf(fact_3227_mult__left__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono
% 5.45/5.71 thf(fact_3228_mult__left__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono
% 5.45/5.71 thf(fact_3229_mult__left__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono
% 5.45/5.71 thf(fact_3230_mult__left__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono
% 5.45/5.71 thf(fact_3231_mult__nonpos__nonpos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonpos
% 5.45/5.71 thf(fact_3232_mult__nonpos__nonpos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonpos
% 5.45/5.71 thf(fact_3233_mult__nonpos__nonpos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_nonpos_nonpos
% 5.45/5.71 thf(fact_3234_mult__left__mono__neg,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono_neg
% 5.45/5.71 thf(fact_3235_mult__left__mono__neg,axiom,
% 5.45/5.71 ! [B: rat,A: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono_neg
% 5.45/5.71 thf(fact_3236_mult__left__mono__neg,axiom,
% 5.45/5.71 ! [B: int,A: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_mono_neg
% 5.45/5.71 thf(fact_3237_split__mult__pos__le,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B ) )
% 5.45/5.71 | ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_pos_le
% 5.45/5.71 thf(fact_3238_split__mult__pos__le,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.45/5.71 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.45/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_pos_le
% 5.45/5.71 thf(fact_3239_split__mult__pos__le,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.45/5.71 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.45/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % split_mult_pos_le
% 5.45/5.71 thf(fact_3240_zero__le__square,axiom,
% 5.45/5.71 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_square
% 5.45/5.71 thf(fact_3241_zero__le__square,axiom,
% 5.45/5.71 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_square
% 5.45/5.71 thf(fact_3242_zero__le__square,axiom,
% 5.45/5.71 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_square
% 5.45/5.71 thf(fact_3243_mult__mono_H,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono'
% 5.45/5.71 thf(fact_3244_mult__mono_H,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono'
% 5.45/5.71 thf(fact_3245_mult__mono_H,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono'
% 5.45/5.71 thf(fact_3246_mult__mono_H,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono'
% 5.45/5.71 thf(fact_3247_mult__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono
% 5.45/5.71 thf(fact_3248_mult__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono
% 5.45/5.71 thf(fact_3249_mult__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono
% 5.45/5.71 thf(fact_3250_mult__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_mono
% 5.45/5.71 thf(fact_3251_pos__add__strict,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % pos_add_strict
% 5.45/5.71 thf(fact_3252_pos__add__strict,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ B @ C )
% 5.45/5.71 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % pos_add_strict
% 5.45/5.71 thf(fact_3253_pos__add__strict,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ B @ C )
% 5.45/5.71 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % pos_add_strict
% 5.45/5.71 thf(fact_3254_pos__add__strict,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ B @ C )
% 5.45/5.71 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % pos_add_strict
% 5.45/5.71 thf(fact_3255_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ~ ! [C2: nat] :
% 5.45/5.71 ( ( B
% 5.45/5.71 = ( plus_plus_nat @ A @ C2 ) )
% 5.45/5.71 => ( C2 = zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % canonically_ordered_monoid_add_class.lessE
% 5.45/5.71 thf(fact_3256_add__pos__pos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_pos
% 5.45/5.71 thf(fact_3257_add__pos__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_pos
% 5.45/5.71 thf(fact_3258_add__pos__pos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_pos
% 5.45/5.71 thf(fact_3259_add__pos__pos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_pos
% 5.45/5.71 thf(fact_3260_add__neg__neg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_neg
% 5.45/5.71 thf(fact_3261_add__neg__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_neg
% 5.45/5.71 thf(fact_3262_add__neg__neg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_neg
% 5.45/5.71 thf(fact_3263_add__neg__neg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_neg
% 5.45/5.71 thf(fact_3264_add__less__zeroD,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ X @ zero_z3403309356797280102nteger )
% 5.45/5.71 | ( ord_le6747313008572928689nteger @ Y @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_less_zeroD
% 5.45/5.71 thf(fact_3265_add__less__zeroD,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.45/5.71 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_less_zeroD
% 5.45/5.71 thf(fact_3266_add__less__zeroD,axiom,
% 5.45/5.71 ! [X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.45/5.71 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_less_zeroD
% 5.45/5.71 thf(fact_3267_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.45/5.71 thf(fact_3268_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.45/5.71 thf(fact_3269_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.45/5.71 thf(fact_3270_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.45/5.71 thf(fact_3271_mult__less__cancel__right__disj,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 5.45/5.71 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right_disj
% 5.45/5.71 thf(fact_3272_mult__less__cancel__right__disj,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 & ( ord_less_rat @ A @ B ) )
% 5.45/5.71 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right_disj
% 5.45/5.71 thf(fact_3273_mult__less__cancel__right__disj,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 & ( ord_less_int @ A @ B ) )
% 5.45/5.71 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right_disj
% 5.45/5.71 thf(fact_3274_mult__strict__right__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono
% 5.45/5.71 thf(fact_3275_mult__strict__right__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono
% 5.45/5.71 thf(fact_3276_mult__strict__right__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono
% 5.45/5.71 thf(fact_3277_mult__strict__right__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono
% 5.45/5.71 thf(fact_3278_mult__strict__right__mono__neg,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono_neg
% 5.45/5.71 thf(fact_3279_mult__strict__right__mono__neg,axiom,
% 5.45/5.71 ! [B: rat,A: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ B @ A )
% 5.45/5.71 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono_neg
% 5.45/5.71 thf(fact_3280_mult__strict__right__mono__neg,axiom,
% 5.45/5.71 ! [B: int,A: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ B @ A )
% 5.45/5.71 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_right_mono_neg
% 5.45/5.71 thf(fact_3281_mult__less__cancel__left__disj,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ A @ B ) )
% 5.45/5.71 | ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_disj
% 5.45/5.71 thf(fact_3282_mult__less__cancel__left__disj,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 & ( ord_less_rat @ A @ B ) )
% 5.45/5.71 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_disj
% 5.45/5.71 thf(fact_3283_mult__less__cancel__left__disj,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 & ( ord_less_int @ A @ B ) )
% 5.45/5.71 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_disj
% 5.45/5.71 thf(fact_3284_mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono
% 5.45/5.71 thf(fact_3285_mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono
% 5.45/5.71 thf(fact_3286_mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono
% 5.45/5.71 thf(fact_3287_mult__strict__left__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono
% 5.45/5.71 thf(fact_3288_mult__strict__left__mono__neg,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono_neg
% 5.45/5.71 thf(fact_3289_mult__strict__left__mono__neg,axiom,
% 5.45/5.71 ! [B: rat,A: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ B @ A )
% 5.45/5.71 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono_neg
% 5.45/5.71 thf(fact_3290_mult__strict__left__mono__neg,axiom,
% 5.45/5.71 ! [B: int,A: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ B @ A )
% 5.45/5.71 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_left_mono_neg
% 5.45/5.71 thf(fact_3291_mult__less__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_pos
% 5.45/5.71 thf(fact_3292_mult__less__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_pos
% 5.45/5.71 thf(fact_3293_mult__less__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_pos
% 5.45/5.71 thf(fact_3294_mult__less__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ord_le6747313008572928689nteger @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_neg
% 5.45/5.71 thf(fact_3295_mult__less__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_neg
% 5.45/5.71 thf(fact_3296_mult__less__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ord_less_int @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left_neg
% 5.45/5.71 thf(fact_3297_zero__less__mult__pos2,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos2
% 5.45/5.71 thf(fact_3298_zero__less__mult__pos2,axiom,
% 5.45/5.71 ! [B: rat,A: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos2
% 5.45/5.71 thf(fact_3299_zero__less__mult__pos2,axiom,
% 5.45/5.71 ! [B: nat,A: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos2
% 5.45/5.71 thf(fact_3300_zero__less__mult__pos2,axiom,
% 5.45/5.71 ! [B: int,A: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos2
% 5.45/5.71 thf(fact_3301_zero__less__mult__pos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos
% 5.45/5.71 thf(fact_3302_zero__less__mult__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos
% 5.45/5.71 thf(fact_3303_zero__less__mult__pos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos
% 5.45/5.71 thf(fact_3304_zero__less__mult__pos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_pos
% 5.45/5.71 thf(fact_3305_zero__less__mult__iff,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) )
% 5.45/5.71 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_iff
% 5.45/5.71 thf(fact_3306_zero__less__mult__iff,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.45/5.71 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_iff
% 5.45/5.71 thf(fact_3307_zero__less__mult__iff,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.45/5.71 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_mult_iff
% 5.45/5.71 thf(fact_3308_mult__pos__neg2,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ B @ A ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg2
% 5.45/5.71 thf(fact_3309_mult__pos__neg2,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg2
% 5.45/5.71 thf(fact_3310_mult__pos__neg2,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg2
% 5.45/5.71 thf(fact_3311_mult__pos__neg2,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg2
% 5.45/5.71 thf(fact_3312_mult__pos__pos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_pos
% 5.45/5.71 thf(fact_3313_mult__pos__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_pos
% 5.45/5.71 thf(fact_3314_mult__pos__pos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_pos
% 5.45/5.71 thf(fact_3315_mult__pos__pos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_pos
% 5.45/5.71 thf(fact_3316_mult__pos__neg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg
% 5.45/5.71 thf(fact_3317_mult__pos__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg
% 5.45/5.71 thf(fact_3318_mult__pos__neg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg
% 5.45/5.71 thf(fact_3319_mult__pos__neg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_pos_neg
% 5.45/5.71 thf(fact_3320_mult__neg__pos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_pos
% 5.45/5.71 thf(fact_3321_mult__neg__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_pos
% 5.45/5.71 thf(fact_3322_mult__neg__pos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_pos
% 5.45/5.71 thf(fact_3323_mult__neg__pos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_pos
% 5.45/5.71 thf(fact_3324_mult__less__0__iff,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ B ) @ zero_z3403309356797280102nteger )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger ) )
% 5.45/5.71 | ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_0_iff
% 5.45/5.71 thf(fact_3325_mult__less__0__iff,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.45/5.71 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_0_iff
% 5.45/5.71 thf(fact_3326_mult__less__0__iff,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.45/5.71 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_0_iff
% 5.45/5.71 thf(fact_3327_not__square__less__zero,axiom,
% 5.45/5.71 ! [A: code_integer] :
% 5.45/5.71 ~ ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.71
% 5.45/5.71 % not_square_less_zero
% 5.45/5.71 thf(fact_3328_not__square__less__zero,axiom,
% 5.45/5.71 ! [A: rat] :
% 5.45/5.71 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.45/5.71
% 5.45/5.71 % not_square_less_zero
% 5.45/5.71 thf(fact_3329_not__square__less__zero,axiom,
% 5.45/5.71 ! [A: int] :
% 5.45/5.71 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.45/5.71
% 5.45/5.71 % not_square_less_zero
% 5.45/5.71 thf(fact_3330_mult__neg__neg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_neg
% 5.45/5.71 thf(fact_3331_mult__neg__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_neg
% 5.45/5.71 thf(fact_3332_mult__neg__neg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_neg_neg
% 5.45/5.71 thf(fact_3333_add__scale__eq__noteq,axiom,
% 5.45/5.71 ! [R3: code_integer,A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( R3 != zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ( A = B )
% 5.45/5.71 & ( C != D2 ) )
% 5.45/5.71 => ( ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ R3 @ C ) )
% 5.45/5.71 != ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ R3 @ D2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_scale_eq_noteq
% 5.45/5.71 thf(fact_3334_add__scale__eq__noteq,axiom,
% 5.45/5.71 ! [R3: rat,A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( R3 != zero_zero_rat )
% 5.45/5.71 => ( ( ( A = B )
% 5.45/5.71 & ( C != D2 ) )
% 5.45/5.71 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 5.45/5.71 != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_scale_eq_noteq
% 5.45/5.71 thf(fact_3335_add__scale__eq__noteq,axiom,
% 5.45/5.71 ! [R3: nat,A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( R3 != zero_zero_nat )
% 5.45/5.71 => ( ( ( A = B )
% 5.45/5.71 & ( C != D2 ) )
% 5.45/5.71 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 5.45/5.71 != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_scale_eq_noteq
% 5.45/5.71 thf(fact_3336_add__scale__eq__noteq,axiom,
% 5.45/5.71 ! [R3: int,A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( R3 != zero_zero_int )
% 5.45/5.71 => ( ( ( A = B )
% 5.45/5.71 & ( C != D2 ) )
% 5.45/5.71 => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 5.45/5.71 != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_scale_eq_noteq
% 5.45/5.71 thf(fact_3337_ex__least__nat__le,axiom,
% 5.45/5.71 ! [P: nat > $o,N2: nat] :
% 5.45/5.71 ( ( P @ N2 )
% 5.45/5.71 => ( ~ ( P @ zero_zero_nat )
% 5.45/5.71 => ? [K2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.45/5.71 & ! [I: nat] :
% 5.45/5.71 ( ( ord_less_nat @ I @ K2 )
% 5.45/5.71 => ~ ( P @ I ) )
% 5.45/5.71 & ( P @ K2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % ex_least_nat_le
% 5.45/5.71 thf(fact_3338_less__imp__add__positive,axiom,
% 5.45/5.71 ! [I2: nat,J: nat] :
% 5.45/5.71 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.71 => ? [K2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ K2 )
% 5.45/5.71 & ( ( plus_plus_nat @ I2 @ K2 )
% 5.45/5.71 = J ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % less_imp_add_positive
% 5.45/5.71 thf(fact_3339_mult__less__mono1,axiom,
% 5.45/5.71 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.71 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_mono1
% 5.45/5.71 thf(fact_3340_mult__less__mono2,axiom,
% 5.45/5.71 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.71 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_mono2
% 5.45/5.71 thf(fact_3341_bot__nat__0_Oordering__top__axioms,axiom,
% 5.45/5.71 ( ordering_top_nat
% 5.45/5.71 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.45/5.71 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 )
% 5.45/5.71 @ zero_zero_nat ) ).
% 5.45/5.71
% 5.45/5.71 % bot_nat_0.ordering_top_axioms
% 5.45/5.71 thf(fact_3342_add__strict__increasing2,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing2
% 5.45/5.71 thf(fact_3343_add__strict__increasing2,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ B @ C )
% 5.45/5.71 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing2
% 5.45/5.71 thf(fact_3344_add__strict__increasing2,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ B @ C )
% 5.45/5.71 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing2
% 5.45/5.71 thf(fact_3345_add__strict__increasing2,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ B @ C )
% 5.45/5.71 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing2
% 5.45/5.71 thf(fact_3346_add__strict__increasing,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ B @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ B @ ( plus_p5714425477246183910nteger @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing
% 5.45/5.71 thf(fact_3347_add__strict__increasing,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ B @ C )
% 5.45/5.71 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing
% 5.45/5.71 thf(fact_3348_add__strict__increasing,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.71 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing
% 5.45/5.71 thf(fact_3349_add__strict__increasing,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ B @ C )
% 5.45/5.71 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_strict_increasing
% 5.45/5.71 thf(fact_3350_add__pos__nonneg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_nonneg
% 5.45/5.71 thf(fact_3351_add__pos__nonneg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_nonneg
% 5.45/5.71 thf(fact_3352_add__pos__nonneg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_nonneg
% 5.45/5.71 thf(fact_3353_add__pos__nonneg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_pos_nonneg
% 5.45/5.71 thf(fact_3354_add__nonpos__neg,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonpos_neg
% 5.45/5.71 thf(fact_3355_add__nonpos__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonpos_neg
% 5.45/5.71 thf(fact_3356_add__nonpos__neg,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonpos_neg
% 5.45/5.71 thf(fact_3357_add__nonpos__neg,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonpos_neg
% 5.45/5.71 thf(fact_3358_add__nonneg__pos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonneg_pos
% 5.45/5.71 thf(fact_3359_add__nonneg__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonneg_pos
% 5.45/5.71 thf(fact_3360_add__nonneg__pos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonneg_pos
% 5.45/5.71 thf(fact_3361_add__nonneg__pos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_nonneg_pos
% 5.45/5.71 thf(fact_3362_add__neg__nonpos,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_nonpos
% 5.45/5.71 thf(fact_3363_add__neg__nonpos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_nonpos
% 5.45/5.71 thf(fact_3364_add__neg__nonpos,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.45/5.71 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.45/5.71 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_nonpos
% 5.45/5.71 thf(fact_3365_add__neg__nonpos,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % add_neg_nonpos
% 5.45/5.71 thf(fact_3366_mult__less__le__imp__less,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_le_imp_less
% 5.45/5.71 thf(fact_3367_mult__less__le__imp__less,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_le_imp_less
% 5.45/5.71 thf(fact_3368_mult__less__le__imp__less,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_le_imp_less
% 5.45/5.71 thf(fact_3369_mult__less__le__imp__less,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_le_imp_less
% 5.45/5.71 thf(fact_3370_mult__le__less__imp__less,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_less_imp_less
% 5.45/5.71 thf(fact_3371_mult__le__less__imp__less,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_less_imp_less
% 5.45/5.71 thf(fact_3372_mult__le__less__imp__less,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_less_imp_less
% 5.45/5.71 thf(fact_3373_mult__le__less__imp__less,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_less_imp_less
% 5.45/5.71 thf(fact_3374_mult__right__le__imp__le,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_le_imp_le
% 5.45/5.71 thf(fact_3375_mult__right__le__imp__le,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_le_imp_le
% 5.45/5.71 thf(fact_3376_mult__right__le__imp__le,axiom,
% 5.45/5.71 ! [A: nat,C: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_le_imp_le
% 5.45/5.71 thf(fact_3377_mult__right__le__imp__le,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_le_imp_le
% 5.45/5.71 thf(fact_3378_mult__left__le__imp__le,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_le_imp_le
% 5.45/5.71 thf(fact_3379_mult__left__le__imp__le,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_le_imp_le
% 5.45/5.71 thf(fact_3380_mult__left__le__imp__le,axiom,
% 5.45/5.71 ! [C: nat,A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_le_imp_le
% 5.45/5.71 thf(fact_3381_mult__left__le__imp__le,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_le_imp_le
% 5.45/5.71 thf(fact_3382_mult__le__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_pos
% 5.45/5.71 thf(fact_3383_mult__le__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_pos
% 5.45/5.71 thf(fact_3384_mult__le__cancel__left__pos,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_pos
% 5.45/5.71 thf(fact_3385_mult__le__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ord_le3102999989581377725nteger @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_neg
% 5.45/5.71 thf(fact_3386_mult__le__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_neg
% 5.45/5.71 thf(fact_3387_mult__le__cancel__left__neg,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left_neg
% 5.45/5.71 thf(fact_3388_mult__less__cancel__right,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 5.45/5.71 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right
% 5.45/5.71 thf(fact_3389_mult__less__cancel__right,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right
% 5.45/5.71 thf(fact_3390_mult__less__cancel__right,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_right
% 5.45/5.71 thf(fact_3391_mult__strict__mono_H,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono'
% 5.45/5.71 thf(fact_3392_mult__strict__mono_H,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono'
% 5.45/5.71 thf(fact_3393_mult__strict__mono_H,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono'
% 5.45/5.71 thf(fact_3394_mult__strict__mono_H,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono'
% 5.45/5.71 thf(fact_3395_mult__right__less__imp__less,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_less_imp_less
% 5.45/5.71 thf(fact_3396_mult__right__less__imp__less,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_less_imp_less
% 5.45/5.71 thf(fact_3397_mult__right__less__imp__less,axiom,
% 5.45/5.71 ! [A: nat,C: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_less_imp_less
% 5.45/5.71 thf(fact_3398_mult__right__less__imp__less,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_right_less_imp_less
% 5.45/5.71 thf(fact_3399_mult__less__cancel__left,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ A @ B ) )
% 5.45/5.71 & ( ( ord_le3102999989581377725nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left
% 5.45/5.71 thf(fact_3400_mult__less__cancel__left,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left
% 5.45/5.71 thf(fact_3401_mult__less__cancel__left,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_cancel_left
% 5.45/5.71 thf(fact_3402_mult__strict__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono
% 5.45/5.71 thf(fact_3403_mult__strict__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono
% 5.45/5.71 thf(fact_3404_mult__strict__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono
% 5.45/5.71 thf(fact_3405_mult__strict__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.71 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_strict_mono
% 5.45/5.71 thf(fact_3406_mult__left__less__imp__less,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_less_imp_less
% 5.45/5.71 thf(fact_3407_mult__left__less__imp__less,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_less_imp_less
% 5.45/5.71 thf(fact_3408_mult__left__less__imp__less,axiom,
% 5.45/5.71 ! [C: nat,A: nat,B: nat] :
% 5.45/5.71 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.71 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_less_imp_less
% 5.45/5.71 thf(fact_3409_mult__left__less__imp__less,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_left_less_imp_less
% 5.45/5.71 thf(fact_3410_mult__le__cancel__right,axiom,
% 5.45/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 5.45/5.71 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_right
% 5.45/5.71 thf(fact_3411_mult__le__cancel__right,axiom,
% 5.45/5.71 ! [A: rat,C: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_right
% 5.45/5.71 thf(fact_3412_mult__le__cancel__right,axiom,
% 5.45/5.71 ! [A: int,C: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_right
% 5.45/5.71 thf(fact_3413_mult__le__cancel__left,axiom,
% 5.45/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ A @ B ) )
% 5.45/5.71 & ( ( ord_le6747313008572928689nteger @ C @ zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left
% 5.45/5.71 thf(fact_3414_mult__le__cancel__left,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.71 => ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left
% 5.45/5.71 thf(fact_3415_mult__le__cancel__left,axiom,
% 5.45/5.71 ! [C: int,A: int,B: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.71 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.45/5.71 => ( ord_less_eq_int @ A @ B ) )
% 5.45/5.71 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.45/5.71 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_left
% 5.45/5.71 thf(fact_3416_sum__squares__ge__zero,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_ge_zero
% 5.45/5.71 thf(fact_3417_sum__squares__ge__zero,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_ge_zero
% 5.45/5.71 thf(fact_3418_sum__squares__ge__zero,axiom,
% 5.45/5.71 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_ge_zero
% 5.45/5.71 thf(fact_3419_not__sum__squares__lt__zero,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] :
% 5.45/5.71 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.71
% 5.45/5.71 % not_sum_squares_lt_zero
% 5.45/5.71 thf(fact_3420_not__sum__squares__lt__zero,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.45/5.71
% 5.45/5.71 % not_sum_squares_lt_zero
% 5.45/5.71 thf(fact_3421_not__sum__squares__lt__zero,axiom,
% 5.45/5.71 ! [X: int,Y: int] :
% 5.45/5.71 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.45/5.71
% 5.45/5.71 % not_sum_squares_lt_zero
% 5.45/5.71 thf(fact_3422_mod__emp__simp,axiom,
% 5.45/5.71 ! [H: heap_e7401611519738050253t_unit] : ( rep_assn @ one_one_assn @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 5.45/5.71
% 5.45/5.71 % mod_emp_simp
% 5.45/5.71 thf(fact_3423_nat__mult__le__cancel__disj,axiom,
% 5.45/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.71 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_mult_le_cancel_disj
% 5.45/5.71 thf(fact_3424_nat__mult__less__cancel__disj,axiom,
% 5.45/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.71 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_mult_less_cancel_disj
% 5.45/5.71 thf(fact_3425_field__le__mult__one__interval,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ! [Z2: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.45/5.71 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.45/5.71 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X ) @ Y ) ) )
% 5.45/5.71 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.71
% 5.45/5.71 % field_le_mult_one_interval
% 5.45/5.71 thf(fact_3426_nat__mult__le__cancel1,axiom,
% 5.45/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_mult_le_cancel1
% 5.45/5.71 thf(fact_3427_discrete,axiom,
% 5.45/5.71 ( ord_le6747313008572928689nteger
% 5.45/5.71 = ( ^ [A5: code_integer] : ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ A5 @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % discrete
% 5.45/5.71 thf(fact_3428_discrete,axiom,
% 5.45/5.71 ( ord_less_nat
% 5.45/5.71 = ( ^ [A5: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A5 @ one_one_nat ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % discrete
% 5.45/5.71 thf(fact_3429_discrete,axiom,
% 5.45/5.71 ( ord_less_int
% 5.45/5.71 = ( ^ [A5: int] : ( ord_less_eq_int @ ( plus_plus_int @ A5 @ one_one_int ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % discrete
% 5.45/5.71 thf(fact_3430_sum__squares__gt__zero__iff,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) )
% 5.45/5.71 = ( ( X != zero_z3403309356797280102nteger )
% 5.45/5.71 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_gt_zero_iff
% 5.45/5.71 thf(fact_3431_sum__squares__gt__zero__iff,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.45/5.71 = ( ( X != zero_zero_rat )
% 5.45/5.71 | ( Y != zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_gt_zero_iff
% 5.45/5.71 thf(fact_3432_sum__squares__gt__zero__iff,axiom,
% 5.45/5.71 ! [X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.45/5.71 = ( ( X != zero_zero_int )
% 5.45/5.71 | ( Y != zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_gt_zero_iff
% 5.45/5.71 thf(fact_3433_sum__squares__le__zero__iff,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.71 = ( ( X = zero_z3403309356797280102nteger )
% 5.45/5.71 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_le_zero_iff
% 5.45/5.71 thf(fact_3434_sum__squares__le__zero__iff,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.45/5.71 = ( ( X = zero_zero_rat )
% 5.45/5.71 & ( Y = zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_le_zero_iff
% 5.45/5.71 thf(fact_3435_sum__squares__le__zero__iff,axiom,
% 5.45/5.71 ! [X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.45/5.71 = ( ( X = zero_zero_int )
% 5.45/5.71 & ( Y = zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_le_zero_iff
% 5.45/5.71 thf(fact_3436_mult__le__cancel__iff2,axiom,
% 5.45/5.71 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ Z @ X ) @ ( times_3573771949741848930nteger @ Z @ Y ) )
% 5.45/5.71 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff2
% 5.45/5.71 thf(fact_3437_mult__le__cancel__iff2,axiom,
% 5.45/5.71 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 5.45/5.71 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff2
% 5.45/5.71 thf(fact_3438_mult__le__cancel__iff2,axiom,
% 5.45/5.71 ! [Z: int,X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 5.45/5.71 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff2
% 5.45/5.71 thf(fact_3439_mult__le__cancel__iff1,axiom,
% 5.45/5.71 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 5.45/5.71 = ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff1
% 5.45/5.71 thf(fact_3440_mult__le__cancel__iff1,axiom,
% 5.45/5.71 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.45/5.71 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff1
% 5.45/5.71 thf(fact_3441_mult__le__cancel__iff1,axiom,
% 5.45/5.71 ! [Z: int,X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.45/5.71 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_le_cancel_iff1
% 5.45/5.71 thf(fact_3442_linordered__field__no__lb,axiom,
% 5.45/5.71 ! [X7: rat] :
% 5.45/5.71 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X7 ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_field_no_lb
% 5.45/5.71 thf(fact_3443_linordered__field__no__ub,axiom,
% 5.45/5.71 ! [X7: rat] :
% 5.45/5.71 ? [X_1: rat] : ( ord_less_rat @ X7 @ X_1 ) ).
% 5.45/5.71
% 5.45/5.71 % linordered_field_no_ub
% 5.45/5.71 thf(fact_3444_mult__less__iff1,axiom,
% 5.45/5.71 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ Z )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ X @ Z ) @ ( times_3573771949741848930nteger @ Y @ Z ) )
% 5.45/5.71 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_iff1
% 5.45/5.71 thf(fact_3445_mult__less__iff1,axiom,
% 5.45/5.71 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.45/5.71 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.45/5.71 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_iff1
% 5.45/5.71 thf(fact_3446_mult__less__iff1,axiom,
% 5.45/5.71 ! [Z: int,X: int,Y: int] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.71 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.45/5.71 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_less_iff1
% 5.45/5.71 thf(fact_3447_sum__squares__eq__zero__iff,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer] :
% 5.45/5.71 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 5.45/5.71 = zero_z3403309356797280102nteger )
% 5.45/5.71 = ( ( X = zero_z3403309356797280102nteger )
% 5.45/5.71 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_eq_zero_iff
% 5.45/5.71 thf(fact_3448_sum__squares__eq__zero__iff,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.45/5.71 = zero_zero_rat )
% 5.45/5.71 = ( ( X = zero_zero_rat )
% 5.45/5.71 & ( Y = zero_zero_rat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_eq_zero_iff
% 5.45/5.71 thf(fact_3449_sum__squares__eq__zero__iff,axiom,
% 5.45/5.71 ! [X: int,Y: int] :
% 5.45/5.71 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.45/5.71 = zero_zero_int )
% 5.45/5.71 = ( ( X = zero_zero_int )
% 5.45/5.71 & ( Y = zero_zero_int ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % sum_squares_eq_zero_iff
% 5.45/5.71 thf(fact_3450_nat__mult__eq__cancel1,axiom,
% 5.45/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ( ( times_times_nat @ K @ M )
% 5.45/5.71 = ( times_times_nat @ K @ N2 ) )
% 5.45/5.71 = ( M = N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_mult_eq_cancel1
% 5.45/5.71 thf(fact_3451_nat__mult__less__cancel1,axiom,
% 5.45/5.71 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.71 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.71 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_mult_less_cancel1
% 5.45/5.71 thf(fact_3452_field__le__epsilon,axiom,
% 5.45/5.71 ! [X: rat,Y: rat] :
% 5.45/5.71 ( ! [E2: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.45/5.71 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.45/5.71 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.71
% 5.45/5.71 % field_le_epsilon
% 5.45/5.71 thf(fact_3453_divides__aux__eq,axiom,
% 5.45/5.71 ! [Q6: code_integer,R3: code_integer] :
% 5.45/5.71 ( ( unique5706413561485394159nteger @ ( produc1086072967326762835nteger @ Q6 @ R3 ) )
% 5.45/5.71 = ( R3 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.71
% 5.45/5.71 % divides_aux_eq
% 5.45/5.71 thf(fact_3454_divides__aux__eq,axiom,
% 5.45/5.71 ! [Q6: nat,R3: nat] :
% 5.45/5.71 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q6 @ R3 ) )
% 5.45/5.71 = ( R3 = zero_zero_nat ) ) ).
% 5.45/5.71
% 5.45/5.71 % divides_aux_eq
% 5.45/5.71 thf(fact_3455_divides__aux__eq,axiom,
% 5.45/5.71 ! [Q6: int,R3: int] :
% 5.45/5.71 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.71 = ( R3 = zero_zero_int ) ) ).
% 5.45/5.71
% 5.45/5.71 % divides_aux_eq
% 5.45/5.71 thf(fact_3456_tap__def,axiom,
% 5.45/5.71 ( heap_Time_tap_a
% 5.45/5.71 = ( ^ [F3: heap_e7401611519738050253t_unit > a] :
% 5.45/5.71 ( heap_Time_Heap_a2
% 5.45/5.71 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ ( F3 @ H6 ) @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % tap_def
% 5.45/5.71 thf(fact_3457_tap__def,axiom,
% 5.45/5.71 ( heap_T560649228465745139t_unit
% 5.45/5.71 = ( ^ [F3: heap_e7401611519738050253t_unit > product_unit] :
% 5.45/5.71 ( heap_T6183433275982383450t_unit
% 5.45/5.71 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F3 @ H6 ) @ ( produc584006145561248582it_nat @ H6 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % tap_def
% 5.45/5.71 thf(fact_3458_execute__tap,axiom,
% 5.45/5.71 ! [F: heap_e7401611519738050253t_unit > product_unit,H: heap_e7401611519738050253t_unit] :
% 5.45/5.71 ( ( heap_T875086893843062177t_unit @ ( heap_T560649228465745139t_unit @ F ) @ H )
% 5.45/5.71 = ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ ( F @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % execute_tap
% 5.45/5.71 thf(fact_3459_execute__tap,axiom,
% 5.45/5.71 ! [F: heap_e7401611519738050253t_unit > a,H: heap_e7401611519738050253t_unit] :
% 5.45/5.71 ( ( heap_Time_execute_a @ ( heap_Time_tap_a @ F ) @ H )
% 5.45/5.71 = ( some_P7913643980934408916it_nat @ ( produc9178034014595674355it_nat @ ( F @ H ) @ ( produc584006145561248582it_nat @ H @ one_one_nat ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % execute_tap
% 5.45/5.71 thf(fact_3460_one__assn__raw_Opelims_I3_J,axiom,
% 5.45/5.71 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.71 ( ~ ( one_assn_raw @ X )
% 5.45/5.71 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 5.45/5.71 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.71 ( ( X
% 5.45/5.71 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.71 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.71 => ( As4 = bot_bot_set_nat ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_assn_raw.pelims(3)
% 5.45/5.71 thf(fact_3461_one__assn__raw_Opelims_I2_J,axiom,
% 5.45/5.71 ! [X: produc3658429121746597890et_nat] :
% 5.45/5.71 ( ( one_assn_raw @ X )
% 5.45/5.71 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 5.45/5.71 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.71 ( ( X
% 5.45/5.71 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.71 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.71 => ( As4 != bot_bot_set_nat ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_assn_raw.pelims(2)
% 5.45/5.71 thf(fact_3462_one__assn__raw_Opelims_I1_J,axiom,
% 5.45/5.71 ! [X: produc3658429121746597890et_nat,Y: $o] :
% 5.45/5.71 ( ( ( one_assn_raw @ X )
% 5.45/5.71 = Y )
% 5.45/5.71 => ( ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ X )
% 5.45/5.71 => ~ ! [H4: heap_e7401611519738050253t_unit,As4: set_nat] :
% 5.45/5.71 ( ( X
% 5.45/5.71 = ( produc7507926704131184380et_nat @ H4 @ As4 ) )
% 5.45/5.71 => ( ( Y
% 5.45/5.71 = ( As4 = bot_bot_set_nat ) )
% 5.45/5.71 => ~ ( accp_P5801069581201407417et_nat @ one_assn_raw_rel @ ( produc7507926704131184380et_nat @ H4 @ As4 ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_assn_raw.pelims(1)
% 5.45/5.71 thf(fact_3463_less__numeral__extra_I1_J,axiom,
% 5.45/5.71 ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ one_one_Code_integer ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(1)
% 5.45/5.71 thf(fact_3464_less__numeral__extra_I1_J,axiom,
% 5.45/5.71 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(1)
% 5.45/5.71 thf(fact_3465_less__numeral__extra_I1_J,axiom,
% 5.45/5.71 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(1)
% 5.45/5.71 thf(fact_3466_less__numeral__extra_I1_J,axiom,
% 5.45/5.71 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(1)
% 5.45/5.71 thf(fact_3467_less__numeral__extra_I4_J,axiom,
% 5.45/5.71 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ one_one_Code_integer ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(4)
% 5.45/5.71 thf(fact_3468_less__numeral__extra_I4_J,axiom,
% 5.45/5.71 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(4)
% 5.45/5.71 thf(fact_3469_less__numeral__extra_I4_J,axiom,
% 5.45/5.71 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(4)
% 5.45/5.71 thf(fact_3470_less__numeral__extra_I4_J,axiom,
% 5.45/5.71 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(4)
% 5.45/5.71 thf(fact_3471_bounded__Max__nat,axiom,
% 5.45/5.71 ! [P: nat > $o,X: nat,M6: nat] :
% 5.45/5.71 ( ( P @ X )
% 5.45/5.71 => ( ! [X3: nat] :
% 5.45/5.71 ( ( P @ X3 )
% 5.45/5.71 => ( ord_less_eq_nat @ X3 @ M6 ) )
% 5.45/5.71 => ~ ! [M5: nat] :
% 5.45/5.71 ( ( P @ M5 )
% 5.45/5.71 => ~ ! [X7: nat] :
% 5.45/5.71 ( ( P @ X7 )
% 5.45/5.71 => ( ord_less_eq_nat @ X7 @ M5 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % bounded_Max_nat
% 5.45/5.71 thf(fact_3472_le__numeral__extra_I3_J,axiom,
% 5.45/5.71 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(3)
% 5.45/5.71 thf(fact_3473_le__numeral__extra_I3_J,axiom,
% 5.45/5.71 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(3)
% 5.45/5.71 thf(fact_3474_le__numeral__extra_I3_J,axiom,
% 5.45/5.71 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(3)
% 5.45/5.71 thf(fact_3475_le__numeral__extra_I3_J,axiom,
% 5.45/5.71 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(3)
% 5.45/5.71 thf(fact_3476_less__numeral__extra_I3_J,axiom,
% 5.45/5.71 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(3)
% 5.45/5.71 thf(fact_3477_less__numeral__extra_I3_J,axiom,
% 5.45/5.71 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(3)
% 5.45/5.71 thf(fact_3478_less__numeral__extra_I3_J,axiom,
% 5.45/5.71 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(3)
% 5.45/5.71 thf(fact_3479_less__numeral__extra_I3_J,axiom,
% 5.45/5.71 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.45/5.71
% 5.45/5.71 % less_numeral_extra(3)
% 5.45/5.71 thf(fact_3480_le__numeral__extra_I4_J,axiom,
% 5.45/5.71 ord_le3102999989581377725nteger @ one_one_Code_integer @ one_one_Code_integer ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(4)
% 5.45/5.71 thf(fact_3481_le__numeral__extra_I4_J,axiom,
% 5.45/5.71 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(4)
% 5.45/5.71 thf(fact_3482_le__numeral__extra_I4_J,axiom,
% 5.45/5.71 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(4)
% 5.45/5.71 thf(fact_3483_le__numeral__extra_I4_J,axiom,
% 5.45/5.71 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.45/5.71
% 5.45/5.71 % le_numeral_extra(4)
% 5.45/5.71 thf(fact_3484_power__decreasing__iff,axiom,
% 5.45/5.71 ! [B: code_integer,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_decreasing_iff
% 5.45/5.71 thf(fact_3485_power__decreasing__iff,axiom,
% 5.45/5.71 ! [B: rat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_decreasing_iff
% 5.45/5.71 thf(fact_3486_power__decreasing__iff,axiom,
% 5.45/5.71 ! [B: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.45/5.71 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_decreasing_iff
% 5.45/5.71 thf(fact_3487_power__decreasing__iff,axiom,
% 5.45/5.71 ! [B: int,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ( ord_less_int @ B @ one_one_int )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_decreasing_iff
% 5.45/5.71 thf(fact_3488_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.45/5.71 ( set_fo2584398358068434914at_nat
% 5.45/5.71 = ( ^ [F3: nat > nat > nat,A5: nat,B5: nat,Acc: nat] : ( if_nat @ ( ord_less_nat @ B5 @ A5 ) @ Acc @ ( set_fo2584398358068434914at_nat @ F3 @ ( plus_plus_nat @ A5 @ one_one_nat ) @ B5 @ ( F3 @ A5 @ Acc ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % fold_atLeastAtMost_nat.simps
% 5.45/5.71 thf(fact_3489_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.45/5.71 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.45/5.71 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 5.45/5.71 = Y )
% 5.45/5.71 => ( ( ( ord_less_nat @ Xb @ Xa )
% 5.45/5.71 => ( Y = Xc ) )
% 5.45/5.71 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.45/5.71 => ( Y
% 5.45/5.71 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % fold_atLeastAtMost_nat.elims
% 5.45/5.71 thf(fact_3490_power__strict__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_mono
% 5.45/5.71 thf(fact_3491_power__strict__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_mono
% 5.45/5.71 thf(fact_3492_power__strict__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_mono
% 5.45/5.71 thf(fact_3493_power__strict__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_mono
% 5.45/5.71 thf(fact_3494_power__increasing__iff,axiom,
% 5.45/5.71 ! [B: code_integer,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 5.45/5.71 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_increasing_iff
% 5.45/5.71 thf(fact_3495_power__increasing__iff,axiom,
% 5.45/5.71 ! [B: rat,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_rat @ one_one_rat @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.45/5.71 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_increasing_iff
% 5.45/5.71 thf(fact_3496_power__increasing__iff,axiom,
% 5.45/5.71 ! [B: nat,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_nat @ one_one_nat @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.45/5.71 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_increasing_iff
% 5.45/5.71 thf(fact_3497_power__increasing__iff,axiom,
% 5.45/5.71 ! [B: int,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_int @ one_one_int @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.45/5.71 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_increasing_iff
% 5.45/5.71 thf(fact_3498_divide__le__eq__1__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.71 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_le_eq_1_neg
% 5.45/5.71 thf(fact_3499_divide__le__eq__1__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.71 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_le_eq_1_pos
% 5.45/5.71 thf(fact_3500_le__divide__eq__1__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.71 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % le_divide_eq_1_neg
% 5.45/5.71 thf(fact_3501_times__divide__eq__right,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.71 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.45/5.71
% 5.45/5.71 % times_divide_eq_right
% 5.45/5.71 thf(fact_3502_divide__divide__eq__right,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.71 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_divide_eq_right
% 5.45/5.71 thf(fact_3503_divide__divide__eq__left,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.45/5.71 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_divide_eq_left
% 5.45/5.71 thf(fact_3504_times__divide__eq__left,axiom,
% 5.45/5.71 ! [B: rat,C: rat,A: rat] :
% 5.45/5.71 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.71 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.45/5.71
% 5.45/5.71 % times_divide_eq_left
% 5.45/5.71 thf(fact_3505_nat__zero__less__power__iff,axiom,
% 5.45/5.71 ! [X: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N2 ) )
% 5.45/5.71 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.71 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nat_zero_less_power_iff
% 5.45/5.71 thf(fact_3506_mult__divide__mult__cancel__left__if,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( ( C = zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = zero_zero_rat ) )
% 5.45/5.71 & ( ( C != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % mult_divide_mult_cancel_left_if
% 5.45/5.71 thf(fact_3507_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( C != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_divide_mult_cancel_left
% 5.45/5.71 thf(fact_3508_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( C != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_divide_mult_cancel_left2
% 5.45/5.71 thf(fact_3509_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( C != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.71 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_divide_mult_cancel_right
% 5.45/5.71 thf(fact_3510_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.45/5.71 ! [C: rat,A: rat,B: rat] :
% 5.45/5.71 ( ( C != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.71 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_divide_mult_cancel_right2
% 5.45/5.71 thf(fact_3511_nonzero__mult__div__cancel__right,axiom,
% 5.45/5.71 ! [B: nat,A: nat] :
% 5.45/5.71 ( ( B != zero_zero_nat )
% 5.45/5.71 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.45/5.71 = A ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_right
% 5.45/5.71 thf(fact_3512_nonzero__mult__div__cancel__right,axiom,
% 5.45/5.71 ! [B: int,A: int] :
% 5.45/5.71 ( ( B != zero_zero_int )
% 5.45/5.71 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.45/5.71 = A ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_right
% 5.45/5.71 thf(fact_3513_nonzero__mult__div__cancel__right,axiom,
% 5.45/5.71 ! [B: code_integer,A: code_integer] :
% 5.45/5.71 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.45/5.71 = A ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_right
% 5.45/5.71 thf(fact_3514_nonzero__mult__div__cancel__right,axiom,
% 5.45/5.71 ! [B: rat,A: rat] :
% 5.45/5.71 ( ( B != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.45/5.71 = A ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_right
% 5.45/5.71 thf(fact_3515_nonzero__mult__div__cancel__right,axiom,
% 5.45/5.71 ! [B: code_natural,A: code_natural] :
% 5.45/5.71 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.71 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 5.45/5.71 = A ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_right
% 5.45/5.71 thf(fact_3516_nonzero__mult__div__cancel__left,axiom,
% 5.45/5.71 ! [A: nat,B: nat] :
% 5.45/5.71 ( ( A != zero_zero_nat )
% 5.45/5.71 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.45/5.71 = B ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_left
% 5.45/5.71 thf(fact_3517_nonzero__mult__div__cancel__left,axiom,
% 5.45/5.71 ! [A: int,B: int] :
% 5.45/5.71 ( ( A != zero_zero_int )
% 5.45/5.71 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.45/5.71 = B ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_left
% 5.45/5.71 thf(fact_3518_nonzero__mult__div__cancel__left,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer] :
% 5.45/5.71 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.71 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 5.45/5.71 = B ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_left
% 5.45/5.71 thf(fact_3519_nonzero__mult__div__cancel__left,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( A != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.45/5.71 = B ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_left
% 5.45/5.71 thf(fact_3520_nonzero__mult__div__cancel__left,axiom,
% 5.45/5.71 ! [A: code_natural,B: code_natural] :
% 5.45/5.71 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.71 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ A )
% 5.45/5.71 = B ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_mult_div_cancel_left
% 5.45/5.71 thf(fact_3521_power__inject__exp,axiom,
% 5.45/5.71 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.71 => ( ( ( power_8256067586552552935nteger @ A @ M )
% 5.45/5.71 = ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.71 = ( M = N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_inject_exp
% 5.45/5.71 thf(fact_3522_power__inject__exp,axiom,
% 5.45/5.71 ! [A: rat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.71 => ( ( ( power_power_rat @ A @ M )
% 5.45/5.71 = ( power_power_rat @ A @ N2 ) )
% 5.45/5.71 = ( M = N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_inject_exp
% 5.45/5.71 thf(fact_3523_power__inject__exp,axiom,
% 5.45/5.71 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.71 => ( ( ( power_power_nat @ A @ M )
% 5.45/5.71 = ( power_power_nat @ A @ N2 ) )
% 5.45/5.71 = ( M = N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_inject_exp
% 5.45/5.71 thf(fact_3524_power__inject__exp,axiom,
% 5.45/5.71 ! [A: int,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.71 => ( ( ( power_power_int @ A @ M )
% 5.45/5.71 = ( power_power_int @ A @ N2 ) )
% 5.45/5.71 = ( M = N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_inject_exp
% 5.45/5.71 thf(fact_3525_divide__le__0__1__iff,axiom,
% 5.45/5.71 ! [A: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.45/5.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_le_0_1_iff
% 5.45/5.71 thf(fact_3526_zero__le__divide__1__iff,axiom,
% 5.45/5.71 ! [A: rat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.45/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_divide_1_iff
% 5.45/5.71 thf(fact_3527_divide__less__0__1__iff,axiom,
% 5.45/5.71 ! [A: rat] :
% 5.45/5.71 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.45/5.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_less_0_1_iff
% 5.45/5.71 thf(fact_3528_divide__less__eq__1__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.71 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_less_eq_1_neg
% 5.45/5.71 thf(fact_3529_divide__less__eq__1__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.71 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_less_eq_1_pos
% 5.45/5.71 thf(fact_3530_less__divide__eq__1__neg,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.71 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.71 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % less_divide_eq_1_neg
% 5.45/5.71 thf(fact_3531_less__divide__eq__1__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.71 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % less_divide_eq_1_pos
% 5.45/5.71 thf(fact_3532_zero__less__divide__1__iff,axiom,
% 5.45/5.71 ! [A: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.45/5.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_divide_1_iff
% 5.45/5.71 thf(fact_3533_nonzero__divide__mult__cancel__left,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( A != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.45/5.71 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_divide_mult_cancel_left
% 5.45/5.71 thf(fact_3534_nonzero__divide__mult__cancel__right,axiom,
% 5.45/5.71 ! [B: rat,A: rat] :
% 5.45/5.71 ( ( B != zero_zero_rat )
% 5.45/5.71 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.45/5.71 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % nonzero_divide_mult_cancel_right
% 5.45/5.71 thf(fact_3535_power__strict__increasing__iff,axiom,
% 5.45/5.71 ! [B: code_integer,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ X ) @ ( power_8256067586552552935nteger @ B @ Y ) )
% 5.45/5.71 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_increasing_iff
% 5.45/5.71 thf(fact_3536_power__strict__increasing__iff,axiom,
% 5.45/5.71 ! [B: rat,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_rat @ one_one_rat @ B )
% 5.45/5.71 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.45/5.71 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_increasing_iff
% 5.45/5.71 thf(fact_3537_power__strict__increasing__iff,axiom,
% 5.45/5.71 ! [B: nat,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_nat @ one_one_nat @ B )
% 5.45/5.71 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.45/5.71 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_increasing_iff
% 5.45/5.71 thf(fact_3538_power__strict__increasing__iff,axiom,
% 5.45/5.71 ! [B: int,X: nat,Y: nat] :
% 5.45/5.71 ( ( ord_less_int @ one_one_int @ B )
% 5.45/5.71 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.45/5.71 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_increasing_iff
% 5.45/5.71 thf(fact_3539_power__eq__0__iff,axiom,
% 5.45/5.71 ! [A: code_integer,N2: nat] :
% 5.45/5.71 ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 5.45/5.71 = zero_z3403309356797280102nteger )
% 5.45/5.71 = ( ( A = zero_z3403309356797280102nteger )
% 5.45/5.71 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_eq_0_iff
% 5.45/5.71 thf(fact_3540_power__eq__0__iff,axiom,
% 5.45/5.71 ! [A: rat,N2: nat] :
% 5.45/5.71 ( ( ( power_power_rat @ A @ N2 )
% 5.45/5.71 = zero_zero_rat )
% 5.45/5.71 = ( ( A = zero_zero_rat )
% 5.45/5.71 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_eq_0_iff
% 5.45/5.71 thf(fact_3541_power__eq__0__iff,axiom,
% 5.45/5.71 ! [A: nat,N2: nat] :
% 5.45/5.71 ( ( ( power_power_nat @ A @ N2 )
% 5.45/5.71 = zero_zero_nat )
% 5.45/5.71 = ( ( A = zero_zero_nat )
% 5.45/5.71 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_eq_0_iff
% 5.45/5.71 thf(fact_3542_power__eq__0__iff,axiom,
% 5.45/5.71 ! [A: int,N2: nat] :
% 5.45/5.71 ( ( ( power_power_int @ A @ N2 )
% 5.45/5.71 = zero_zero_int )
% 5.45/5.71 = ( ( A = zero_zero_int )
% 5.45/5.71 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_eq_0_iff
% 5.45/5.71 thf(fact_3543_le__divide__eq__1__pos,axiom,
% 5.45/5.71 ! [A: rat,B: rat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.71 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % le_divide_eq_1_pos
% 5.45/5.71 thf(fact_3544_power__strict__decreasing__iff,axiom,
% 5.45/5.71 ! [B: code_integer,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ B @ one_one_Code_integer )
% 5.45/5.71 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ B @ M ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_decreasing_iff
% 5.45/5.71 thf(fact_3545_power__strict__decreasing__iff,axiom,
% 5.45/5.71 ! [B: rat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.45/5.71 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_decreasing_iff
% 5.45/5.71 thf(fact_3546_power__strict__decreasing__iff,axiom,
% 5.45/5.71 ! [B: nat,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.45/5.71 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_decreasing_iff
% 5.45/5.71 thf(fact_3547_power__strict__decreasing__iff,axiom,
% 5.45/5.71 ! [B: int,M: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ( ord_less_int @ B @ one_one_int )
% 5.45/5.71 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_strict_decreasing_iff
% 5.45/5.71 thf(fact_3548_power__mono__iff,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.71 = ( ord_le3102999989581377725nteger @ A @ B ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono_iff
% 5.45/5.71 thf(fact_3549_power__mono__iff,axiom,
% 5.45/5.71 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono_iff
% 5.45/5.71 thf(fact_3550_power__mono__iff,axiom,
% 5.45/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono_iff
% 5.45/5.71 thf(fact_3551_power__mono__iff,axiom,
% 5.45/5.71 ! [A: int,B: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.71 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.45/5.71 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono_iff
% 5.45/5.71 thf(fact_3552_power__commuting__commutes,axiom,
% 5.45/5.71 ! [X: code_integer,Y: code_integer,N2: nat] :
% 5.45/5.71 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 5.45/5.71 = ( times_3573771949741848930nteger @ Y @ X ) )
% 5.45/5.71 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ Y )
% 5.45/5.71 = ( times_3573771949741848930nteger @ Y @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commuting_commutes
% 5.45/5.71 thf(fact_3553_power__commuting__commutes,axiom,
% 5.45/5.71 ! [X: assn,Y: assn,N2: nat] :
% 5.45/5.71 ( ( ( times_times_assn @ X @ Y )
% 5.45/5.71 = ( times_times_assn @ Y @ X ) )
% 5.45/5.71 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ Y )
% 5.45/5.71 = ( times_times_assn @ Y @ ( power_power_assn @ X @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commuting_commutes
% 5.45/5.71 thf(fact_3554_power__commuting__commutes,axiom,
% 5.45/5.71 ! [X: rat,Y: rat,N2: nat] :
% 5.45/5.71 ( ( ( times_times_rat @ X @ Y )
% 5.45/5.71 = ( times_times_rat @ Y @ X ) )
% 5.45/5.71 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ Y )
% 5.45/5.71 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commuting_commutes
% 5.45/5.71 thf(fact_3555_power__commuting__commutes,axiom,
% 5.45/5.71 ! [X: nat,Y: nat,N2: nat] :
% 5.45/5.71 ( ( ( times_times_nat @ X @ Y )
% 5.45/5.71 = ( times_times_nat @ Y @ X ) )
% 5.45/5.71 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ Y )
% 5.45/5.71 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commuting_commutes
% 5.45/5.71 thf(fact_3556_power__commuting__commutes,axiom,
% 5.45/5.71 ! [X: int,Y: int,N2: nat] :
% 5.45/5.71 ( ( ( times_times_int @ X @ Y )
% 5.45/5.71 = ( times_times_int @ Y @ X ) )
% 5.45/5.71 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ Y )
% 5.45/5.71 = ( times_times_int @ Y @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commuting_commutes
% 5.45/5.71 thf(fact_3557_power__mult__distrib,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.71 ( ( power_8256067586552552935nteger @ ( times_3573771949741848930nteger @ A @ B ) @ N2 )
% 5.45/5.71 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mult_distrib
% 5.45/5.71 thf(fact_3558_power__mult__distrib,axiom,
% 5.45/5.71 ! [A: assn,B: assn,N2: nat] :
% 5.45/5.71 ( ( power_power_assn @ ( times_times_assn @ A @ B ) @ N2 )
% 5.45/5.71 = ( times_times_assn @ ( power_power_assn @ A @ N2 ) @ ( power_power_assn @ B @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mult_distrib
% 5.45/5.71 thf(fact_3559_power__mult__distrib,axiom,
% 5.45/5.71 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.71 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N2 )
% 5.45/5.71 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mult_distrib
% 5.45/5.71 thf(fact_3560_power__mult__distrib,axiom,
% 5.45/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.71 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 5.45/5.71 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mult_distrib
% 5.45/5.71 thf(fact_3561_power__mult__distrib,axiom,
% 5.45/5.71 ! [A: int,B: int,N2: nat] :
% 5.45/5.71 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 5.45/5.71 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mult_distrib
% 5.45/5.71 thf(fact_3562_power__commutes,axiom,
% 5.45/5.71 ! [A: code_integer,N2: nat] :
% 5.45/5.71 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ A )
% 5.45/5.71 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commutes
% 5.45/5.71 thf(fact_3563_power__commutes,axiom,
% 5.45/5.71 ! [A: assn,N2: nat] :
% 5.45/5.71 ( ( times_times_assn @ ( power_power_assn @ A @ N2 ) @ A )
% 5.45/5.71 = ( times_times_assn @ A @ ( power_power_assn @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commutes
% 5.45/5.71 thf(fact_3564_power__commutes,axiom,
% 5.45/5.71 ! [A: rat,N2: nat] :
% 5.45/5.71 ( ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A )
% 5.45/5.71 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commutes
% 5.45/5.71 thf(fact_3565_power__commutes,axiom,
% 5.45/5.71 ! [A: nat,N2: nat] :
% 5.45/5.71 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 5.45/5.71 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commutes
% 5.45/5.71 thf(fact_3566_power__commutes,axiom,
% 5.45/5.71 ! [A: int,N2: nat] :
% 5.45/5.71 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 5.45/5.71 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_commutes
% 5.45/5.71 thf(fact_3567_divide__divide__eq__left_H,axiom,
% 5.45/5.71 ! [A: rat,B: rat,C: rat] :
% 5.45/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.45/5.71 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_divide_eq_left'
% 5.45/5.71 thf(fact_3568_divide__divide__times__eq,axiom,
% 5.45/5.71 ! [X: rat,Y: rat,Z: rat,W2: rat] :
% 5.45/5.71 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W2 ) )
% 5.45/5.71 = ( divide_divide_rat @ ( times_times_rat @ X @ W2 ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % divide_divide_times_eq
% 5.45/5.71 thf(fact_3569_times__divide__times__eq,axiom,
% 5.45/5.71 ! [X: rat,Y: rat,Z: rat,W2: rat] :
% 5.45/5.71 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W2 ) )
% 5.45/5.71 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % times_divide_times_eq
% 5.45/5.71 thf(fact_3570_power__mono,axiom,
% 5.45/5.71 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.71 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono
% 5.45/5.71 thf(fact_3571_power__mono,axiom,
% 5.45/5.71 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono
% 5.45/5.71 thf(fact_3572_power__mono,axiom,
% 5.45/5.71 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono
% 5.45/5.71 thf(fact_3573_power__mono,axiom,
% 5.45/5.71 ! [A: int,B: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.71 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % power_mono
% 5.45/5.71 thf(fact_3574_zero__le__power,axiom,
% 5.45/5.71 ! [A: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_power
% 5.45/5.71 thf(fact_3575_zero__le__power,axiom,
% 5.45/5.71 ! [A: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_power
% 5.45/5.71 thf(fact_3576_zero__le__power,axiom,
% 5.45/5.71 ! [A: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_power
% 5.45/5.71 thf(fact_3577_zero__le__power,axiom,
% 5.45/5.71 ! [A: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_le_power
% 5.45/5.71 thf(fact_3578_zero__less__power,axiom,
% 5.45/5.71 ! [A: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.71 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_power
% 5.45/5.71 thf(fact_3579_zero__less__power,axiom,
% 5.45/5.71 ! [A: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.71 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_power
% 5.45/5.71 thf(fact_3580_zero__less__power,axiom,
% 5.45/5.71 ! [A: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.71 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_power
% 5.45/5.71 thf(fact_3581_zero__less__power,axiom,
% 5.45/5.71 ! [A: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.71 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % zero_less_power
% 5.45/5.71 thf(fact_3582_one__le__power,axiom,
% 5.45/5.71 ! [A: code_integer,N2: nat] :
% 5.45/5.71 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.45/5.71 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_le_power
% 5.45/5.71 thf(fact_3583_one__le__power,axiom,
% 5.45/5.71 ! [A: rat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.45/5.71 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_le_power
% 5.45/5.71 thf(fact_3584_one__le__power,axiom,
% 5.45/5.71 ! [A: nat,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.45/5.71 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_le_power
% 5.45/5.71 thf(fact_3585_one__le__power,axiom,
% 5.45/5.71 ! [A: int,N2: nat] :
% 5.45/5.71 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.45/5.71 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.71
% 5.45/5.71 % one_le_power
% 5.45/5.72 thf(fact_3586_divide__le__0__iff,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.45/5.72 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.45/5.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_le_0_iff
% 5.45/5.72 thf(fact_3587_divide__right__mono,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_right_mono
% 5.45/5.72 thf(fact_3588_zero__le__divide__iff,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.45/5.72 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.45/5.72 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_le_divide_iff
% 5.45/5.72 thf(fact_3589_divide__nonneg__nonneg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonneg_nonneg
% 5.45/5.72 thf(fact_3590_divide__nonneg__nonpos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonneg_nonpos
% 5.45/5.72 thf(fact_3591_divide__nonpos__nonneg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonpos_nonneg
% 5.45/5.72 thf(fact_3592_divide__nonpos__nonpos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonpos_nonpos
% 5.45/5.72 thf(fact_3593_divide__right__mono__neg,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.72 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_right_mono_neg
% 5.45/5.72 thf(fact_3594_divide__neg__neg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_neg_neg
% 5.45/5.72 thf(fact_3595_divide__neg__pos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_neg_pos
% 5.45/5.72 thf(fact_3596_divide__pos__neg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_pos_neg
% 5.45/5.72 thf(fact_3597_divide__pos__pos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_pos_pos
% 5.45/5.72 thf(fact_3598_divide__less__0__iff,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_less_0_iff
% 5.45/5.72 thf(fact_3599_divide__less__cancel,axiom,
% 5.45/5.72 ! [A: rat,C: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_rat @ A @ B ) )
% 5.45/5.72 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ B @ A ) )
% 5.45/5.72 & ( C != zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_less_cancel
% 5.45/5.72 thf(fact_3600_zero__less__divide__iff,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_less_divide_iff
% 5.45/5.72 thf(fact_3601_divide__strict__right__mono,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_rat @ A @ B )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_strict_right_mono
% 5.45/5.72 thf(fact_3602_divide__strict__right__mono__neg,axiom,
% 5.45/5.72 ! [B: rat,A: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_rat @ B @ A )
% 5.45/5.72 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_strict_right_mono_neg
% 5.45/5.72 thf(fact_3603_left__right__inverse__power,axiom,
% 5.45/5.72 ! [X: code_integer,Y: code_integer,N2: nat] :
% 5.45/5.72 ( ( ( times_3573771949741848930nteger @ X @ Y )
% 5.45/5.72 = one_one_Code_integer )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 5.45/5.72 = one_one_Code_integer ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_right_inverse_power
% 5.45/5.72 thf(fact_3604_left__right__inverse__power,axiom,
% 5.45/5.72 ! [X: assn,Y: assn,N2: nat] :
% 5.45/5.72 ( ( ( times_times_assn @ X @ Y )
% 5.45/5.72 = one_one_assn )
% 5.45/5.72 => ( ( times_times_assn @ ( power_power_assn @ X @ N2 ) @ ( power_power_assn @ Y @ N2 ) )
% 5.45/5.72 = one_one_assn ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_right_inverse_power
% 5.45/5.72 thf(fact_3605_left__right__inverse__power,axiom,
% 5.45/5.72 ! [X: rat,Y: rat,N2: nat] :
% 5.45/5.72 ( ( ( times_times_rat @ X @ Y )
% 5.45/5.72 = one_one_rat )
% 5.45/5.72 => ( ( times_times_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.45/5.72 = one_one_rat ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_right_inverse_power
% 5.45/5.72 thf(fact_3606_left__right__inverse__power,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,N2: nat] :
% 5.45/5.72 ( ( ( times_times_nat @ X @ Y )
% 5.45/5.72 = one_one_nat )
% 5.45/5.72 => ( ( times_times_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 5.45/5.72 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_right_inverse_power
% 5.45/5.72 thf(fact_3607_left__right__inverse__power,axiom,
% 5.45/5.72 ! [X: int,Y: int,N2: nat] :
% 5.45/5.72 ( ( ( times_times_int @ X @ Y )
% 5.45/5.72 = one_one_int )
% 5.45/5.72 => ( ( times_times_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.45/5.72 = one_one_int ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_right_inverse_power
% 5.45/5.72 thf(fact_3608_frac__eq__eq,axiom,
% 5.45/5.72 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 5.45/5.72 ( ( Y != zero_zero_rat )
% 5.45/5.72 => ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( ( divide_divide_rat @ X @ Y )
% 5.45/5.72 = ( divide_divide_rat @ W2 @ Z ) )
% 5.45/5.72 = ( ( times_times_rat @ X @ Z )
% 5.45/5.72 = ( times_times_rat @ W2 @ Y ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % frac_eq_eq
% 5.45/5.72 thf(fact_3609_divide__eq__eq,axiom,
% 5.45/5.72 ! [B: rat,C: rat,A: rat] :
% 5.45/5.72 ( ( ( divide_divide_rat @ B @ C )
% 5.45/5.72 = A )
% 5.45/5.72 = ( ( ( C != zero_zero_rat )
% 5.45/5.72 => ( B
% 5.45/5.72 = ( times_times_rat @ A @ C ) ) )
% 5.45/5.72 & ( ( C = zero_zero_rat )
% 5.45/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_eq_eq
% 5.45/5.72 thf(fact_3610_eq__divide__eq,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( A
% 5.45/5.72 = ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( C != zero_zero_rat )
% 5.45/5.72 => ( ( times_times_rat @ A @ C )
% 5.45/5.72 = B ) )
% 5.45/5.72 & ( ( C = zero_zero_rat )
% 5.45/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % eq_divide_eq
% 5.45/5.72 thf(fact_3611_divide__eq__imp,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( C != zero_zero_rat )
% 5.45/5.72 => ( ( B
% 5.45/5.72 = ( times_times_rat @ A @ C ) )
% 5.45/5.72 => ( ( divide_divide_rat @ B @ C )
% 5.45/5.72 = A ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_eq_imp
% 5.45/5.72 thf(fact_3612_eq__divide__imp,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( C != zero_zero_rat )
% 5.45/5.72 => ( ( ( times_times_rat @ A @ C )
% 5.45/5.72 = B )
% 5.45/5.72 => ( A
% 5.45/5.72 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % eq_divide_imp
% 5.45/5.72 thf(fact_3613_nonzero__divide__eq__eq,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( C != zero_zero_rat )
% 5.45/5.72 => ( ( ( divide_divide_rat @ B @ C )
% 5.45/5.72 = A )
% 5.45/5.72 = ( B
% 5.45/5.72 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % nonzero_divide_eq_eq
% 5.45/5.72 thf(fact_3614_nonzero__eq__divide__eq,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( C != zero_zero_rat )
% 5.45/5.72 => ( ( A
% 5.45/5.72 = ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( times_times_rat @ A @ C )
% 5.45/5.72 = B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % nonzero_eq_divide_eq
% 5.45/5.72 thf(fact_3615_power__add,axiom,
% 5.45/5.72 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.72 ( ( power_8256067586552552935nteger @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add
% 5.45/5.72 thf(fact_3616_power__add,axiom,
% 5.45/5.72 ! [A: assn,M: nat,N2: nat] :
% 5.45/5.72 ( ( power_power_assn @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_assn @ ( power_power_assn @ A @ M ) @ ( power_power_assn @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add
% 5.45/5.72 thf(fact_3617_power__add,axiom,
% 5.45/5.72 ! [A: rat,M: nat,N2: nat] :
% 5.45/5.72 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add
% 5.45/5.72 thf(fact_3618_power__add,axiom,
% 5.45/5.72 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add
% 5.45/5.72 thf(fact_3619_power__add,axiom,
% 5.45/5.72 ! [A: int,M: nat,N2: nat] :
% 5.45/5.72 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add
% 5.45/5.72 thf(fact_3620_nat__power__less__imp__less,axiom,
% 5.45/5.72 ! [I2: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ I2 )
% 5.45/5.72 => ( ( ord_less_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % nat_power_less_imp_less
% 5.45/5.72 thf(fact_3621_power__less__imp__less__base,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat,B: code_integer] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_base
% 5.45/5.72 thf(fact_3622_power__less__imp__less__base,axiom,
% 5.45/5.72 ! [A: rat,N2: nat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.72 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_base
% 5.45/5.72 thf(fact_3623_power__less__imp__less__base,axiom,
% 5.45/5.72 ! [A: nat,N2: nat,B: nat] :
% 5.45/5.72 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.72 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_base
% 5.45/5.72 thf(fact_3624_power__less__imp__less__base,axiom,
% 5.45/5.72 ! [A: int,N2: nat,B: int] :
% 5.45/5.72 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.72 => ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_base
% 5.45/5.72 thf(fact_3625_power__le__one,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.45/5.72 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_one
% 5.45/5.72 thf(fact_3626_power__le__one,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ one_one_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_one
% 5.45/5.72 thf(fact_3627_power__le__one,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.45/5.72 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_one
% 5.45/5.72 thf(fact_3628_power__le__one,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.45/5.72 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ one_one_int ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_one
% 5.45/5.72 thf(fact_3629_frac__le,axiom,
% 5.45/5.72 ! [Y: rat,X: rat,W2: rat,Z: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.45/5.72 => ( ( ord_less_eq_rat @ W2 @ Z )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % frac_le
% 5.45/5.72 thf(fact_3630_frac__less,axiom,
% 5.45/5.72 ! [X: rat,Y: rat,W2: rat,Z: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_rat @ X @ Y )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.45/5.72 => ( ( ord_less_eq_rat @ W2 @ Z )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % frac_less
% 5.45/5.72 thf(fact_3631_frac__less2,axiom,
% 5.45/5.72 ! [X: rat,Y: rat,W2: rat,Z: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ W2 )
% 5.45/5.72 => ( ( ord_less_rat @ W2 @ Z )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W2 ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % frac_less2
% 5.45/5.72 thf(fact_3632_divide__le__cancel,axiom,
% 5.45/5.72 ! [A: rat,C: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.72 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_le_cancel
% 5.45/5.72 thf(fact_3633_divide__nonneg__neg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonneg_neg
% 5.45/5.72 thf(fact_3634_divide__nonneg__pos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonneg_pos
% 5.45/5.72 thf(fact_3635_divide__nonpos__neg,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonpos_neg
% 5.45/5.72 thf(fact_3636_divide__nonpos__pos,axiom,
% 5.45/5.72 ! [X: rat,Y: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_nonpos_pos
% 5.45/5.72 thf(fact_3637_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ A @ B )
% 5.45/5.72 = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_less
% 5.45/5.72 thf(fact_3638_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.45/5.72 ! [A: nat,B: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ A @ B )
% 5.45/5.72 => ( ( divide_divide_nat @ A @ B )
% 5.45/5.72 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_less
% 5.45/5.72 thf(fact_3639_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_int @ A @ B )
% 5.45/5.72 => ( ( divide_divide_int @ A @ B )
% 5.45/5.72 = zero_zero_int ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_less
% 5.45/5.72 thf(fact_3640_div__positive,axiom,
% 5.45/5.72 ! [B: code_integer,A: code_integer] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_positive
% 5.45/5.72 thf(fact_3641_div__positive,axiom,
% 5.45/5.72 ! [B: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.72 => ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.72 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_positive
% 5.45/5.72 thf(fact_3642_div__positive,axiom,
% 5.45/5.72 ! [B: int,A: int] :
% 5.45/5.72 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.72 => ( ( ord_less_eq_int @ B @ A )
% 5.45/5.72 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_positive
% 5.45/5.72 thf(fact_3643_power__gt1__lemma,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_gt1_lemma
% 5.45/5.72 thf(fact_3644_power__gt1__lemma,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_gt1_lemma
% 5.45/5.72 thf(fact_3645_power__gt1__lemma,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_gt1_lemma
% 5.45/5.72 thf(fact_3646_power__gt1__lemma,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_gt1_lemma
% 5.45/5.72 thf(fact_3647_power__less__power__Suc,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_power_Suc
% 5.45/5.72 thf(fact_3648_power__less__power__Suc,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_power_Suc
% 5.45/5.72 thf(fact_3649_power__less__power__Suc,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_power_Suc
% 5.45/5.72 thf(fact_3650_power__less__power__Suc,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_power_Suc
% 5.45/5.72 thf(fact_3651_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.45/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.72 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.45/5.72 thf(fact_3652_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.45/5.72 ! [C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.72 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.72 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.45/5.72 thf(fact_3653_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.45/5.72 ! [C: int,A: int,B: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.72 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.72 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.45/5.72 thf(fact_3654_divide__less__eq,axiom,
% 5.45/5.72 ! [B: rat,C: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_less_eq
% 5.45/5.72 thf(fact_3655_less__divide__eq,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_divide_eq
% 5.45/5.72 thf(fact_3656_neg__divide__less__eq,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % neg_divide_less_eq
% 5.45/5.72 thf(fact_3657_neg__less__divide__eq,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % neg_less_divide_eq
% 5.45/5.72 thf(fact_3658_pos__divide__less__eq,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % pos_divide_less_eq
% 5.45/5.72 thf(fact_3659_pos__less__divide__eq,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % pos_less_divide_eq
% 5.45/5.72 thf(fact_3660_mult__imp__div__pos__less,axiom,
% 5.45/5.72 ! [Y: rat,X: rat,Z: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_imp_div_pos_less
% 5.45/5.72 thf(fact_3661_mult__imp__less__div__pos,axiom,
% 5.45/5.72 ! [Y: rat,Z: rat,X: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.45/5.72 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_imp_less_div_pos
% 5.45/5.72 thf(fact_3662_divide__strict__left__mono,axiom,
% 5.45/5.72 ! [B: rat,A: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_rat @ B @ A )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_strict_left_mono
% 5.45/5.72 thf(fact_3663_divide__strict__left__mono__neg,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_rat @ A @ B )
% 5.45/5.72 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_strict_left_mono_neg
% 5.45/5.72 thf(fact_3664_divide__less__eq__1,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_rat @ B @ A ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_rat @ A @ B ) )
% 5.45/5.72 | ( A = zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_less_eq_1
% 5.45/5.72 thf(fact_3665_less__divide__eq__1,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_rat @ A @ B ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_divide_eq_1
% 5.45/5.72 thf(fact_3666_add__divide__eq__if__simps_I2_J,axiom,
% 5.45/5.72 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ( Z = zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.45/5.72 = B ) )
% 5.45/5.72 & ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_divide_eq_if_simps(2)
% 5.45/5.72 thf(fact_3667_add__divide__eq__if__simps_I1_J,axiom,
% 5.45/5.72 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ( Z = zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.45/5.72 = A ) )
% 5.45/5.72 & ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_divide_eq_if_simps(1)
% 5.45/5.72 thf(fact_3668_add__frac__eq,axiom,
% 5.45/5.72 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 5.45/5.72 ( ( Y != zero_zero_rat )
% 5.45/5.72 => ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_frac_eq
% 5.45/5.72 thf(fact_3669_add__frac__num,axiom,
% 5.45/5.72 ! [Y: rat,X: rat,Z: rat] :
% 5.45/5.72 ( ( Y != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_frac_num
% 5.45/5.72 thf(fact_3670_add__num__frac,axiom,
% 5.45/5.72 ! [Y: rat,Z: rat,X: rat] :
% 5.45/5.72 ( ( Y != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_num_frac
% 5.45/5.72 thf(fact_3671_add__divide__eq__iff,axiom,
% 5.45/5.72 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.72 ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_divide_eq_iff
% 5.45/5.72 thf(fact_3672_divide__add__eq__iff,axiom,
% 5.45/5.72 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.72 ( ( Z != zero_zero_rat )
% 5.45/5.72 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.45/5.72 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_add_eq_iff
% 5.45/5.72 thf(fact_3673_power__less__imp__less__exp,axiom,
% 5.45/5.72 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_exp
% 5.45/5.72 thf(fact_3674_power__less__imp__less__exp,axiom,
% 5.45/5.72 ! [A: rat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_exp
% 5.45/5.72 thf(fact_3675_power__less__imp__less__exp,axiom,
% 5.45/5.72 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_exp
% 5.45/5.72 thf(fact_3676_power__less__imp__less__exp,axiom,
% 5.45/5.72 ! [A: int,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_less_imp_less_exp
% 5.45/5.72 thf(fact_3677_power__strict__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: code_integer] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_increasing
% 5.45/5.72 thf(fact_3678_power__strict__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: rat] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_increasing
% 5.45/5.72 thf(fact_3679_power__strict__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_increasing
% 5.45/5.72 thf(fact_3680_power__strict__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: int] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_increasing
% 5.45/5.72 thf(fact_3681_power__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: code_integer] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_increasing
% 5.45/5.72 thf(fact_3682_power__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_increasing
% 5.45/5.72 thf(fact_3683_power__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_increasing
% 5.45/5.72 thf(fact_3684_power__increasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: int] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.45/5.72 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_increasing
% 5.45/5.72 thf(fact_3685_zero__power,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( power_8256067586552552935nteger @ zero_z3403309356797280102nteger @ N2 )
% 5.45/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_power
% 5.45/5.72 thf(fact_3686_zero__power,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.45/5.72 = zero_zero_rat ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_power
% 5.45/5.72 thf(fact_3687_zero__power,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_power
% 5.45/5.72 thf(fact_3688_zero__power,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.45/5.72 = zero_zero_int ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_power
% 5.45/5.72 thf(fact_3689_gt__half__sum,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ A @ B )
% 5.45/5.72 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % gt_half_sum
% 5.45/5.72 thf(fact_3690_less__half__sum,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ A @ B )
% 5.45/5.72 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_half_sum
% 5.45/5.72 thf(fact_3691_nat__mult__div__cancel1,axiom,
% 5.45/5.72 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.72 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % nat_mult_div_cancel1
% 5.45/5.72 thf(fact_3692_fold__atLeastAtMost__nat_Opelims,axiom,
% 5.45/5.72 ! [X: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.45/5.72 ( ( ( set_fo2584398358068434914at_nat @ X @ Xa @ Xb @ Xc )
% 5.45/5.72 = Y )
% 5.45/5.72 => ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) )
% 5.45/5.72 => ~ ( ( ( ( ord_less_nat @ Xb @ Xa )
% 5.45/5.72 => ( Y = Xc ) )
% 5.45/5.72 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.45/5.72 => ( Y
% 5.45/5.72 = ( set_fo2584398358068434914at_nat @ X @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X @ Xa @ Xc ) ) ) ) )
% 5.45/5.72 => ~ ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ X @ ( produc487386426758144856at_nat @ Xa @ ( product_Pair_nat_nat @ Xb @ Xc ) ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % fold_atLeastAtMost_nat.pelims
% 5.45/5.72 thf(fact_3693_fold__atLeastAtMost__nat_Opsimps,axiom,
% 5.45/5.72 ! [F: nat > nat > nat,A: nat,B: nat,Acc2: nat] :
% 5.45/5.72 ( ( accp_P6019419558468335806at_nat @ set_fo3699595496184130361el_nat @ ( produc3209952032786966637at_nat @ F @ ( produc487386426758144856at_nat @ A @ ( product_Pair_nat_nat @ B @ Acc2 ) ) ) )
% 5.45/5.72 => ( ( ( ord_less_nat @ B @ A )
% 5.45/5.72 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc2 )
% 5.45/5.72 = Acc2 ) )
% 5.45/5.72 & ( ~ ( ord_less_nat @ B @ A )
% 5.45/5.72 => ( ( set_fo2584398358068434914at_nat @ F @ A @ B @ Acc2 )
% 5.45/5.72 = ( set_fo2584398358068434914at_nat @ F @ ( plus_plus_nat @ A @ one_one_nat ) @ B @ ( F @ A @ Acc2 ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % fold_atLeastAtMost_nat.psimps
% 5.45/5.72 thf(fact_3694_power__Suc__less,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_Suc_less
% 5.45/5.72 thf(fact_3695_power__Suc__less,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.45/5.72 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_Suc_less
% 5.45/5.72 thf(fact_3696_power__Suc__less,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.45/5.72 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_Suc_less
% 5.45/5.72 thf(fact_3697_power__Suc__less,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_int @ A @ one_one_int )
% 5.45/5.72 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_Suc_less
% 5.45/5.72 thf(fact_3698_divide__left__mono__neg,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.72 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_left_mono_neg
% 5.45/5.72 thf(fact_3699_mult__imp__le__div__pos,axiom,
% 5.45/5.72 ! [Y: rat,Z: rat,X: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.45/5.72 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_imp_le_div_pos
% 5.45/5.72 thf(fact_3700_mult__imp__div__pos__le,axiom,
% 5.45/5.72 ! [Y: rat,X: rat,Z: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.72 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_imp_div_pos_le
% 5.45/5.72 thf(fact_3701_pos__le__divide__eq,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % pos_le_divide_eq
% 5.45/5.72 thf(fact_3702_pos__divide__le__eq,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % pos_divide_le_eq
% 5.45/5.72 thf(fact_3703_neg__le__divide__eq,axiom,
% 5.45/5.72 ! [C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % neg_le_divide_eq
% 5.45/5.72 thf(fact_3704_neg__divide__le__eq,axiom,
% 5.45/5.72 ! [C: rat,B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % neg_divide_le_eq
% 5.45/5.72 thf(fact_3705_divide__left__mono,axiom,
% 5.45/5.72 ! [B: rat,A: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.72 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_left_mono
% 5.45/5.72 thf(fact_3706_le__divide__eq,axiom,
% 5.45/5.72 ! [A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_divide_eq
% 5.45/5.72 thf(fact_3707_divide__le__eq,axiom,
% 5.45/5.72 ! [B: rat,C: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_le_eq
% 5.45/5.72 thf(fact_3708_divide__le__eq__1,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_eq_rat @ B @ A ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.72 | ( A = zero_zero_rat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_le_eq_1
% 5.45/5.72 thf(fact_3709_le__divide__eq__1,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 & ( ord_less_eq_rat @ A @ B ) )
% 5.45/5.72 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.72 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_divide_eq_1
% 5.45/5.72 thf(fact_3710_power__strict__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: code_integer] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N7 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_decreasing
% 5.45/5.72 thf(fact_3711_power__strict__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: rat] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.45/5.72 => ( ord_less_rat @ ( power_power_rat @ A @ N7 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_decreasing
% 5.45/5.72 thf(fact_3712_power__strict__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.45/5.72 => ( ord_less_nat @ ( power_power_nat @ A @ N7 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_decreasing
% 5.45/5.72 thf(fact_3713_power__strict__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: int] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_int @ A @ one_one_int )
% 5.45/5.72 => ( ord_less_int @ ( power_power_int @ A @ N7 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_strict_decreasing
% 5.45/5.72 thf(fact_3714_power__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: code_integer] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.45/5.72 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N7 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_decreasing
% 5.45/5.72 thf(fact_3715_power__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N7 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_decreasing
% 5.45/5.72 thf(fact_3716_power__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.45/5.72 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N7 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_decreasing
% 5.45/5.72 thf(fact_3717_power__decreasing,axiom,
% 5.45/5.72 ! [N2: nat,N7: nat,A: int] :
% 5.45/5.72 ( ( ord_less_eq_nat @ N2 @ N7 )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.45/5.72 => ( ord_less_eq_int @ ( power_power_int @ A @ N7 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_decreasing
% 5.45/5.72 thf(fact_3718_power__eq__iff__eq__base,axiom,
% 5.45/5.72 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.72 => ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 5.45/5.72 = ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.72 = ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_iff_eq_base
% 5.45/5.72 thf(fact_3719_power__eq__iff__eq__base,axiom,
% 5.45/5.72 ! [N2: nat,A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.72 => ( ( ( power_power_rat @ A @ N2 )
% 5.45/5.72 = ( power_power_rat @ B @ N2 ) )
% 5.45/5.72 = ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_iff_eq_base
% 5.45/5.72 thf(fact_3720_power__eq__iff__eq__base,axiom,
% 5.45/5.72 ! [N2: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.72 => ( ( ( power_power_nat @ A @ N2 )
% 5.45/5.72 = ( power_power_nat @ B @ N2 ) )
% 5.45/5.72 = ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_iff_eq_base
% 5.45/5.72 thf(fact_3721_power__eq__iff__eq__base,axiom,
% 5.45/5.72 ! [N2: nat,A: int,B: int] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.72 => ( ( ( power_power_int @ A @ N2 )
% 5.45/5.72 = ( power_power_int @ B @ N2 ) )
% 5.45/5.72 = ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_iff_eq_base
% 5.45/5.72 thf(fact_3722_power__eq__imp__eq__base,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat,B: code_integer] :
% 5.45/5.72 ( ( ( power_8256067586552552935nteger @ A @ N2 )
% 5.45/5.72 = ( power_8256067586552552935nteger @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_imp_eq_base
% 5.45/5.72 thf(fact_3723_power__eq__imp__eq__base,axiom,
% 5.45/5.72 ! [A: rat,N2: nat,B: rat] :
% 5.45/5.72 ( ( ( power_power_rat @ A @ N2 )
% 5.45/5.72 = ( power_power_rat @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_imp_eq_base
% 5.45/5.72 thf(fact_3724_power__eq__imp__eq__base,axiom,
% 5.45/5.72 ! [A: nat,N2: nat,B: nat] :
% 5.45/5.72 ( ( ( power_power_nat @ A @ N2 )
% 5.45/5.72 = ( power_power_nat @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.72 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_imp_eq_base
% 5.45/5.72 thf(fact_3725_power__eq__imp__eq__base,axiom,
% 5.45/5.72 ! [A: int,N2: nat,B: int] :
% 5.45/5.72 ( ( ( power_power_int @ A @ N2 )
% 5.45/5.72 = ( power_power_int @ B @ N2 ) )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.72 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( A = B ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_imp_eq_base
% 5.45/5.72 thf(fact_3726_power__le__imp__le__exp,axiom,
% 5.45/5.72 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_imp_le_exp
% 5.45/5.72 thf(fact_3727_power__le__imp__le__exp,axiom,
% 5.45/5.72 ! [A: rat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_imp_le_exp
% 5.45/5.72 thf(fact_3728_power__le__imp__le__exp,axiom,
% 5.45/5.72 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_imp_le_exp
% 5.45/5.72 thf(fact_3729_power__le__imp__le__exp,axiom,
% 5.45/5.72 ! [A: int,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.45/5.72 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_le_imp_le_exp
% 5.45/5.72 thf(fact_3730_self__le__power,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_le3102999989581377725nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % self_le_power
% 5.45/5.72 thf(fact_3731_self__le__power,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % self_le_power
% 5.45/5.72 thf(fact_3732_self__le__power,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % self_le_power
% 5.45/5.72 thf(fact_3733_self__le__power,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % self_le_power
% 5.45/5.72 thf(fact_3734_one__less__power,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_less_power
% 5.45/5.72 thf(fact_3735_one__less__power,axiom,
% 5.45/5.72 ! [A: rat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_less_power
% 5.45/5.72 thf(fact_3736_one__less__power,axiom,
% 5.45/5.72 ! [A: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_less_power
% 5.45/5.72 thf(fact_3737_one__less__power,axiom,
% 5.45/5.72 ! [A: int,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_less_power
% 5.45/5.72 thf(fact_3738_div__mult__self1,axiom,
% 5.45/5.72 ! [B: nat,A: nat,C: nat] :
% 5.45/5.72 ( ( B != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.45/5.72 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self1
% 5.45/5.72 thf(fact_3739_div__mult__self1,axiom,
% 5.45/5.72 ! [B: int,A: int,C: int] :
% 5.45/5.72 ( ( B != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.45/5.72 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self1
% 5.45/5.72 thf(fact_3740_div__mult__self1,axiom,
% 5.45/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.72 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self1
% 5.45/5.72 thf(fact_3741_div__mult__self1,axiom,
% 5.45/5.72 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.72 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self1
% 5.45/5.72 thf(fact_3742_div__mult__self2,axiom,
% 5.45/5.72 ! [B: nat,A: nat,C: nat] :
% 5.45/5.72 ( ( B != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.45/5.72 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self2
% 5.45/5.72 thf(fact_3743_div__mult__self2,axiom,
% 5.45/5.72 ! [B: int,A: int,C: int] :
% 5.45/5.72 ( ( B != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.45/5.72 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self2
% 5.45/5.72 thf(fact_3744_div__mult__self2,axiom,
% 5.45/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.72 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self2
% 5.45/5.72 thf(fact_3745_div__mult__self2,axiom,
% 5.45/5.72 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.72 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self2
% 5.45/5.72 thf(fact_3746_div__mult__self3,axiom,
% 5.45/5.72 ! [B: nat,C: nat,A: nat] :
% 5.45/5.72 ( ( B != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self3
% 5.45/5.72 thf(fact_3747_div__mult__self3,axiom,
% 5.45/5.72 ! [B: int,C: int,A: int] :
% 5.45/5.72 ( ( B != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self3
% 5.45/5.72 thf(fact_3748_div__mult__self3,axiom,
% 5.45/5.72 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.72 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self3
% 5.45/5.72 thf(fact_3749_div__mult__self3,axiom,
% 5.45/5.72 ! [B: code_natural,C: code_natural,A: code_natural] :
% 5.45/5.72 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self3
% 5.45/5.72 thf(fact_3750_div__mult__self4,axiom,
% 5.45/5.72 ! [B: nat,C: nat,A: nat] :
% 5.45/5.72 ( ( B != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self4
% 5.45/5.72 thf(fact_3751_div__mult__self4,axiom,
% 5.45/5.72 ! [B: int,C: int,A: int] :
% 5.45/5.72 ( ( B != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self4
% 5.45/5.72 thf(fact_3752_div__mult__self4,axiom,
% 5.45/5.72 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.72 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self4
% 5.45/5.72 thf(fact_3753_div__mult__self4,axiom,
% 5.45/5.72 ! [B: code_natural,C: code_natural,A: code_natural] :
% 5.45/5.72 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ C @ ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self4
% 5.45/5.72 thf(fact_3754_div__mult__self1__is__m,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 5.45/5.72 = M ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self1_is_m
% 5.45/5.72 thf(fact_3755_div__mult__self__is__m,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 5.45/5.72 = M ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_self_is_m
% 5.45/5.72 thf(fact_3756_div__mult__mult1,axiom,
% 5.45/5.72 ! [C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( C != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.45/5.72 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1
% 5.45/5.72 thf(fact_3757_div__mult__mult1,axiom,
% 5.45/5.72 ! [C: int,A: int,B: int] :
% 5.45/5.72 ( ( C != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.72 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1
% 5.45/5.72 thf(fact_3758_div__mult__mult1,axiom,
% 5.45/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.72 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1
% 5.45/5.72 thf(fact_3759_div__mult__mult1,axiom,
% 5.45/5.72 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.45/5.72 ( ( C != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 5.45/5.72 = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1
% 5.45/5.72 thf(fact_3760_div__mult__mult2,axiom,
% 5.45/5.72 ! [C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( C != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.45/5.72 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult2
% 5.45/5.72 thf(fact_3761_div__mult__mult2,axiom,
% 5.45/5.72 ! [C: int,A: int,B: int] :
% 5.45/5.72 ( ( C != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.72 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult2
% 5.45/5.72 thf(fact_3762_div__mult__mult2,axiom,
% 5.45/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.72 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult2
% 5.45/5.72 thf(fact_3763_div__mult__mult2,axiom,
% 5.45/5.72 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.45/5.72 ( ( C != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 5.45/5.72 = ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult2
% 5.45/5.72 thf(fact_3764_div__mult__mult1__if,axiom,
% 5.45/5.72 ! [C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( ( C = zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.45/5.72 = zero_zero_nat ) )
% 5.45/5.72 & ( ( C != zero_zero_nat )
% 5.45/5.72 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.45/5.72 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1_if
% 5.45/5.72 thf(fact_3765_div__mult__mult1__if,axiom,
% 5.45/5.72 ! [C: int,A: int,B: int] :
% 5.45/5.72 ( ( ( C = zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.72 = zero_zero_int ) )
% 5.45/5.72 & ( ( C != zero_zero_int )
% 5.45/5.72 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.72 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1_if
% 5.45/5.72 thf(fact_3766_div__mult__mult1__if,axiom,
% 5.45/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.72 = zero_z3403309356797280102nteger ) )
% 5.45/5.72 & ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.72 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1_if
% 5.45/5.72 thf(fact_3767_div__mult__mult1__if,axiom,
% 5.45/5.72 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.45/5.72 ( ( ( C = zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 5.45/5.72 = zero_z2226904508553997617atural ) )
% 5.45/5.72 & ( ( C != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) )
% 5.45/5.72 = ( divide5121882707175180666atural @ A @ B ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_mult_mult1_if
% 5.45/5.72 thf(fact_3768_div__less,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.72 => ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.72 = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_less
% 5.45/5.72 thf(fact_3769_div__le__mono,axiom,
% 5.45/5.72 ! [M: nat,N2: nat,K: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.72 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_le_mono
% 5.45/5.72 thf(fact_3770_div__le__dividend,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 5.45/5.72
% 5.45/5.72 % div_le_dividend
% 5.45/5.72 thf(fact_3771_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.72 = zero_zero_nat )
% 5.45/5.72 = ( ( ord_less_nat @ M @ N2 )
% 5.45/5.72 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % Euclidean_Division.div_eq_0_iff
% 5.45/5.72 thf(fact_3772_less__mult__imp__div__less,axiom,
% 5.45/5.72 ! [M: nat,I2: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 5.45/5.72 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_mult_imp_div_less
% 5.45/5.72 thf(fact_3773_times__div__less__eq__dividend,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 5.45/5.72
% 5.45/5.72 % times_div_less_eq_dividend
% 5.45/5.72 thf(fact_3774_div__times__less__eq__dividend,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 5.45/5.72
% 5.45/5.72 % div_times_less_eq_dividend
% 5.45/5.72 thf(fact_3775_div__greater__zero__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.45/5.72 = ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_greater_zero_iff
% 5.45/5.72 thf(fact_3776_div__le__mono2,axiom,
% 5.45/5.72 ! [M: nat,N2: nat,K: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.72 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.72 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_le_mono2
% 5.45/5.72 thf(fact_3777_div__less__iff__less__mult,axiom,
% 5.45/5.72 ! [Q6: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 5.45/5.72 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q6 ) @ N2 )
% 5.45/5.72 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q6 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_less_iff_less_mult
% 5.45/5.72 thf(fact_3778_div__eq__dividend__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.72 => ( ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.72 = M )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_eq_dividend_iff
% 5.45/5.72 thf(fact_3779_div__less__dividend,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.72 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % div_less_dividend
% 5.45/5.72 thf(fact_3780_less__eq__div__iff__mult__less__eq,axiom,
% 5.45/5.72 ! [Q6: nat,M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ Q6 )
% 5.45/5.72 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q6 ) )
% 5.45/5.72 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q6 ) @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_eq_div_iff_mult_less_eq
% 5.45/5.72 thf(fact_3781_split__div,axiom,
% 5.45/5.72 ! [P: nat > $o,M: nat,N2: nat] :
% 5.45/5.72 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.45/5.72 = ( ( ( N2 = zero_zero_nat )
% 5.45/5.72 => ( P @ zero_zero_nat ) )
% 5.45/5.72 & ( ( N2 != zero_zero_nat )
% 5.45/5.72 => ! [I4: nat,J3: nat] :
% 5.45/5.72 ( ( ord_less_nat @ J3 @ N2 )
% 5.45/5.72 => ( ( M
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I4 ) @ J3 ) )
% 5.45/5.72 => ( P @ I4 ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % split_div
% 5.45/5.72 thf(fact_3782_dividend__less__div__times,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % dividend_less_div_times
% 5.45/5.72 thf(fact_3783_dividend__less__times__div,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % dividend_less_times_div
% 5.45/5.72 thf(fact_3784_verit__le__mono__div,axiom,
% 5.45/5.72 ! [A3: nat,B3: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ A3 @ B3 )
% 5.45/5.72 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ord_less_eq_nat
% 5.45/5.72 @ ( plus_plus_nat @ ( divide_divide_nat @ A3 @ N2 )
% 5.45/5.72 @ ( if_nat
% 5.45/5.72 @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.45/5.72 = zero_zero_nat )
% 5.45/5.72 @ one_one_nat
% 5.45/5.72 @ zero_zero_nat ) )
% 5.45/5.72 @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % verit_le_mono_div
% 5.45/5.72 thf(fact_3785_of__nat__zero__less__power__iff,axiom,
% 5.45/5.72 ! [X: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N2 ) )
% 5.45/5.72 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.72 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_zero_less_power_iff
% 5.45/5.72 thf(fact_3786_of__nat__zero__less__power__iff,axiom,
% 5.45/5.72 ! [X: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N2 ) )
% 5.45/5.72 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.72 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_zero_less_power_iff
% 5.45/5.72 thf(fact_3787_of__nat__zero__less__power__iff,axiom,
% 5.45/5.72 ! [X: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N2 ) )
% 5.45/5.72 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.72 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_zero_less_power_iff
% 5.45/5.72 thf(fact_3788_of__nat__zero__less__power__iff,axiom,
% 5.45/5.72 ! [X: nat,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ X ) @ N2 ) )
% 5.45/5.72 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.72 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_zero_less_power_iff
% 5.45/5.72 thf(fact_3789_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3790_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3791_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3792_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 5.45/5.72 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3793_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3794_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3795_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,C: nat,A: nat,B: nat] :
% 5.45/5.72 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3796_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,C: int,A: int,B: int] :
% 5.45/5.72 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3797_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3798_distrib__right__NO__MATCH,axiom,
% 5.45/5.72 ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 5.45/5.72 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 5.45/5.72 => ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_NO_MATCH
% 5.45/5.72 thf(fact_3799_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3800_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3801_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,A: nat,B: nat,C: nat] :
% 5.45/5.72 ( ( nO_MATCH_nat_nat @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3802_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 5.45/5.72 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3803_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3804_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3805_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,A: nat,B: nat,C: nat] :
% 5.45/5.72 ( ( nO_MATCH_int_nat @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3806_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: int,Y: int,A: int,B: int,C: int] :
% 5.45/5.72 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3807_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3808_distrib__left__NO__MATCH,axiom,
% 5.45/5.72 ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 5.45/5.72 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 5.45/5.72 => ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_NO_MATCH
% 5.45/5.72 thf(fact_3809_split__div_H,axiom,
% 5.45/5.72 ! [P: nat > $o,M: nat,N2: nat] :
% 5.45/5.72 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.45/5.72 = ( ( ( N2 = zero_zero_nat )
% 5.45/5.72 & ( P @ zero_zero_nat ) )
% 5.45/5.72 | ? [Q7: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q7 ) @ M )
% 5.45/5.72 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q7 ) ) )
% 5.45/5.72 & ( P @ Q7 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % split_div'
% 5.45/5.72 thf(fact_3810_power__minus__mult,axiom,
% 5.45/5.72 ! [N2: nat,A: code_integer] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.45/5.72 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_minus_mult
% 5.45/5.72 thf(fact_3811_power__minus__mult,axiom,
% 5.45/5.72 ! [N2: nat,A: assn] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( times_times_assn @ ( power_power_assn @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.45/5.72 = ( power_power_assn @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_minus_mult
% 5.45/5.72 thf(fact_3812_power__minus__mult,axiom,
% 5.45/5.72 ! [N2: nat,A: rat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.45/5.72 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_minus_mult
% 5.45/5.72 thf(fact_3813_power__minus__mult,axiom,
% 5.45/5.72 ! [N2: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.45/5.72 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_minus_mult
% 5.45/5.72 thf(fact_3814_power__minus__mult,axiom,
% 5.45/5.72 ! [N2: nat,A: int] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.45/5.72 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_minus_mult
% 5.45/5.72 thf(fact_3815_power__eq__if,axiom,
% 5.45/5.72 ( power_8256067586552552935nteger
% 5.45/5.72 = ( ^ [P7: code_integer,M3: nat] : ( if_Code_integer @ ( M3 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ P7 @ ( power_8256067586552552935nteger @ P7 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_if
% 5.45/5.72 thf(fact_3816_power__eq__if,axiom,
% 5.45/5.72 ( power_power_assn
% 5.45/5.72 = ( ^ [P7: assn,M3: nat] : ( if_assn @ ( M3 = zero_zero_nat ) @ one_one_assn @ ( times_times_assn @ P7 @ ( power_power_assn @ P7 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_if
% 5.45/5.72 thf(fact_3817_power__eq__if,axiom,
% 5.45/5.72 ( power_power_rat
% 5.45/5.72 = ( ^ [P7: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P7 @ ( power_power_rat @ P7 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_if
% 5.45/5.72 thf(fact_3818_power__eq__if,axiom,
% 5.45/5.72 ( power_power_nat
% 5.45/5.72 = ( ^ [P7: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P7 @ ( power_power_nat @ P7 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_if
% 5.45/5.72 thf(fact_3819_power__eq__if,axiom,
% 5.45/5.72 ( power_power_int
% 5.45/5.72 = ( ^ [P7: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P7 @ ( power_power_int @ P7 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_eq_if
% 5.45/5.72 thf(fact_3820_power__diff__power__eq,axiom,
% 5.45/5.72 ! [A: nat,N2: nat,M: nat] :
% 5.45/5.72 ( ( A != zero_zero_nat )
% 5.45/5.72 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.45/5.72 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.45/5.72 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.45/5.72 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_diff_power_eq
% 5.45/5.72 thf(fact_3821_power__diff__power__eq,axiom,
% 5.45/5.72 ! [A: int,N2: nat,M: nat] :
% 5.45/5.72 ( ( A != zero_zero_int )
% 5.45/5.72 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.45/5.72 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.45/5.72 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.45/5.72 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_diff_power_eq
% 5.45/5.72 thf(fact_3822_power__diff__power__eq,axiom,
% 5.45/5.72 ! [A: code_integer,N2: nat,M: nat] :
% 5.45/5.72 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.72 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.72 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.45/5.72 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.72 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_diff_power_eq
% 5.45/5.72 thf(fact_3823_power__diff__power__eq,axiom,
% 5.45/5.72 ! [A: code_natural,N2: nat,M: nat] :
% 5.45/5.72 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.72 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 5.45/5.72 = ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.45/5.72 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.72 => ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 5.45/5.72 = ( divide5121882707175180666atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_diff_power_eq
% 5.45/5.72 thf(fact_3824_le__divide__eq__numeral_I1_J,axiom,
% 5.45/5.72 ! [W2: num,B: rat,C: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.72 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.72 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.45/5.72 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.72 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_divide_eq_numeral(1)
% 5.45/5.72 thf(fact_3825_old_Onat_Oinject,axiom,
% 5.45/5.72 ! [Nat: nat,Nat2: nat] :
% 5.45/5.72 ( ( ( suc @ Nat )
% 5.45/5.72 = ( suc @ Nat2 ) )
% 5.45/5.72 = ( Nat = Nat2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % old.nat.inject
% 5.45/5.72 thf(fact_3826_nat_Oinject,axiom,
% 5.45/5.72 ! [X2: nat,Y2: nat] :
% 5.45/5.72 ( ( ( suc @ X2 )
% 5.45/5.72 = ( suc @ Y2 ) )
% 5.45/5.72 = ( X2 = Y2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % nat.inject
% 5.45/5.72 thf(fact_3827_of__nat__eq__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( semiri1314217659103216013at_int @ M )
% 5.45/5.72 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.72 = ( M = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_iff
% 5.45/5.72 thf(fact_3828_of__nat__eq__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.45/5.72 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.72 = ( M = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_iff
% 5.45/5.72 thf(fact_3829_of__nat__eq__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( semiri4939895301339042750nteger @ M )
% 5.45/5.72 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.72 = ( M = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_iff
% 5.45/5.72 thf(fact_3830_numeral__le__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_le_iff
% 5.45/5.72 thf(fact_3831_numeral__le__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_le_iff
% 5.45/5.72 thf(fact_3832_numeral__le__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_le_iff
% 5.45/5.72 thf(fact_3833_numeral__le__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_le_iff
% 5.45/5.72 thf(fact_3834_numeral__le__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_le_iff
% 5.45/5.72 thf(fact_3835_numeral__less__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.45/5.72 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_less_iff
% 5.45/5.72 thf(fact_3836_numeral__less__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.72 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_less_iff
% 5.45/5.72 thf(fact_3837_numeral__less__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.72 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_less_iff
% 5.45/5.72 thf(fact_3838_numeral__less__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.72 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_less_iff
% 5.45/5.72 thf(fact_3839_numeral__less__iff,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 5.45/5.72 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_less_iff
% 5.45/5.72 thf(fact_3840_mult__numeral__left__semiring__numeral,axiom,
% 5.45/5.72 ! [V: num,W2: num,Z: nat] :
% 5.45/5.72 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W2 ) @ Z ) )
% 5.45/5.72 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_numeral_left_semiring_numeral
% 5.45/5.72 thf(fact_3841_mult__numeral__left__semiring__numeral,axiom,
% 5.45/5.72 ! [V: num,W2: num,Z: int] :
% 5.45/5.72 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Z ) )
% 5.45/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_numeral_left_semiring_numeral
% 5.45/5.72 thf(fact_3842_mult__numeral__left__semiring__numeral,axiom,
% 5.45/5.72 ! [V: num,W2: num,Z: code_integer] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Z ) )
% 5.45/5.72 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_numeral_left_semiring_numeral
% 5.45/5.72 thf(fact_3843_mult__numeral__left__semiring__numeral,axiom,
% 5.45/5.72 ! [V: num,W2: num,Z: rat] :
% 5.45/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Z ) )
% 5.45/5.72 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_numeral_left_semiring_numeral
% 5.45/5.72 thf(fact_3844_mult__numeral__left__semiring__numeral,axiom,
% 5.45/5.72 ! [V: num,W2: num,Z: code_natural] :
% 5.45/5.72 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ W2 ) @ Z ) )
% 5.45/5.72 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( times_times_num @ V @ W2 ) ) @ Z ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_numeral_left_semiring_numeral
% 5.45/5.72 thf(fact_3845_numeral__times__numeral,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.45/5.72 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_times_numeral
% 5.45/5.72 thf(fact_3846_numeral__times__numeral,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.72 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_times_numeral
% 5.45/5.72 thf(fact_3847_numeral__times__numeral,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.72 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_times_numeral
% 5.45/5.72 thf(fact_3848_numeral__times__numeral,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.72 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_times_numeral
% 5.45/5.72 thf(fact_3849_numeral__times__numeral,axiom,
% 5.45/5.72 ! [M: num,N2: num] :
% 5.45/5.72 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 5.45/5.72 = ( numera5444537566228673987atural @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % numeral_times_numeral
% 5.45/5.72 thf(fact_3850_power__add__numeral,axiom,
% 5.45/5.72 ! [A: code_integer,M: num,N2: num] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.45/5.72 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral
% 5.45/5.72 thf(fact_3851_power__add__numeral,axiom,
% 5.45/5.72 ! [A: assn,M: num,N2: num] :
% 5.45/5.72 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.45/5.72 = ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral
% 5.45/5.72 thf(fact_3852_power__add__numeral,axiom,
% 5.45/5.72 ! [A: rat,M: num,N2: num] :
% 5.45/5.72 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.45/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral
% 5.45/5.72 thf(fact_3853_power__add__numeral,axiom,
% 5.45/5.72 ! [A: nat,M: num,N2: num] :
% 5.45/5.72 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.45/5.72 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral
% 5.45/5.72 thf(fact_3854_power__add__numeral,axiom,
% 5.45/5.72 ! [A: int,M: num,N2: num] :
% 5.45/5.72 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.45/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral
% 5.45/5.72 thf(fact_3855_power__add__numeral2,axiom,
% 5.45/5.72 ! [A: code_integer,M: num,N2: num,B: code_integer] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.45/5.72 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral2
% 5.45/5.72 thf(fact_3856_power__add__numeral2,axiom,
% 5.45/5.72 ! [A: assn,M: num,N2: num,B: assn] :
% 5.45/5.72 ( ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.45/5.72 = ( times_times_assn @ ( power_power_assn @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral2
% 5.45/5.72 thf(fact_3857_power__add__numeral2,axiom,
% 5.45/5.72 ! [A: rat,M: num,N2: num,B: rat] :
% 5.45/5.72 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.45/5.72 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral2
% 5.45/5.72 thf(fact_3858_power__add__numeral2,axiom,
% 5.45/5.72 ! [A: nat,M: num,N2: num,B: nat] :
% 5.45/5.72 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.45/5.72 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral2
% 5.45/5.72 thf(fact_3859_power__add__numeral2,axiom,
% 5.45/5.72 ! [A: int,M: num,N2: num,B: int] :
% 5.45/5.72 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.45/5.72 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % power_add_numeral2
% 5.45/5.72 thf(fact_3860_lessI,axiom,
% 5.45/5.72 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % lessI
% 5.45/5.72 thf(fact_3861_Suc__mono,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.72 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % Suc_mono
% 5.45/5.72 thf(fact_3862_Suc__less__eq,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % Suc_less_eq
% 5.45/5.72 thf(fact_3863_Suc__le__mono,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 5.45/5.72 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.45/5.72
% 5.45/5.72 % Suc_le_mono
% 5.45/5.72 thf(fact_3864_add__Suc__right,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 5.45/5.72 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % add_Suc_right
% 5.45/5.72 thf(fact_3865_diff__self__eq__0,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ M @ M )
% 5.45/5.72 = zero_zero_nat ) ).
% 5.45/5.72
% 5.45/5.72 % diff_self_eq_0
% 5.45/5.72 thf(fact_3866_diff__0__eq__0,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 = zero_zero_nat ) ).
% 5.45/5.72
% 5.45/5.72 % diff_0_eq_0
% 5.45/5.72 thf(fact_3867_Suc__diff__diff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat,K: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.45/5.72 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.45/5.72
% 5.45/5.72 % Suc_diff_diff
% 5.45/5.72 thf(fact_3868_diff__Suc__Suc,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.45/5.72 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_Suc_Suc
% 5.45/5.72 thf(fact_3869_diff__diff__cancel,axiom,
% 5.45/5.72 ! [I2: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.45/5.72 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.45/5.72 = I2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_diff_cancel
% 5.45/5.72 thf(fact_3870_diff__diff__left,axiom,
% 5.45/5.72 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.45/5.72 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_diff_left
% 5.45/5.72 thf(fact_3871_mod__less,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.72 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.45/5.72 = M ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_less
% 5.45/5.72 thf(fact_3872_zero__comp__diff__simps_I1_J,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.45/5.72 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(1)
% 5.45/5.72 thf(fact_3873_zero__comp__diff__simps_I1_J,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.72 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(1)
% 5.45/5.72 thf(fact_3874_zero__comp__diff__simps_I1_J,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.45/5.72 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(1)
% 5.45/5.72 thf(fact_3875_diff__ge__0__iff__ge,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.45/5.72 = ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_ge_0_iff_ge
% 5.45/5.72 thf(fact_3876_diff__ge__0__iff__ge,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.72 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_ge_0_iff_ge
% 5.45/5.72 thf(fact_3877_diff__ge__0__iff__ge,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.45/5.72 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_ge_0_iff_ge
% 5.45/5.72 thf(fact_3878_zero__comp__diff__simps_I2_J,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.45/5.72 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(2)
% 5.45/5.72 thf(fact_3879_zero__comp__diff__simps_I2_J,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.72 = ( ord_less_rat @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(2)
% 5.45/5.72 thf(fact_3880_zero__comp__diff__simps_I2_J,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.45/5.72 = ( ord_less_int @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_comp_diff_simps(2)
% 5.45/5.72 thf(fact_3881_diff__gt__0__iff__gt,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.45/5.72 = ( ord_le6747313008572928689nteger @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_gt_0_iff_gt
% 5.45/5.72 thf(fact_3882_diff__gt__0__iff__gt,axiom,
% 5.45/5.72 ! [A: rat,B: rat] :
% 5.45/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.72 = ( ord_less_rat @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_gt_0_iff_gt
% 5.45/5.72 thf(fact_3883_diff__gt__0__iff__gt,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.45/5.72 = ( ord_less_int @ B @ A ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_gt_0_iff_gt
% 5.45/5.72 thf(fact_3884_le__add__diff__inverse,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.72 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse
% 5.45/5.72 thf(fact_3885_le__add__diff__inverse,axiom,
% 5.45/5.72 ! [B: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.72 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse
% 5.45/5.72 thf(fact_3886_le__add__diff__inverse,axiom,
% 5.45/5.72 ! [B: int,A: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.72 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse
% 5.45/5.72 thf(fact_3887_le__add__diff__inverse2,axiom,
% 5.45/5.72 ! [B: rat,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.72 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse2
% 5.45/5.72 thf(fact_3888_le__add__diff__inverse2,axiom,
% 5.45/5.72 ! [B: nat,A: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse2
% 5.45/5.72 thf(fact_3889_le__add__diff__inverse2,axiom,
% 5.45/5.72 ! [B: int,A: int] :
% 5.45/5.72 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.72 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.45/5.72 = A ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_add_diff_inverse2
% 5.45/5.72 thf(fact_3890_distrib__left__numeral,axiom,
% 5.45/5.72 ! [V: num,B: nat,C: nat] :
% 5.45/5.72 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_numeral
% 5.45/5.72 thf(fact_3891_distrib__left__numeral,axiom,
% 5.45/5.72 ! [V: num,B: int,C: int] :
% 5.45/5.72 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_numeral
% 5.45/5.72 thf(fact_3892_distrib__left__numeral,axiom,
% 5.45/5.72 ! [V: num,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_numeral
% 5.45/5.72 thf(fact_3893_distrib__left__numeral,axiom,
% 5.45/5.72 ! [V: num,B: rat,C: rat] :
% 5.45/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_numeral
% 5.45/5.72 thf(fact_3894_distrib__left__numeral,axiom,
% 5.45/5.72 ! [V: num,B: code_natural,C: code_natural] :
% 5.45/5.72 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ ( plus_p4538020629002901425atural @ B @ C ) )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ B ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_left_numeral
% 5.45/5.72 thf(fact_3895_distrib__right__numeral,axiom,
% 5.45/5.72 ! [A: nat,B: nat,V: num] :
% 5.45/5.72 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.45/5.72 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_numeral
% 5.45/5.72 thf(fact_3896_distrib__right__numeral,axiom,
% 5.45/5.72 ! [A: int,B: int,V: num] :
% 5.45/5.72 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.72 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_numeral
% 5.45/5.72 thf(fact_3897_distrib__right__numeral,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer,V: num] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_numeral
% 5.45/5.72 thf(fact_3898_distrib__right__numeral,axiom,
% 5.45/5.72 ! [A: rat,B: rat,V: num] :
% 5.45/5.72 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.45/5.72 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_numeral
% 5.45/5.72 thf(fact_3899_distrib__right__numeral,axiom,
% 5.45/5.72 ! [A: code_natural,B: code_natural,V: num] :
% 5.45/5.72 ( ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ A @ B ) @ ( numera5444537566228673987atural @ V ) )
% 5.45/5.72 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ V ) ) @ ( times_2397367101498566445atural @ B @ ( numera5444537566228673987atural @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % distrib_right_numeral
% 5.45/5.72 thf(fact_3900_right__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [V: num,B: int,C: int] :
% 5.45/5.72 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.45/5.72 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % right_diff_distrib_numeral
% 5.45/5.72 thf(fact_3901_right__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [V: num,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.72 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ B ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % right_diff_distrib_numeral
% 5.45/5.72 thf(fact_3902_right__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [V: num,B: rat,C: rat] :
% 5.45/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.72 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % right_diff_distrib_numeral
% 5.45/5.72 thf(fact_3903_left__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [A: int,B: int,V: num] :
% 5.45/5.72 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.72 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_diff_distrib_numeral
% 5.45/5.72 thf(fact_3904_left__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer,V: num] :
% 5.45/5.72 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ ( numera6620942414471956472nteger @ V ) )
% 5.45/5.72 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ B @ ( numera6620942414471956472nteger @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_diff_distrib_numeral
% 5.45/5.72 thf(fact_3905_left__diff__distrib__numeral,axiom,
% 5.45/5.72 ! [A: rat,B: rat,V: num] :
% 5.45/5.72 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.45/5.72 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % left_diff_distrib_numeral
% 5.45/5.72 thf(fact_3906_mod__mult__self1__is__0,axiom,
% 5.45/5.72 ! [B: nat,A: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.45/5.72 = zero_zero_nat ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1_is_0
% 5.45/5.72 thf(fact_3907_mod__mult__self1__is__0,axiom,
% 5.45/5.72 ! [B: int,A: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.45/5.72 = zero_zero_int ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1_is_0
% 5.45/5.72 thf(fact_3908_mod__mult__self1__is__0,axiom,
% 5.45/5.72 ! [B: code_integer,A: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.45/5.72 = zero_z3403309356797280102nteger ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1_is_0
% 5.45/5.72 thf(fact_3909_mod__mult__self1__is__0,axiom,
% 5.45/5.72 ! [B: code_natural,A: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ B @ A ) @ B )
% 5.45/5.72 = zero_z2226904508553997617atural ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1_is_0
% 5.45/5.72 thf(fact_3910_mod__mult__self2__is__0,axiom,
% 5.45/5.72 ! [A: nat,B: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.45/5.72 = zero_zero_nat ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2_is_0
% 5.45/5.72 thf(fact_3911_mod__mult__self2__is__0,axiom,
% 5.45/5.72 ! [A: int,B: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.45/5.72 = zero_zero_int ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2_is_0
% 5.45/5.72 thf(fact_3912_mod__mult__self2__is__0,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.45/5.72 = zero_z3403309356797280102nteger ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2_is_0
% 5.45/5.72 thf(fact_3913_mod__mult__self2__is__0,axiom,
% 5.45/5.72 ! [A: code_natural,B: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ B )
% 5.45/5.72 = zero_z2226904508553997617atural ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2_is_0
% 5.45/5.72 thf(fact_3914_of__nat__eq__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ( semiri681578069525770553at_rat @ M )
% 5.45/5.72 = zero_zero_rat )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_0_iff
% 5.45/5.72 thf(fact_3915_of__nat__eq__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ( semiri1314217659103216013at_int @ M )
% 5.45/5.72 = zero_zero_int )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_0_iff
% 5.45/5.72 thf(fact_3916_of__nat__eq__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.45/5.72 = zero_zero_nat )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_0_iff
% 5.45/5.72 thf(fact_3917_of__nat__eq__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ( semiri4939895301339042750nteger @ M )
% 5.45/5.72 = zero_z3403309356797280102nteger )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_0_iff
% 5.45/5.72 thf(fact_3918_of__nat__0__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( zero_zero_rat
% 5.45/5.72 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.72 = ( zero_zero_nat = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0_eq_iff
% 5.45/5.72 thf(fact_3919_of__nat__0__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( zero_zero_int
% 5.45/5.72 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.72 = ( zero_zero_nat = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0_eq_iff
% 5.45/5.72 thf(fact_3920_of__nat__0__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( zero_zero_nat
% 5.45/5.72 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.72 = ( zero_zero_nat = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0_eq_iff
% 5.45/5.72 thf(fact_3921_of__nat__0__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( zero_z3403309356797280102nteger
% 5.45/5.72 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.72 = ( zero_zero_nat = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0_eq_iff
% 5.45/5.72 thf(fact_3922_of__nat__0,axiom,
% 5.45/5.72 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.45/5.72 = zero_zero_rat ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0
% 5.45/5.72 thf(fact_3923_of__nat__0,axiom,
% 5.45/5.72 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.45/5.72 = zero_zero_int ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0
% 5.45/5.72 thf(fact_3924_of__nat__0,axiom,
% 5.45/5.72 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.45/5.72 = zero_zero_nat ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0
% 5.45/5.72 thf(fact_3925_of__nat__0,axiom,
% 5.45/5.72 ( ( semiri4939895301339042750nteger @ zero_zero_nat )
% 5.45/5.72 = zero_z3403309356797280102nteger ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_0
% 5.45/5.72 thf(fact_3926_mod__mult__self1,axiom,
% 5.45/5.72 ! [A: nat,C: nat,B: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.45/5.72 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1
% 5.45/5.72 thf(fact_3927_mod__mult__self1,axiom,
% 5.45/5.72 ! [A: int,C: int,B: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.45/5.72 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1
% 5.45/5.72 thf(fact_3928_mod__mult__self1,axiom,
% 5.45/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.45/5.72 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1
% 5.45/5.72 thf(fact_3929_mod__mult__self1,axiom,
% 5.45/5.72 ! [A: code_natural,C: code_natural,B: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ C @ B ) ) @ B )
% 5.45/5.72 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self1
% 5.45/5.72 thf(fact_3930_mod__mult__self2,axiom,
% 5.45/5.72 ! [A: nat,B: nat,C: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.45/5.72 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2
% 5.45/5.72 thf(fact_3931_mod__mult__self2,axiom,
% 5.45/5.72 ! [A: int,B: int,C: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.45/5.72 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2
% 5.45/5.72 thf(fact_3932_mod__mult__self2,axiom,
% 5.45/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.45/5.72 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2
% 5.45/5.72 thf(fact_3933_mod__mult__self2,axiom,
% 5.45/5.72 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ B @ C ) ) @ B )
% 5.45/5.72 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self2
% 5.45/5.72 thf(fact_3934_mod__mult__self3,axiom,
% 5.45/5.72 ! [C: nat,B: nat,A: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self3
% 5.45/5.72 thf(fact_3935_mod__mult__self3,axiom,
% 5.45/5.72 ! [C: int,B: int,A: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self3
% 5.45/5.72 thf(fact_3936_mod__mult__self3,axiom,
% 5.45/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self3
% 5.45/5.72 thf(fact_3937_mod__mult__self3,axiom,
% 5.45/5.72 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ C @ B ) @ A ) @ B )
% 5.45/5.72 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self3
% 5.45/5.72 thf(fact_3938_mod__mult__self4,axiom,
% 5.45/5.72 ! [B: nat,C: nat,A: nat] :
% 5.45/5.72 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self4
% 5.45/5.72 thf(fact_3939_mod__mult__self4,axiom,
% 5.45/5.72 ! [B: int,C: int,A: int] :
% 5.45/5.72 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self4
% 5.45/5.72 thf(fact_3940_mod__mult__self4,axiom,
% 5.45/5.72 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.72 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self4
% 5.45/5.72 thf(fact_3941_mod__mult__self4,axiom,
% 5.45/5.72 ! [B: code_natural,C: code_natural,A: code_natural] :
% 5.45/5.72 ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ C ) @ A ) @ B )
% 5.45/5.72 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % mod_mult_self4
% 5.45/5.72 thf(fact_3942_of__nat__less__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_less_iff
% 5.45/5.72 thf(fact_3943_of__nat__less__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_less_iff
% 5.45/5.72 thf(fact_3944_of__nat__less__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_less_iff
% 5.45/5.72 thf(fact_3945_of__nat__less__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_less_iff
% 5.45/5.72 thf(fact_3946_of__nat__le__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_iff
% 5.45/5.72 thf(fact_3947_of__nat__le__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_iff
% 5.45/5.72 thf(fact_3948_of__nat__le__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_iff
% 5.45/5.72 thf(fact_3949_of__nat__le__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.72 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_iff
% 5.45/5.72 thf(fact_3950_zero__less__Suc,axiom,
% 5.45/5.72 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_less_Suc
% 5.45/5.72 thf(fact_3951_less__Suc0,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.45/5.72 = ( N2 = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_Suc0
% 5.45/5.72 thf(fact_3952_of__nat__add,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_add
% 5.45/5.72 thf(fact_3953_of__nat__add,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_add
% 5.45/5.72 thf(fact_3954_of__nat__add,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_add
% 5.45/5.72 thf(fact_3955_of__nat__add,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri4939895301339042750nteger @ ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_add
% 5.45/5.72 thf(fact_3956_zero__less__diff,axiom,
% 5.45/5.72 ! [N2: nat,M: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.45/5.72 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % zero_less_diff
% 5.45/5.72 thf(fact_3957_mult__eq__1__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( times_times_nat @ M @ N2 )
% 5.45/5.72 = ( suc @ zero_zero_nat ) )
% 5.45/5.72 = ( ( M
% 5.45/5.72 = ( suc @ zero_zero_nat ) )
% 5.45/5.72 & ( N2
% 5.45/5.72 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_eq_1_iff
% 5.45/5.72 thf(fact_3958_one__eq__mult__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( suc @ zero_zero_nat )
% 5.45/5.72 = ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( ( M
% 5.45/5.72 = ( suc @ zero_zero_nat ) )
% 5.45/5.72 & ( N2
% 5.45/5.72 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_eq_mult_iff
% 5.45/5.72 thf(fact_3959_of__nat__mult,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_mult
% 5.45/5.72 thf(fact_3960_of__nat__mult,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_mult
% 5.45/5.72 thf(fact_3961_of__nat__mult,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_mult
% 5.45/5.72 thf(fact_3962_of__nat__mult,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( semiri4939895301339042750nteger @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_mult
% 5.45/5.72 thf(fact_3963_diff__is__0__eq_H,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.72 => ( ( minus_minus_nat @ M @ N2 )
% 5.45/5.72 = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_is_0_eq'
% 5.45/5.72 thf(fact_3964_diff__is__0__eq,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ( minus_minus_nat @ M @ N2 )
% 5.45/5.72 = zero_zero_nat )
% 5.45/5.72 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % diff_is_0_eq
% 5.45/5.72 thf(fact_3965_of__nat__eq__1__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ( semiri681578069525770553at_rat @ N2 )
% 5.45/5.72 = one_one_rat )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_1_iff
% 5.45/5.72 thf(fact_3966_of__nat__eq__1__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.45/5.72 = one_one_int )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_1_iff
% 5.45/5.72 thf(fact_3967_of__nat__eq__1__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.45/5.72 = one_one_nat )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_1_iff
% 5.45/5.72 thf(fact_3968_of__nat__eq__1__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ( semiri4939895301339042750nteger @ N2 )
% 5.45/5.72 = one_one_Code_integer )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_eq_1_iff
% 5.45/5.72 thf(fact_3969_of__nat__1__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( one_one_rat
% 5.45/5.72 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1_eq_iff
% 5.45/5.72 thf(fact_3970_of__nat__1__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( one_one_int
% 5.45/5.72 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1_eq_iff
% 5.45/5.72 thf(fact_3971_of__nat__1__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( one_one_nat
% 5.45/5.72 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1_eq_iff
% 5.45/5.72 thf(fact_3972_of__nat__1__eq__iff,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( one_one_Code_integer
% 5.45/5.72 = ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.72 = ( N2 = one_one_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1_eq_iff
% 5.45/5.72 thf(fact_3973_of__nat__1,axiom,
% 5.45/5.72 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.45/5.72 = one_one_rat ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1
% 5.45/5.72 thf(fact_3974_of__nat__1,axiom,
% 5.45/5.72 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.45/5.72 = one_one_int ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1
% 5.45/5.72 thf(fact_3975_of__nat__1,axiom,
% 5.45/5.72 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.45/5.72 = one_one_nat ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1
% 5.45/5.72 thf(fact_3976_of__nat__1,axiom,
% 5.45/5.72 ( ( semiri4939895301339042750nteger @ one_one_nat )
% 5.45/5.72 = one_one_Code_integer ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_1
% 5.45/5.72 thf(fact_3977_mult__Suc__right,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 5.45/5.72 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % mult_Suc_right
% 5.45/5.72 thf(fact_3978_Nat_Odiff__diff__right,axiom,
% 5.45/5.72 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.72 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.45/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % Nat.diff_diff_right
% 5.45/5.72 thf(fact_3979_Nat_Oadd__diff__assoc2,axiom,
% 5.45/5.72 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.72 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.45/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % Nat.add_diff_assoc2
% 5.45/5.72 thf(fact_3980_Nat_Oadd__diff__assoc,axiom,
% 5.45/5.72 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.72 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.45/5.72 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % Nat.add_diff_assoc
% 5.45/5.72 thf(fact_3981_diff__Suc__1,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.45/5.72 = N2 ) ).
% 5.45/5.72
% 5.45/5.72 % diff_Suc_1
% 5.45/5.72 thf(fact_3982_divide__le__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [B: rat,W2: num,A: rat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.45/5.72 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_le_eq_numeral1(1)
% 5.45/5.72 thf(fact_3983_le__divide__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [A: rat,B: rat,W2: num] :
% 5.45/5.72 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % le_divide_eq_numeral1(1)
% 5.45/5.72 thf(fact_3984_divide__eq__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [B: rat,W2: num,A: rat] :
% 5.45/5.72 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.72 = A )
% 5.45/5.72 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.45/5.72 != zero_zero_rat )
% 5.45/5.72 => ( B
% 5.45/5.72 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.45/5.72 & ( ( ( numeral_numeral_rat @ W2 )
% 5.45/5.72 = zero_zero_rat )
% 5.45/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_eq_eq_numeral1(1)
% 5.45/5.72 thf(fact_3985_eq__divide__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [A: rat,B: rat,W2: num] :
% 5.45/5.72 ( ( A
% 5.45/5.72 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.72 = ( ( ( ( numeral_numeral_rat @ W2 )
% 5.45/5.72 != zero_zero_rat )
% 5.45/5.72 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.72 = B ) )
% 5.45/5.72 & ( ( ( numeral_numeral_rat @ W2 )
% 5.45/5.72 = zero_zero_rat )
% 5.45/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % eq_divide_eq_numeral1(1)
% 5.45/5.72 thf(fact_3986_divide__less__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [B: rat,W2: num,A: rat] :
% 5.45/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) @ A )
% 5.45/5.72 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % divide_less_eq_numeral1(1)
% 5.45/5.72 thf(fact_3987_less__divide__eq__numeral1_I1_J,axiom,
% 5.45/5.72 ! [A: rat,B: rat,W2: num] :
% 5.45/5.72 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W2 ) ) @ B ) ) ).
% 5.45/5.72
% 5.45/5.72 % less_divide_eq_numeral1(1)
% 5.45/5.72 thf(fact_3988_of__nat__le__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_0_iff
% 5.45/5.72 thf(fact_3989_of__nat__le__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_0_iff
% 5.45/5.72 thf(fact_3990_of__nat__le__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_0_iff
% 5.45/5.72 thf(fact_3991_of__nat__le__0__iff,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.45/5.72 = ( M = zero_zero_nat ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_le_0_iff
% 5.45/5.72 thf(fact_3992_of__nat__Suc,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.45/5.72 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_Suc
% 5.45/5.72 thf(fact_3993_of__nat__Suc,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.45/5.72 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_Suc
% 5.45/5.72 thf(fact_3994_of__nat__Suc,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.45/5.72 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_Suc
% 5.45/5.72 thf(fact_3995_of__nat__Suc,axiom,
% 5.45/5.72 ! [M: nat] :
% 5.45/5.72 ( ( semiri4939895301339042750nteger @ ( suc @ M ) )
% 5.45/5.72 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( semiri4939895301339042750nteger @ M ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % of_nat_Suc
% 5.45/5.72 thf(fact_3996_Suc__pred,axiom,
% 5.45/5.72 ! [N2: nat] :
% 5.45/5.72 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.72 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.45/5.72 = N2 ) ) ).
% 5.45/5.72
% 5.45/5.72 % Suc_pred
% 5.45/5.72 thf(fact_3997_one__le__mult__iff,axiom,
% 5.45/5.72 ! [M: nat,N2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 5.45/5.72 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.45/5.72 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 5.45/5.72
% 5.45/5.72 % one_le_mult_iff
% 5.45/5.72 thf(fact_3998_diff__Suc__diff__eq1,axiom,
% 5.45/5.72 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.72 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.73 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.45/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_Suc_diff_eq1
% 5.45/5.73 thf(fact_3999_diff__Suc__diff__eq2,axiom,
% 5.45/5.73 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.73 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.45/5.73 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_Suc_diff_eq2
% 5.45/5.73 thf(fact_4000_Suc__diff,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.45/5.73 => ( ( suc @ ( minus_minus_nat @ N2 @ M ) )
% 5.45/5.73 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_diff
% 5.45/5.73 thf(fact_4001_of__nat__0__less__iff,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_less_iff
% 5.45/5.73 thf(fact_4002_of__nat__0__less__iff,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_less_iff
% 5.45/5.73 thf(fact_4003_of__nat__0__less__iff,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_less_iff
% 5.45/5.73 thf(fact_4004_of__nat__0__less__iff,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_less_iff
% 5.45/5.73 thf(fact_4005_Suc__diff__1,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.45/5.73 = N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_diff_1
% 5.45/5.73 thf(fact_4006_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4007_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4008_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4009_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4010_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4011_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4012_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4013_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4014_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4015_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4016_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4017_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,B: nat,W2: nat] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4018_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( semiri4939895301339042750nteger @ B ) @ W2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4019_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4020_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4021_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.45/5.73 ! [B: nat,W2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_of_nat_power_cancel_iff
% 5.45/5.73 thf(fact_4022_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4023_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_le5570908160329646204atural @ ( semiri3763490453095760265atural @ X ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4024_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4025_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4026_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4027_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4028_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le5570908160329646204atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) @ ( semiri3763490453095760265atural @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4029_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4030_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4031_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.45/5.73 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_less_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4032_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_le1926595141338095240atural @ ( semiri3763490453095760265atural @ X ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4033_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ X ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4034_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4035_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4036_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.73 ! [X: nat,I2: num,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_le_numeral_power_cancel_iff
% 5.45/5.73 thf(fact_4037_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le1926595141338095240atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ I2 ) @ N2 ) @ ( semiri3763490453095760265atural @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4038_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ I2 ) @ N2 ) @ ( semiri4939895301339042750nteger @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4039_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4040_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4041_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.45/5.73 ! [I2: num,N2: nat,X: nat] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X ) ) ).
% 5.45/5.73
% 5.45/5.73 % numeral_power_le_of_nat_cancel_iff
% 5.45/5.73 thf(fact_4042_mod__induct,axiom,
% 5.45/5.73 ! [P: nat > $o,N2: nat,P3: nat,M: nat] :
% 5.45/5.73 ( ( P @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ P3 )
% 5.45/5.73 => ( ( ord_less_nat @ M @ P3 )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( ord_less_nat @ N5 @ P3 )
% 5.45/5.73 => ( ( P @ N5 )
% 5.45/5.73 => ( P @ ( modulo_modulo_nat @ ( suc @ N5 ) @ P3 ) ) ) )
% 5.45/5.73 => ( P @ M ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_induct
% 5.45/5.73 thf(fact_4043_mod__if,axiom,
% 5.45/5.73 ( modulo_modulo_nat
% 5.45/5.73 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_if
% 5.45/5.73 thf(fact_4044_mod__Suc__le__divisor,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 5.45/5.73
% 5.45/5.73 % mod_Suc_le_divisor
% 5.45/5.73 thf(fact_4045_le__mod__geq,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.45/5.73 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_mod_geq
% 5.45/5.73 thf(fact_4046_Suc__diff__Suc,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ N2 @ M )
% 5.45/5.73 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.73 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_diff_Suc
% 5.45/5.73 thf(fact_4047_diff__less__Suc,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less_Suc
% 5.45/5.73 thf(fact_4048_Suc__diff__le,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_diff_le
% 5.45/5.73 thf(fact_4049_zero__induct__lemma,axiom,
% 5.45/5.73 ! [P: nat > $o,K: nat,I2: nat] :
% 5.45/5.73 ( ( P @ K )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( P @ ( suc @ N5 ) )
% 5.45/5.73 => ( P @ N5 ) )
% 5.45/5.73 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_induct_lemma
% 5.45/5.73 thf(fact_4050_diff__commute,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.45/5.73 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_commute
% 5.45/5.73 thf(fact_4051_n__not__Suc__n,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 != ( suc @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % n_not_Suc_n
% 5.45/5.73 thf(fact_4052_Suc__inject,axiom,
% 5.45/5.73 ! [X: nat,Y: nat] :
% 5.45/5.73 ( ( ( suc @ X )
% 5.45/5.73 = ( suc @ Y ) )
% 5.45/5.73 => ( X = Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_inject
% 5.45/5.73 thf(fact_4053_of__nat__diff,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_diff
% 5.45/5.73 thf(fact_4054_of__nat__diff,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_diff
% 5.45/5.73 thf(fact_4055_of__nat__diff,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_diff
% 5.45/5.73 thf(fact_4056_of__nat__diff,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( semiri4939895301339042750nteger @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_diff
% 5.45/5.73 thf(fact_4057_mod__geq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ~ ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.45/5.73 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_geq
% 5.45/5.73 thf(fact_4058_Suc__to__right,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ( suc @ N2 )
% 5.45/5.73 = M )
% 5.45/5.73 => ( N2
% 5.45/5.73 = ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_to_right
% 5.45/5.73 thf(fact_4059_diff__Suc__eq__diff__pred,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_Suc_eq_diff_pred
% 5.45/5.73 thf(fact_4060_of__nat__neq__0,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 5.45/5.73 != zero_zero_rat ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_neq_0
% 5.45/5.73 thf(fact_4061_of__nat__neq__0,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.45/5.73 != zero_zero_int ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_neq_0
% 5.45/5.73 thf(fact_4062_of__nat__neq__0,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.45/5.73 != zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_neq_0
% 5.45/5.73 thf(fact_4063_of__nat__neq__0,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( semiri4939895301339042750nteger @ ( suc @ N2 ) )
% 5.45/5.73 != zero_z3403309356797280102nteger ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_neq_0
% 5.45/5.73 thf(fact_4064_minus__div__mult__eq__mod,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.45/5.73 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_div_mult_eq_mod
% 5.45/5.73 thf(fact_4065_minus__div__mult__eq__mod,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.45/5.73 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_div_mult_eq_mod
% 5.45/5.73 thf(fact_4066_minus__div__mult__eq__mod,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.45/5.73 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_div_mult_eq_mod
% 5.45/5.73 thf(fact_4067_minus__div__mult__eq__mod,axiom,
% 5.45/5.73 ! [A: code_natural,B: code_natural] :
% 5.45/5.73 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.45/5.73 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_div_mult_eq_mod
% 5.45/5.73 thf(fact_4068_minus__mod__eq__div__mult,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.45/5.73 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_div_mult
% 5.45/5.73 thf(fact_4069_minus__mod__eq__div__mult,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.73 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_div_mult
% 5.45/5.73 thf(fact_4070_minus__mod__eq__div__mult,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_div_mult
% 5.45/5.73 thf(fact_4071_minus__mod__eq__div__mult,axiom,
% 5.45/5.73 ! [A: code_natural,B: code_natural] :
% 5.45/5.73 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.45/5.73 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_div_mult
% 5.45/5.73 thf(fact_4072_minus__mod__eq__mult__div,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.45/5.73 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_mult_div
% 5.45/5.73 thf(fact_4073_minus__mod__eq__mult__div,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.73 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_mult_div
% 5.45/5.73 thf(fact_4074_minus__mod__eq__mult__div,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_mult_div
% 5.45/5.73 thf(fact_4075_minus__mod__eq__mult__div,axiom,
% 5.45/5.73 ! [A: code_natural,B: code_natural] :
% 5.45/5.73 ( ( minus_7197305767214868737atural @ A @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.45/5.73 = ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mod_eq_mult_div
% 5.45/5.73 thf(fact_4076_minus__mult__div__eq__mod,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.45/5.73 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mult_div_eq_mod
% 5.45/5.73 thf(fact_4077_minus__mult__div__eq__mod,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.45/5.73 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mult_div_eq_mod
% 5.45/5.73 thf(fact_4078_minus__mult__div__eq__mod,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.45/5.73 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mult_div_eq_mod
% 5.45/5.73 thf(fact_4079_minus__mult__div__eq__mod,axiom,
% 5.45/5.73 ! [A: code_natural,B: code_natural] :
% 5.45/5.73 ( ( minus_7197305767214868737atural @ A @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.45/5.73 = ( modulo8411746178871703098atural @ A @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % minus_mult_div_eq_mod
% 5.45/5.73 thf(fact_4080_int__power__div__base,axiom,
% 5.45/5.73 ! [M: nat,K: int] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.73 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.73 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.45/5.73 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % int_power_div_base
% 5.45/5.73 thf(fact_4081_diff__Suc__less,axiom,
% 5.45/5.73 ! [N2: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_Suc_less
% 5.45/5.73 thf(fact_4082_mod__mult__eq,axiom,
% 5.45/5.73 ! [A: nat,C: nat,B: nat] :
% 5.45/5.73 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_eq
% 5.45/5.73 thf(fact_4083_mod__mult__eq,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_eq
% 5.45/5.73 thf(fact_4084_mod__mult__eq,axiom,
% 5.45/5.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.73 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_eq
% 5.45/5.73 thf(fact_4085_mod__mult__eq,axiom,
% 5.45/5.73 ! [A: code_natural,C: code_natural,B: code_natural] :
% 5.45/5.73 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_eq
% 5.45/5.73 thf(fact_4086_mod__mult__cong,axiom,
% 5.45/5.73 ! [A: nat,C: nat,A2: nat,B: nat,B2: nat] :
% 5.45/5.73 ( ( ( modulo_modulo_nat @ A @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ A2 @ C ) )
% 5.45/5.73 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ B2 @ C ) )
% 5.45/5.73 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ ( times_times_nat @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_cong
% 5.45/5.73 thf(fact_4087_mod__mult__cong,axiom,
% 5.45/5.73 ! [A: int,C: int,A2: int,B: int,B2: int] :
% 5.45/5.73 ( ( ( modulo_modulo_int @ A @ C )
% 5.45/5.73 = ( modulo_modulo_int @ A2 @ C ) )
% 5.45/5.73 => ( ( ( modulo_modulo_int @ B @ C )
% 5.45/5.73 = ( modulo_modulo_int @ B2 @ C ) )
% 5.45/5.73 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.73 = ( modulo_modulo_int @ ( times_times_int @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_cong
% 5.45/5.73 thf(fact_4088_mod__mult__cong,axiom,
% 5.45/5.73 ! [A: code_integer,C: code_integer,A2: code_integer,B: code_integer,B2: code_integer] :
% 5.45/5.73 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ A2 @ C ) )
% 5.45/5.73 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ B2 @ C ) )
% 5.45/5.73 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_cong
% 5.45/5.73 thf(fact_4089_mod__mult__cong,axiom,
% 5.45/5.73 ! [A: code_natural,C: code_natural,A2: code_natural,B: code_natural,B2: code_natural] :
% 5.45/5.73 ( ( ( modulo8411746178871703098atural @ A @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ A2 @ C ) )
% 5.45/5.73 => ( ( ( modulo8411746178871703098atural @ B @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ B2 @ C ) )
% 5.45/5.73 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A2 @ B2 ) @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_cong
% 5.45/5.73 thf(fact_4090_mod__mult__mult2,axiom,
% 5.45/5.73 ! [A: nat,C: nat,B: nat] :
% 5.45/5.73 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.45/5.73 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_mult2
% 5.45/5.73 thf(fact_4091_mod__mult__mult2,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.73 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_mult2
% 5.45/5.73 thf(fact_4092_mod__mult__mult2,axiom,
% 5.45/5.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.73 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_mult2
% 5.45/5.73 thf(fact_4093_mod__mult__mult2,axiom,
% 5.45/5.73 ! [A: code_natural,C: code_natural,B: code_natural] :
% 5.45/5.73 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ C ) )
% 5.45/5.73 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_mult2
% 5.45/5.73 thf(fact_4094_mult__mod__right,axiom,
% 5.45/5.73 ! [C: nat,A: nat,B: nat] :
% 5.45/5.73 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.45/5.73 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_mod_right
% 5.45/5.73 thf(fact_4095_mult__mod__right,axiom,
% 5.45/5.73 ! [C: int,A: int,B: int] :
% 5.45/5.73 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.73 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_mod_right
% 5.45/5.73 thf(fact_4096_mult__mod__right,axiom,
% 5.45/5.73 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.45/5.73 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_mod_right
% 5.45/5.73 thf(fact_4097_mult__mod__right,axiom,
% 5.45/5.73 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.45/5.73 ( ( times_2397367101498566445atural @ C @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.45/5.73 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ C @ A ) @ ( times_2397367101498566445atural @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_mod_right
% 5.45/5.73 thf(fact_4098_mod__mult__left__eq,axiom,
% 5.45/5.73 ! [A: nat,C: nat,B: nat] :
% 5.45/5.73 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_left_eq
% 5.45/5.73 thf(fact_4099_mod__mult__left__eq,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.45/5.73 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_left_eq
% 5.45/5.73 thf(fact_4100_mod__mult__left__eq,axiom,
% 5.45/5.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.73 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_left_eq
% 5.45/5.73 thf(fact_4101_mod__mult__left__eq,axiom,
% 5.45/5.73 ! [A: code_natural,C: code_natural,B: code_natural] :
% 5.45/5.73 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ C ) @ B ) @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_left_eq
% 5.45/5.73 thf(fact_4102_mod__mult__right__eq,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_right_eq
% 5.45/5.73 thf(fact_4103_mod__mult__right__eq,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_right_eq
% 5.45/5.73 thf(fact_4104_mod__mult__right__eq,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_right_eq
% 5.45/5.73 thf(fact_4105_mod__mult__right__eq,axiom,
% 5.45/5.73 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.45/5.73 ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C )
% 5.45/5.73 = ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult_right_eq
% 5.45/5.73 thf(fact_4106_diff__mono,axiom,
% 5.45/5.73 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.73 => ( ( ord_less_eq_rat @ D2 @ C )
% 5.45/5.73 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_mono
% 5.45/5.73 thf(fact_4107_diff__mono,axiom,
% 5.45/5.73 ! [A: int,B: int,D2: int,C: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.73 => ( ( ord_less_eq_int @ D2 @ C )
% 5.45/5.73 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_mono
% 5.45/5.73 thf(fact_4108_diff__left__mono,axiom,
% 5.45/5.73 ! [B: rat,A: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.73 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_left_mono
% 5.45/5.73 thf(fact_4109_diff__left__mono,axiom,
% 5.45/5.73 ! [B: int,A: int,C: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.73 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_left_mono
% 5.45/5.73 thf(fact_4110_diff__right__mono,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.73 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_right_mono
% 5.45/5.73 thf(fact_4111_diff__right__mono,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.73 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_right_mono
% 5.45/5.73 thf(fact_4112_diff__eq__diff__less__eq,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.73 ( ( ( minus_minus_rat @ A @ B )
% 5.45/5.73 = ( minus_minus_rat @ C @ D2 ) )
% 5.45/5.73 => ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.73 = ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_eq_diff_less_eq
% 5.45/5.73 thf(fact_4113_diff__eq__diff__less__eq,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.73 ( ( ( minus_minus_int @ A @ B )
% 5.45/5.73 = ( minus_minus_int @ C @ D2 ) )
% 5.45/5.73 => ( ( ord_less_eq_int @ A @ B )
% 5.45/5.73 = ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_eq_diff_less_eq
% 5.45/5.73 thf(fact_4114_mult__of__nat__commute,axiom,
% 5.45/5.73 ! [X: nat,Y: rat] :
% 5.45/5.73 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.45/5.73 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_of_nat_commute
% 5.45/5.73 thf(fact_4115_mult__of__nat__commute,axiom,
% 5.45/5.73 ! [X: nat,Y: int] :
% 5.45/5.73 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.45/5.73 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_of_nat_commute
% 5.45/5.73 thf(fact_4116_mult__of__nat__commute,axiom,
% 5.45/5.73 ! [X: nat,Y: nat] :
% 5.45/5.73 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.45/5.73 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_of_nat_commute
% 5.45/5.73 thf(fact_4117_mult__of__nat__commute,axiom,
% 5.45/5.73 ! [X: nat,Y: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ X ) @ Y )
% 5.45/5.73 = ( times_3573771949741848930nteger @ Y @ ( semiri4939895301339042750nteger @ X ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_of_nat_commute
% 5.45/5.73 thf(fact_4118_diff__strict__mono,axiom,
% 5.45/5.73 ! [A: rat,B: rat,D2: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_rat @ A @ B )
% 5.45/5.73 => ( ( ord_less_rat @ D2 @ C )
% 5.45/5.73 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_mono
% 5.45/5.73 thf(fact_4119_diff__strict__mono,axiom,
% 5.45/5.73 ! [A: int,B: int,D2: int,C: int] :
% 5.45/5.73 ( ( ord_less_int @ A @ B )
% 5.45/5.73 => ( ( ord_less_int @ D2 @ C )
% 5.45/5.73 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_mono
% 5.45/5.73 thf(fact_4120_diff__eq__diff__less,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.73 ( ( ( minus_minus_rat @ A @ B )
% 5.45/5.73 = ( minus_minus_rat @ C @ D2 ) )
% 5.45/5.73 => ( ( ord_less_rat @ A @ B )
% 5.45/5.73 = ( ord_less_rat @ C @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_eq_diff_less
% 5.45/5.73 thf(fact_4121_diff__eq__diff__less,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.73 ( ( ( minus_minus_int @ A @ B )
% 5.45/5.73 = ( minus_minus_int @ C @ D2 ) )
% 5.45/5.73 => ( ( ord_less_int @ A @ B )
% 5.45/5.73 = ( ord_less_int @ C @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_eq_diff_less
% 5.45/5.73 thf(fact_4122_diff__strict__left__mono,axiom,
% 5.45/5.73 ! [B: rat,A: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_rat @ B @ A )
% 5.45/5.73 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_left_mono
% 5.45/5.73 thf(fact_4123_diff__strict__left__mono,axiom,
% 5.45/5.73 ! [B: int,A: int,C: int] :
% 5.45/5.73 ( ( ord_less_int @ B @ A )
% 5.45/5.73 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_left_mono
% 5.45/5.73 thf(fact_4124_diff__strict__right__mono,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_rat @ A @ B )
% 5.45/5.73 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_right_mono
% 5.45/5.73 thf(fact_4125_diff__strict__right__mono,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( ord_less_int @ A @ B )
% 5.45/5.73 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_strict_right_mono
% 5.45/5.73 thf(fact_4126_right__diff__distrib_H,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib'
% 5.45/5.73 thf(fact_4127_right__diff__distrib_H,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib'
% 5.45/5.73 thf(fact_4128_right__diff__distrib_H,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib'
% 5.45/5.73 thf(fact_4129_right__diff__distrib_H,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib'
% 5.45/5.73 thf(fact_4130_left__diff__distrib_H,axiom,
% 5.45/5.73 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ C ) @ A )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib'
% 5.45/5.73 thf(fact_4131_left__diff__distrib_H,axiom,
% 5.45/5.73 ! [B: rat,C: rat,A: rat] :
% 5.45/5.73 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib'
% 5.45/5.73 thf(fact_4132_left__diff__distrib_H,axiom,
% 5.45/5.73 ! [B: nat,C: nat,A: nat] :
% 5.45/5.73 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.45/5.73 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib'
% 5.45/5.73 thf(fact_4133_left__diff__distrib_H,axiom,
% 5.45/5.73 ! [B: int,C: int,A: int] :
% 5.45/5.73 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib'
% 5.45/5.73 thf(fact_4134_right__diff__distrib,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib
% 5.45/5.73 thf(fact_4135_right__diff__distrib,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib
% 5.45/5.73 thf(fact_4136_right__diff__distrib,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib
% 5.45/5.73 thf(fact_4137_left__diff__distrib,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib
% 5.45/5.73 thf(fact_4138_left__diff__distrib,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib
% 5.45/5.73 thf(fact_4139_left__diff__distrib,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib
% 5.45/5.73 thf(fact_4140_inf__period_I1_J,axiom,
% 5.45/5.73 ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 5.45/5.73 ( ! [X3: code_integer,K2: code_integer] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: code_integer,K2: code_integer] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: code_integer,K4: code_integer] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 & ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 5.45/5.73 & ( Q @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(1)
% 5.45/5.73 thf(fact_4141_inf__period_I1_J,axiom,
% 5.45/5.73 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.45/5.73 ( ! [X3: rat,K2: rat] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: rat,K2: rat] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: rat,K4: rat] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 & ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.45/5.73 & ( Q @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(1)
% 5.45/5.73 thf(fact_4142_inf__period_I1_J,axiom,
% 5.45/5.73 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.45/5.73 ( ! [X3: int,K2: int] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: int,K2: int] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: int,K4: int] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 & ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.45/5.73 & ( Q @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(1)
% 5.45/5.73 thf(fact_4143_inf__period_I2_J,axiom,
% 5.45/5.73 ! [P: code_integer > $o,D3: code_integer,Q: code_integer > $o] :
% 5.45/5.73 ( ! [X3: code_integer,K2: code_integer] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: code_integer,K2: code_integer] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_8373710615458151222nteger @ X3 @ ( times_3573771949741848930nteger @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: code_integer,K4: code_integer] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 | ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) )
% 5.45/5.73 | ( Q @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(2)
% 5.45/5.73 thf(fact_4144_inf__period_I2_J,axiom,
% 5.45/5.73 ! [P: rat > $o,D3: rat,Q: rat > $o] :
% 5.45/5.73 ( ! [X3: rat,K2: rat] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: rat,K2: rat] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_minus_rat @ X3 @ ( times_times_rat @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: rat,K4: rat] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 | ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) )
% 5.45/5.73 | ( Q @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(2)
% 5.45/5.73 thf(fact_4145_inf__period_I2_J,axiom,
% 5.45/5.73 ! [P: int > $o,D3: int,Q: int > $o] :
% 5.45/5.73 ( ! [X3: int,K2: int] :
% 5.45/5.73 ( ( P @ X3 )
% 5.45/5.73 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ( ! [X3: int,K2: int] :
% 5.45/5.73 ( ( Q @ X3 )
% 5.45/5.73 = ( Q @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.73 => ! [X7: int,K4: int] :
% 5.45/5.73 ( ( ( P @ X7 )
% 5.45/5.73 | ( Q @ X7 ) )
% 5.45/5.73 = ( ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) )
% 5.45/5.73 | ( Q @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inf_period(2)
% 5.45/5.73 thf(fact_4146_mod__less__eq__dividend,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 5.45/5.73
% 5.45/5.73 % mod_less_eq_dividend
% 5.45/5.73 thf(fact_4147_nat__int__comparison_I2_J,axiom,
% 5.45/5.73 ( ord_less_nat
% 5.45/5.73 = ( ^ [A5: nat,B5: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_int_comparison(2)
% 5.45/5.73 thf(fact_4148_nat__int__comparison_I3_J,axiom,
% 5.45/5.73 ( ord_less_eq_nat
% 5.45/5.73 = ( ^ [A5: nat,B5: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_int_comparison(3)
% 5.45/5.73 thf(fact_4149_diffs0__imp__equal,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ( minus_minus_nat @ M @ N2 )
% 5.45/5.73 = zero_zero_nat )
% 5.45/5.73 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.45/5.73 = zero_zero_nat )
% 5.45/5.73 => ( M = N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diffs0_imp_equal
% 5.45/5.73 thf(fact_4150_minus__nat_Odiff__0,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.45/5.73 = M ) ).
% 5.45/5.73
% 5.45/5.73 % minus_nat.diff_0
% 5.45/5.73 thf(fact_4151_diff__less__mono2,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,L: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ M @ L )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less_mono2
% 5.45/5.73 thf(fact_4152_less__imp__diff__less,axiom,
% 5.45/5.73 ! [J: nat,K: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ J @ K )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_diff_less
% 5.45/5.73 thf(fact_4153_not0__implies__Suc,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( N2 != zero_zero_nat )
% 5.45/5.73 => ? [M5: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 = ( suc @ M5 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % not0_implies_Suc
% 5.45/5.73 thf(fact_4154_Zero__not__Suc,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ( zero_zero_nat
% 5.45/5.73 != ( suc @ M ) ) ).
% 5.45/5.73
% 5.45/5.73 % Zero_not_Suc
% 5.45/5.73 thf(fact_4155_Zero__neq__Suc,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ( zero_zero_nat
% 5.45/5.73 != ( suc @ M ) ) ).
% 5.45/5.73
% 5.45/5.73 % Zero_neq_Suc
% 5.45/5.73 thf(fact_4156_Suc__neq__Zero,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ( ( suc @ M )
% 5.45/5.73 != zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_neq_Zero
% 5.45/5.73 thf(fact_4157_zero__induct,axiom,
% 5.45/5.73 ! [P: nat > $o,K: nat] :
% 5.45/5.73 ( ( P @ K )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( P @ ( suc @ N5 ) )
% 5.45/5.73 => ( P @ N5 ) )
% 5.45/5.73 => ( P @ zero_zero_nat ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_induct
% 5.45/5.73 thf(fact_4158_diff__induct,axiom,
% 5.45/5.73 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.45/5.73 ( ! [X3: nat] : ( P @ X3 @ zero_zero_nat )
% 5.45/5.73 => ( ! [Y3: nat] : ( P @ zero_zero_nat @ ( suc @ Y3 ) )
% 5.45/5.73 => ( ! [X3: nat,Y3: nat] :
% 5.45/5.73 ( ( P @ X3 @ Y3 )
% 5.45/5.73 => ( P @ ( suc @ X3 ) @ ( suc @ Y3 ) ) )
% 5.45/5.73 => ( P @ M @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_induct
% 5.45/5.73 thf(fact_4159_nat__induct,axiom,
% 5.45/5.73 ! [P: nat > $o,N2: nat] :
% 5.45/5.73 ( ( P @ zero_zero_nat )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( P @ N5 )
% 5.45/5.73 => ( P @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( P @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_induct
% 5.45/5.73 thf(fact_4160_old_Onat_Oexhaust,axiom,
% 5.45/5.73 ! [Y: nat] :
% 5.45/5.73 ( ( Y != zero_zero_nat )
% 5.45/5.73 => ~ ! [Nat3: nat] :
% 5.45/5.73 ( Y
% 5.45/5.73 != ( suc @ Nat3 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % old.nat.exhaust
% 5.45/5.73 thf(fact_4161_nat_OdiscI,axiom,
% 5.45/5.73 ! [Nat: nat,X2: nat] :
% 5.45/5.73 ( ( Nat
% 5.45/5.73 = ( suc @ X2 ) )
% 5.45/5.73 => ( Nat != zero_zero_nat ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat.discI
% 5.45/5.73 thf(fact_4162_old_Onat_Odistinct_I1_J,axiom,
% 5.45/5.73 ! [Nat2: nat] :
% 5.45/5.73 ( zero_zero_nat
% 5.45/5.73 != ( suc @ Nat2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % old.nat.distinct(1)
% 5.45/5.73 thf(fact_4163_old_Onat_Odistinct_I2_J,axiom,
% 5.45/5.73 ! [Nat2: nat] :
% 5.45/5.73 ( ( suc @ Nat2 )
% 5.45/5.73 != zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % old.nat.distinct(2)
% 5.45/5.73 thf(fact_4164_nat_Odistinct_I1_J,axiom,
% 5.45/5.73 ! [X2: nat] :
% 5.45/5.73 ( zero_zero_nat
% 5.45/5.73 != ( suc @ X2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat.distinct(1)
% 5.45/5.73 thf(fact_4165_Nat_OlessE,axiom,
% 5.45/5.73 ! [I2: nat,K: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ K )
% 5.45/5.73 => ( ( K
% 5.45/5.73 != ( suc @ I2 ) )
% 5.45/5.73 => ~ ! [J2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ J2 )
% 5.45/5.73 => ( K
% 5.45/5.73 != ( suc @ J2 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.lessE
% 5.45/5.73 thf(fact_4166_Suc__lessD,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_lessD
% 5.45/5.73 thf(fact_4167_Suc__lessE,axiom,
% 5.45/5.73 ! [I2: nat,K: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.45/5.73 => ~ ! [J2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ J2 )
% 5.45/5.73 => ( K
% 5.45/5.73 != ( suc @ J2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_lessE
% 5.45/5.73 thf(fact_4168_Suc__lessI,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ( ( suc @ M )
% 5.45/5.73 != N2 )
% 5.45/5.73 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_lessI
% 5.45/5.73 thf(fact_4169_less__SucE,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( M = N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_SucE
% 5.45/5.73 thf(fact_4170_less__SucI,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_SucI
% 5.45/5.73 thf(fact_4171_Ex__less__Suc,axiom,
% 5.45/5.73 ! [N2: nat,P: nat > $o] :
% 5.45/5.73 ( ( ? [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N2 ) )
% 5.45/5.73 & ( P @ I4 ) ) )
% 5.45/5.73 = ( ( P @ N2 )
% 5.45/5.73 | ? [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ N2 )
% 5.45/5.73 & ( P @ I4 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Ex_less_Suc
% 5.45/5.73 thf(fact_4172_less__Suc__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 = ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 | ( M = N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_Suc_eq
% 5.45/5.73 thf(fact_4173_not__less__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % not_less_eq
% 5.45/5.73 thf(fact_4174_All__less__Suc,axiom,
% 5.45/5.73 ! [N2: nat,P: nat > $o] :
% 5.45/5.73 ( ( ! [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N2 ) )
% 5.45/5.73 => ( P @ I4 ) ) )
% 5.45/5.73 = ( ( P @ N2 )
% 5.45/5.73 & ! [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ N2 )
% 5.45/5.73 => ( P @ I4 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % All_less_Suc
% 5.45/5.73 thf(fact_4175_Suc__less__eq2,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.73 = ( ? [M7: nat] :
% 5.45/5.73 ( ( M
% 5.45/5.73 = ( suc @ M7 ) )
% 5.45/5.73 & ( ord_less_nat @ N2 @ M7 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_less_eq2
% 5.45/5.73 thf(fact_4176_less__antisym,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.45/5.73 => ( M = N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_antisym
% 5.45/5.73 thf(fact_4177_Suc__less__SucD,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_less_SucD
% 5.45/5.73 thf(fact_4178_less__trans__Suc,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.73 => ( ( ord_less_nat @ J @ K )
% 5.45/5.73 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_trans_Suc
% 5.45/5.73 thf(fact_4179_less__Suc__induct,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.73 => ( ! [I3: nat] : ( P @ I3 @ ( suc @ I3 ) )
% 5.45/5.73 => ( ! [I3: nat,J2: nat,K2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I3 @ J2 )
% 5.45/5.73 => ( ( ord_less_nat @ J2 @ K2 )
% 5.45/5.73 => ( ( P @ I3 @ J2 )
% 5.45/5.73 => ( ( P @ J2 @ K2 )
% 5.45/5.73 => ( P @ I3 @ K2 ) ) ) ) )
% 5.45/5.73 => ( P @ I2 @ J ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_Suc_induct
% 5.45/5.73 thf(fact_4180_strict__inc__induct,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,P: nat > $o] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ J )
% 5.45/5.73 => ( ! [I3: nat] :
% 5.45/5.73 ( ( J
% 5.45/5.73 = ( suc @ I3 ) )
% 5.45/5.73 => ( P @ I3 ) )
% 5.45/5.73 => ( ! [I3: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I3 @ J )
% 5.45/5.73 => ( ( P @ ( suc @ I3 ) )
% 5.45/5.73 => ( P @ I3 ) ) )
% 5.45/5.73 => ( P @ I2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % strict_inc_induct
% 5.45/5.73 thf(fact_4181_not__less__less__Suc__eq,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.45/5.73 = ( N2 = M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % not_less_less_Suc_eq
% 5.45/5.73 thf(fact_4182_eq__diff__iff,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.73 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.73 => ( ( ( minus_minus_nat @ M @ K )
% 5.45/5.73 = ( minus_minus_nat @ N2 @ K ) )
% 5.45/5.73 = ( M = N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_diff_iff
% 5.45/5.73 thf(fact_4183_le__diff__iff,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.73 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.45/5.73 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_diff_iff
% 5.45/5.73 thf(fact_4184_Nat_Odiff__diff__eq,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.73 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.73 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.45/5.73 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.diff_diff_eq
% 5.45/5.73 thf(fact_4185_diff__le__mono,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,L: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_le_mono
% 5.45/5.73 thf(fact_4186_diff__le__self,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.45/5.73
% 5.45/5.73 % diff_le_self
% 5.45/5.73 thf(fact_4187_le__diff__iff_H,axiom,
% 5.45/5.73 ! [A: nat,C: nat,B: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ C )
% 5.45/5.73 => ( ( ord_less_eq_nat @ B @ C )
% 5.45/5.73 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.45/5.73 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_diff_iff'
% 5.45/5.73 thf(fact_4188_diff__le__mono2,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,L: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_le_mono2
% 5.45/5.73 thf(fact_4189_diff__add__inverse2,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.45/5.73 = M ) ).
% 5.45/5.73
% 5.45/5.73 % diff_add_inverse2
% 5.45/5.73 thf(fact_4190_diff__add__inverse,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.45/5.73 = M ) ).
% 5.45/5.73
% 5.45/5.73 % diff_add_inverse
% 5.45/5.73 thf(fact_4191_diff__cancel2,axiom,
% 5.45/5.73 ! [M: nat,K: nat,N2: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.45/5.73 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_cancel2
% 5.45/5.73 thf(fact_4192_Nat_Odiff__cancel,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.45/5.73 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.diff_cancel
% 5.45/5.73 thf(fact_4193_Suc__leD,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_leD
% 5.45/5.73 thf(fact_4194_le__SucE,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( M
% 5.45/5.73 = ( suc @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_SucE
% 5.45/5.73 thf(fact_4195_le__SucI,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_SucI
% 5.45/5.73 thf(fact_4196_Suc__le__D,axiom,
% 5.45/5.73 ! [N2: nat,M8: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M8 )
% 5.45/5.73 => ? [M5: nat] :
% 5.45/5.73 ( M8
% 5.45/5.73 = ( suc @ M5 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_le_D
% 5.45/5.73 thf(fact_4197_le__Suc__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 | ( M
% 5.45/5.73 = ( suc @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_Suc_eq
% 5.45/5.73 thf(fact_4198_Suc__n__not__le__n,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_n_not_le_n
% 5.45/5.73 thf(fact_4199_not__less__eq__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 5.45/5.73
% 5.45/5.73 % not_less_eq_eq
% 5.45/5.73 thf(fact_4200_full__nat__induct,axiom,
% 5.45/5.73 ! [P: nat > $o,N2: nat] :
% 5.45/5.73 ( ! [N5: nat] :
% 5.45/5.73 ( ! [M4: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( suc @ M4 ) @ N5 )
% 5.45/5.73 => ( P @ M4 ) )
% 5.45/5.73 => ( P @ N5 ) )
% 5.45/5.73 => ( P @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % full_nat_induct
% 5.45/5.73 thf(fact_4201_nat__induct__at__least,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,P: nat > $o] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ( P @ M )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N5 )
% 5.45/5.73 => ( ( P @ N5 )
% 5.45/5.73 => ( P @ ( suc @ N5 ) ) ) )
% 5.45/5.73 => ( P @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_induct_at_least
% 5.45/5.73 thf(fact_4202_transitive__stepwise__le,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ! [X3: nat] : ( R @ X3 @ X3 )
% 5.45/5.73 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.73 ( ( R @ X3 @ Y3 )
% 5.45/5.73 => ( ( R @ Y3 @ Z2 )
% 5.45/5.73 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.73 => ( ! [N5: nat] : ( R @ N5 @ ( suc @ N5 ) )
% 5.45/5.73 => ( R @ M @ N2 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % transitive_stepwise_le
% 5.45/5.73 thf(fact_4203_add__Suc__shift,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_Suc_shift
% 5.45/5.73 thf(fact_4204_add__Suc,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_Suc
% 5.45/5.73 thf(fact_4205_nat__arith_Osuc1,axiom,
% 5.45/5.73 ! [A3: nat,K: nat,A: nat] :
% 5.45/5.73 ( ( A3
% 5.45/5.73 = ( plus_plus_nat @ K @ A ) )
% 5.45/5.73 => ( ( suc @ A3 )
% 5.45/5.73 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_arith.suc1
% 5.45/5.73 thf(fact_4206_diff__mult__distrib,axiom,
% 5.45/5.73 ! [M: nat,N2: nat,K: nat] :
% 5.45/5.73 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.45/5.73 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_mult_distrib
% 5.45/5.73 thf(fact_4207_diff__mult__distrib2,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_mult_distrib2
% 5.45/5.73 thf(fact_4208_Suc__mult__cancel1,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.45/5.73 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.45/5.73 = ( M = N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_mult_cancel1
% 5.45/5.73 thf(fact_4209_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4210_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,C: rat,A: rat,B: rat] :
% 5.45/5.73 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4211_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,C: int,A: int,B: int] :
% 5.45/5.73 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4212_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4213_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,C: rat,A: rat,B: rat] :
% 5.45/5.73 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4214_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,C: int,A: int,B: int] :
% 5.45/5.73 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4215_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4216_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,C: rat,A: rat,B: rat] :
% 5.45/5.73 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4217_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,C: int,A: int,B: int] :
% 5.45/5.73 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4218_left__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: rat,Y: rat,C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ C )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % left_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4219_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( nO_MAT8694959213317031834nteger @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4220_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( nO_MATCH_nat_rat @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4221_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: nat,Y: nat,A: int,B: int,C: int] :
% 5.45/5.73 ( ( nO_MATCH_nat_int @ ( divide_divide_nat @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4222_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( nO_MAT9066612773553876470nteger @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4223_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( nO_MATCH_int_rat @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4224_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: int,Y: int,A: int,B: int,C: int] :
% 5.45/5.73 ( ( nO_MATCH_int_int @ ( divide_divide_int @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4225_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( nO_MAT8252062027627875367nteger @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4226_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( nO_MAT7795273704451493282er_rat @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.45/5.73 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4227_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer,A: int,B: int,C: int] :
% 5.45/5.73 ( ( nO_MAT8427913294028938742er_int @ ( divide6298287555418463151nteger @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.45/5.73 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4228_right__diff__distrib__NO__MATCH,axiom,
% 5.45/5.73 ! [X: rat,Y: rat,A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.73 ( ( nO_MAT243659986023775650nteger @ ( divide_divide_rat @ X @ Y ) @ A )
% 5.45/5.73 => ( ( times_3573771949741848930nteger @ A @ ( minus_8373710615458151222nteger @ B @ C ) )
% 5.45/5.73 = ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % right_diff_distrib_NO_MATCH
% 5.45/5.73 thf(fact_4229_mod__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: code_natural,M: nat,N2: nat] :
% 5.45/5.73 ( ( modulo8411746178871703098atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N2 ) ) )
% 5.45/5.73 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( modulo8411746178871703098atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N2 ) ) ) @ ( modulo8411746178871703098atural @ A @ ( semiri3763490453095760265atural @ M ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult2_eq'
% 5.45/5.73 thf(fact_4230_mod__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: int,M: nat,N2: nat] :
% 5.45/5.73 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.45/5.73 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult2_eq'
% 5.45/5.73 thf(fact_4231_mod__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.45/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult2_eq'
% 5.45/5.73 thf(fact_4232_mod__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.73 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.45/5.73 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_mult2_eq'
% 5.45/5.73 thf(fact_4233_nz__le__conv__less,axiom,
% 5.45/5.73 ! [K: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.73 => ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ K @ ( suc @ zero_zero_nat ) ) @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nz_le_conv_less
% 5.45/5.73 thf(fact_4234_Suc__pred_H,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( N2
% 5.45/5.73 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_pred'
% 5.45/5.73 thf(fact_4235_Suc__diff__eq__diff__pred,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_diff_eq_diff_pred
% 5.45/5.73 thf(fact_4236_add__eq__if,axiom,
% 5.45/5.73 ( plus_plus_nat
% 5.45/5.73 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_eq_if
% 5.45/5.73 thf(fact_4237_Suc__n__minus__m__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ one_one_nat @ M )
% 5.45/5.73 => ( ( suc @ ( minus_minus_nat @ N2 @ M ) )
% 5.45/5.73 = ( minus_minus_nat @ N2 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_n_minus_m_eq
% 5.45/5.73 thf(fact_4238_div__geq,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.73 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_geq
% 5.45/5.73 thf(fact_4239_div__if,axiom,
% 5.45/5.73 ( divide_divide_nat
% 5.45/5.73 = ( ^ [M3: nat,N: nat] :
% 5.45/5.73 ( if_nat
% 5.45/5.73 @ ( ( ord_less_nat @ M3 @ N )
% 5.45/5.73 | ( N = zero_zero_nat ) )
% 5.45/5.73 @ zero_zero_nat
% 5.45/5.73 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_if
% 5.45/5.73 thf(fact_4240_nat__less__as__int,axiom,
% 5.45/5.73 ( ord_less_nat
% 5.45/5.73 = ( ^ [A5: nat,B5: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_less_as_int
% 5.45/5.73 thf(fact_4241_nat__leq__as__int,axiom,
% 5.45/5.73 ( ord_less_eq_nat
% 5.45/5.73 = ( ^ [A5: nat,B5: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_leq_as_int
% 5.45/5.73 thf(fact_4242_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.73 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.45/5.73 thf(fact_4243_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.73 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.45/5.73 thf(fact_4244_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.73 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.45/5.73 thf(fact_4245_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.45/5.73 ! [B: nat,A: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.73 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.45/5.73 thf(fact_4246_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.45/5.73 ! [B: int,A: int] :
% 5.45/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.73 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.45/5.73 thf(fact_4247_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.45/5.73 ! [B: code_integer,A: code_integer] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.73 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.45/5.73 thf(fact_4248_Suc__times__mod__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.45/5.73 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 5.45/5.73 = one_one_nat ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_times_mod_eq
% 5.45/5.73 thf(fact_4249_of__nat__0__le__iff,axiom,
% 5.45/5.73 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_le_iff
% 5.45/5.73 thf(fact_4250_of__nat__0__le__iff,axiom,
% 5.45/5.73 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_le_iff
% 5.45/5.73 thf(fact_4251_of__nat__0__le__iff,axiom,
% 5.45/5.73 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_le_iff
% 5.45/5.73 thf(fact_4252_of__nat__0__le__iff,axiom,
% 5.45/5.73 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_0_le_iff
% 5.45/5.73 thf(fact_4253_of__nat__less__0__iff,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_0_iff
% 5.45/5.73 thf(fact_4254_of__nat__less__0__iff,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_0_iff
% 5.45/5.73 thf(fact_4255_of__nat__less__0__iff,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_0_iff
% 5.45/5.73 thf(fact_4256_of__nat__less__0__iff,axiom,
% 5.45/5.73 ! [M: nat] :
% 5.45/5.73 ~ ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_0_iff
% 5.45/5.73 thf(fact_4257_mod__eqE,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( ( modulo_modulo_int @ A @ C )
% 5.45/5.73 = ( modulo_modulo_int @ B @ C ) )
% 5.45/5.73 => ~ ! [D: int] :
% 5.45/5.73 ( B
% 5.45/5.73 != ( plus_plus_int @ A @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_eqE
% 5.45/5.73 thf(fact_4258_mod__eqE,axiom,
% 5.45/5.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.73 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.45/5.73 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.45/5.73 => ~ ! [D: code_integer] :
% 5.45/5.73 ( B
% 5.45/5.73 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_eqE
% 5.45/5.73 thf(fact_4259_le__iff__diff__le__0,axiom,
% 5.45/5.73 ( ord_le3102999989581377725nteger
% 5.45/5.73 = ( ^ [A5: code_integer,B5: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A5 @ B5 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_iff_diff_le_0
% 5.45/5.73 thf(fact_4260_le__iff__diff__le__0,axiom,
% 5.45/5.73 ( ord_less_eq_rat
% 5.45/5.73 = ( ^ [A5: rat,B5: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A5 @ B5 ) @ zero_zero_rat ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_iff_diff_le_0
% 5.45/5.73 thf(fact_4261_le__iff__diff__le__0,axiom,
% 5.45/5.73 ( ord_less_eq_int
% 5.45/5.73 = ( ^ [A5: int,B5: int] : ( ord_less_eq_int @ ( minus_minus_int @ A5 @ B5 ) @ zero_zero_int ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_iff_diff_le_0
% 5.45/5.73 thf(fact_4262_le__div__geq,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.73 => ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.73 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_div_geq
% 5.45/5.73 thf(fact_4263_less__iff__diff__less__0,axiom,
% 5.45/5.73 ( ord_le6747313008572928689nteger
% 5.45/5.73 = ( ^ [A5: code_integer,B5: code_integer] : ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A5 @ B5 ) @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_iff_diff_less_0
% 5.45/5.73 thf(fact_4264_less__iff__diff__less__0,axiom,
% 5.45/5.73 ( ord_less_rat
% 5.45/5.73 = ( ^ [A5: rat,B5: rat] : ( ord_less_rat @ ( minus_minus_rat @ A5 @ B5 ) @ zero_zero_rat ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_iff_diff_less_0
% 5.45/5.73 thf(fact_4265_less__iff__diff__less__0,axiom,
% 5.45/5.73 ( ord_less_int
% 5.45/5.73 = ( ^ [A5: int,B5: int] : ( ord_less_int @ ( minus_minus_int @ A5 @ B5 ) @ zero_zero_int ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_iff_diff_less_0
% 5.45/5.73 thf(fact_4266_add__le__imp__le__diff,axiom,
% 5.45/5.73 ! [I2: rat,K: rat,N2: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_imp_le_diff
% 5.45/5.73 thf(fact_4267_add__le__imp__le__diff,axiom,
% 5.45/5.73 ! [I2: nat,K: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_imp_le_diff
% 5.45/5.73 thf(fact_4268_add__le__imp__le__diff,axiom,
% 5.45/5.73 ! [I2: int,K: int,N2: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_imp_le_diff
% 5.45/5.73 thf(fact_4269_add__le__add__imp__diff__le,axiom,
% 5.45/5.73 ! [I2: rat,K: rat,N2: rat,J: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.45/5.73 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.45/5.73 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_add_imp_diff_le
% 5.45/5.73 thf(fact_4270_add__le__add__imp__diff__le,axiom,
% 5.45/5.73 ! [I2: nat,K: nat,N2: nat,J: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.45/5.73 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_add_imp_diff_le
% 5.45/5.73 thf(fact_4271_add__le__add__imp__diff__le,axiom,
% 5.45/5.73 ! [I2: int,K: int,N2: int,J: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.45/5.73 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.45/5.73 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.45/5.73 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_le_add_imp_diff_le
% 5.45/5.73 thf(fact_4272_diff__le__eq,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_le_eq
% 5.45/5.73 thf(fact_4273_diff__le__eq,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_le_eq
% 5.45/5.73 thf(fact_4274_le__diff__eq,axiom,
% 5.45/5.73 ! [A: rat,C: rat,B: rat] :
% 5.45/5.73 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.45/5.73 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_diff_eq
% 5.45/5.73 thf(fact_4275_le__diff__eq,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.45/5.73 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_diff_eq
% 5.45/5.73 thf(fact_4276_ordered__cancel__comm__monoid__diff__class_Odiff__add,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.45/5.73 = B ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.diff_add
% 5.45/5.73 thf(fact_4277_le__add__diff,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_add_diff
% 5.45/5.73 thf(fact_4278_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.45/5.73 thf(fact_4279_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.45/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.45/5.73 thf(fact_4280_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.45/5.73 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.45/5.73 thf(fact_4281_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.45/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.45/5.73 thf(fact_4282_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.45/5.73 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.45/5.73 thf(fact_4283_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.45/5.73 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.45/5.73 thf(fact_4284_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.45/5.73 = B ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.45/5.73 thf(fact_4285_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 => ( ( ( minus_minus_nat @ B @ A )
% 5.45/5.73 = C )
% 5.45/5.73 = ( B
% 5.45/5.73 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.45/5.73 thf(fact_4286_less__imp__of__nat__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_of_nat_less
% 5.45/5.73 thf(fact_4287_less__imp__of__nat__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_of_nat_less
% 5.45/5.73 thf(fact_4288_less__imp__of__nat__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_of_nat_less
% 5.45/5.73 thf(fact_4289_less__imp__of__nat__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_of_nat_less
% 5.45/5.73 thf(fact_4290_of__nat__less__imp__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_imp_less
% 5.45/5.73 thf(fact_4291_of__nat__less__imp__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_imp_less
% 5.45/5.73 thf(fact_4292_of__nat__less__imp__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_imp_less
% 5.45/5.73 thf(fact_4293_of__nat__less__imp__less,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_less_imp_less
% 5.45/5.73 thf(fact_4294_of__nat__mono,axiom,
% 5.45/5.73 ! [I2: nat,J: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ord_le3102999989581377725nteger @ ( semiri4939895301339042750nteger @ I2 ) @ ( semiri4939895301339042750nteger @ J ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_mono
% 5.45/5.73 thf(fact_4295_of__nat__mono,axiom,
% 5.45/5.73 ! [I2: nat,J: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_mono
% 5.45/5.73 thf(fact_4296_of__nat__mono,axiom,
% 5.45/5.73 ! [I2: nat,J: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_mono
% 5.45/5.73 thf(fact_4297_of__nat__mono,axiom,
% 5.45/5.73 ! [I2: nat,J: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % of_nat_mono
% 5.45/5.73 thf(fact_4298_diff__shunt__var,axiom,
% 5.45/5.73 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.73 ( ( ( minus_1356011639430497352at_nat @ X @ Y )
% 5.45/5.73 = bot_bo2099793752762293965at_nat )
% 5.45/5.73 = ( ord_le3146513528884898305at_nat @ X @ Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_shunt_var
% 5.45/5.73 thf(fact_4299_diff__shunt__var,axiom,
% 5.45/5.73 ! [X: set_o,Y: set_o] :
% 5.45/5.73 ( ( ( minus_minus_set_o @ X @ Y )
% 5.45/5.73 = bot_bot_set_o )
% 5.45/5.73 = ( ord_less_eq_set_o @ X @ Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_shunt_var
% 5.45/5.73 thf(fact_4300_diff__shunt__var,axiom,
% 5.45/5.73 ! [X: assn,Y: assn] :
% 5.45/5.73 ( ( ( minus_minus_assn @ X @ Y )
% 5.45/5.73 = bot_bot_assn )
% 5.45/5.73 = ( ord_less_eq_assn @ X @ Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_shunt_var
% 5.45/5.73 thf(fact_4301_diff__shunt__var,axiom,
% 5.45/5.73 ! [X: set_nat,Y: set_nat] :
% 5.45/5.73 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.45/5.73 = bot_bot_set_nat )
% 5.45/5.73 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_shunt_var
% 5.45/5.73 thf(fact_4302_diff__shunt__var,axiom,
% 5.45/5.73 ! [X: set_int,Y: set_int] :
% 5.45/5.73 ( ( ( minus_minus_set_int @ X @ Y )
% 5.45/5.73 = bot_bot_set_int )
% 5.45/5.73 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_shunt_var
% 5.45/5.73 thf(fact_4303_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.45/5.73 ! [A: rat,B: rat] :
% 5.45/5.73 ( ~ ( ord_less_rat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.45/5.73 = A ) ) ).
% 5.45/5.73
% 5.45/5.73 % linordered_semidom_class.add_diff_inverse
% 5.45/5.73 thf(fact_4304_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ~ ( ord_less_nat @ A @ B )
% 5.45/5.73 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.73 = A ) ) ).
% 5.45/5.73
% 5.45/5.73 % linordered_semidom_class.add_diff_inverse
% 5.45/5.73 thf(fact_4305_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.45/5.73 ! [A: int,B: int] :
% 5.45/5.73 ( ~ ( ord_less_int @ A @ B )
% 5.45/5.73 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.45/5.73 = A ) ) ).
% 5.45/5.73
% 5.45/5.73 % linordered_semidom_class.add_diff_inverse
% 5.45/5.73 thf(fact_4306_diff__less__eq,axiom,
% 5.45/5.73 ! [A: rat,B: rat,C: rat] :
% 5.45/5.73 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.45/5.73 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less_eq
% 5.45/5.73 thf(fact_4307_diff__less__eq,axiom,
% 5.45/5.73 ! [A: int,B: int,C: int] :
% 5.45/5.73 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.45/5.73 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less_eq
% 5.45/5.73 thf(fact_4308_less__diff__eq,axiom,
% 5.45/5.73 ! [A: rat,C: rat,B: rat] :
% 5.45/5.73 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.45/5.73 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_diff_eq
% 5.45/5.73 thf(fact_4309_less__diff__eq,axiom,
% 5.45/5.73 ! [A: int,C: int,B: int] :
% 5.45/5.73 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.45/5.73 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_diff_eq
% 5.45/5.73 thf(fact_4310_div__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: code_natural,M: nat,N2: nat] :
% 5.45/5.73 ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ M ) @ ( semiri3763490453095760265atural @ N2 ) ) )
% 5.45/5.73 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ ( semiri3763490453095760265atural @ M ) ) @ ( semiri3763490453095760265atural @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_mult2_eq'
% 5.45/5.73 thf(fact_4311_div__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: int,M: nat,N2: nat] :
% 5.45/5.73 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.45/5.73 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_mult2_eq'
% 5.45/5.73 thf(fact_4312_div__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.45/5.73 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_mult2_eq'
% 5.45/5.73 thf(fact_4313_div__mult2__eq_H,axiom,
% 5.45/5.73 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.73 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.45/5.73 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % div_mult2_eq'
% 5.45/5.73 thf(fact_4314_eq__add__iff1,axiom,
% 5.45/5.73 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.73 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 5.45/5.73 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C )
% 5.45/5.73 = D2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff1
% 5.45/5.73 thf(fact_4315_eq__add__iff1,axiom,
% 5.45/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.73 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.45/5.73 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.45/5.73 = D2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff1
% 5.45/5.73 thf(fact_4316_eq__add__iff1,axiom,
% 5.45/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.73 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.45/5.73 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.45/5.73 = D2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff1
% 5.45/5.73 thf(fact_4317_eq__add__iff2,axiom,
% 5.45/5.73 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.73 ( ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C )
% 5.45/5.73 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( C
% 5.45/5.73 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff2
% 5.45/5.73 thf(fact_4318_eq__add__iff2,axiom,
% 5.45/5.73 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.73 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.45/5.73 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( C
% 5.45/5.73 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff2
% 5.45/5.73 thf(fact_4319_eq__add__iff2,axiom,
% 5.45/5.73 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.73 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.45/5.73 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.73 = ( C
% 5.45/5.73 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % eq_add_iff2
% 5.45/5.73 thf(fact_4320_square__diff__square__factored,axiom,
% 5.45/5.73 ! [X: code_integer,Y: code_integer] :
% 5.45/5.73 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ ( times_3573771949741848930nteger @ Y @ Y ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( minus_8373710615458151222nteger @ X @ Y ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % square_diff_square_factored
% 5.45/5.73 thf(fact_4321_square__diff__square__factored,axiom,
% 5.45/5.73 ! [X: rat,Y: rat] :
% 5.45/5.73 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.45/5.73 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % square_diff_square_factored
% 5.45/5.73 thf(fact_4322_square__diff__square__factored,axiom,
% 5.45/5.73 ! [X: int,Y: int] :
% 5.45/5.73 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.45/5.73 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % square_diff_square_factored
% 5.45/5.73 thf(fact_4323_mod__less__divisor,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % mod_less_divisor
% 5.45/5.73 thf(fact_4324_zero__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_le_numeral
% 5.45/5.73 thf(fact_4325_zero__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le1926595141338095240atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_le_numeral
% 5.45/5.73 thf(fact_4326_zero__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_le_numeral
% 5.45/5.73 thf(fact_4327_zero__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_le_numeral
% 5.45/5.73 thf(fact_4328_zero__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_le_numeral
% 5.45/5.73 thf(fact_4329_not__numeral__le__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_le_zero
% 5.45/5.73 thf(fact_4330_not__numeral__le__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ zero_z2226904508553997617atural ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_le_zero
% 5.45/5.73 thf(fact_4331_not__numeral__le__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_le_zero
% 5.45/5.73 thf(fact_4332_not__numeral__le__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_le_zero
% 5.45/5.73 thf(fact_4333_not__numeral__le__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_le_zero
% 5.45/5.73 thf(fact_4334_zero__less__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_less_numeral
% 5.45/5.73 thf(fact_4335_zero__less__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_less_numeral
% 5.45/5.73 thf(fact_4336_zero__less__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_less_numeral
% 5.45/5.73 thf(fact_4337_zero__less__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_less_numeral
% 5.45/5.73 thf(fact_4338_zero__less__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % zero_less_numeral
% 5.45/5.73 thf(fact_4339_not__numeral__less__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_zero
% 5.45/5.73 thf(fact_4340_not__numeral__less__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_zero
% 5.45/5.73 thf(fact_4341_not__numeral__less__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_zero
% 5.45/5.73 thf(fact_4342_not__numeral__less__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_zero
% 5.45/5.73 thf(fact_4343_not__numeral__less__zero,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ zero_z2226904508553997617atural ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_zero
% 5.45/5.73 thf(fact_4344_one__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_le_numeral
% 5.45/5.73 thf(fact_4345_one__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_le1926595141338095240atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_le_numeral
% 5.45/5.73 thf(fact_4346_one__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_le_numeral
% 5.45/5.73 thf(fact_4347_one__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_le_numeral
% 5.45/5.73 thf(fact_4348_one__le__numeral,axiom,
% 5.45/5.73 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_le_numeral
% 5.45/5.73 thf(fact_4349_not__numeral__less__one,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_one
% 5.45/5.73 thf(fact_4350_not__numeral__less__one,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_one
% 5.45/5.73 thf(fact_4351_not__numeral__less__one,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_one
% 5.45/5.73 thf(fact_4352_not__numeral__less__one,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_one
% 5.45/5.73 thf(fact_4353_not__numeral__less__one,axiom,
% 5.45/5.73 ! [N2: num] :
% 5.45/5.73 ~ ( ord_le5570908160329646204atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural ) ).
% 5.45/5.73
% 5.45/5.73 % not_numeral_less_one
% 5.45/5.73 thf(fact_4354_lift__Suc__mono__less,axiom,
% 5.45/5.73 ! [F: nat > assn,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_assn @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_assn @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less
% 5.45/5.73 thf(fact_4355_lift__Suc__mono__less,axiom,
% 5.45/5.73 ! [F: nat > rat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less
% 5.45/5.73 thf(fact_4356_lift__Suc__mono__less,axiom,
% 5.45/5.73 ! [F: nat > num,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less
% 5.45/5.73 thf(fact_4357_lift__Suc__mono__less,axiom,
% 5.45/5.73 ! [F: nat > nat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less
% 5.45/5.73 thf(fact_4358_lift__Suc__mono__less,axiom,
% 5.45/5.73 ! [F: nat > int,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less
% 5.45/5.73 thf(fact_4359_lift__Suc__mono__less__iff,axiom,
% 5.45/5.73 ! [F: nat > assn,N2: nat,M: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_assn @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_assn @ ( F @ N2 ) @ ( F @ M ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less_iff
% 5.45/5.73 thf(fact_4360_lift__Suc__mono__less__iff,axiom,
% 5.45/5.73 ! [F: nat > rat,N2: nat,M: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less_iff
% 5.45/5.73 thf(fact_4361_lift__Suc__mono__less__iff,axiom,
% 5.45/5.73 ! [F: nat > num,N2: nat,M: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less_iff
% 5.45/5.73 thf(fact_4362_lift__Suc__mono__less__iff,axiom,
% 5.45/5.73 ! [F: nat > nat,N2: nat,M: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less_iff
% 5.45/5.73 thf(fact_4363_lift__Suc__mono__less__iff,axiom,
% 5.45/5.73 ! [F: nat > int,N2: nat,M: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 5.45/5.73 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_less_iff
% 5.45/5.73 thf(fact_4364_lift__Suc__mono__le,axiom,
% 5.45/5.73 ! [F: nat > set_int,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_le
% 5.45/5.73 thf(fact_4365_lift__Suc__mono__le,axiom,
% 5.45/5.73 ! [F: nat > rat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_le
% 5.45/5.73 thf(fact_4366_lift__Suc__mono__le,axiom,
% 5.45/5.73 ! [F: nat > num,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_le
% 5.45/5.73 thf(fact_4367_lift__Suc__mono__le,axiom,
% 5.45/5.73 ! [F: nat > nat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_le
% 5.45/5.73 thf(fact_4368_lift__Suc__mono__le,axiom,
% 5.45/5.73 ! [F: nat > int,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N6 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_mono_le
% 5.45/5.73 thf(fact_4369_lift__Suc__antimono__le,axiom,
% 5.45/5.73 ! [F: nat > set_int,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_set_int @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_antimono_le
% 5.45/5.73 thf(fact_4370_lift__Suc__antimono__le,axiom,
% 5.45/5.73 ! [F: nat > rat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_rat @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_antimono_le
% 5.45/5.73 thf(fact_4371_lift__Suc__antimono__le,axiom,
% 5.45/5.73 ! [F: nat > num,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_num @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_antimono_le
% 5.45/5.73 thf(fact_4372_lift__Suc__antimono__le,axiom,
% 5.45/5.73 ! [F: nat > nat,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_nat @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_antimono_le
% 5.45/5.73 thf(fact_4373_lift__Suc__antimono__le,axiom,
% 5.45/5.73 ! [F: nat > int,N2: nat,N6: nat] :
% 5.45/5.73 ( ! [N5: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N5 ) ) @ ( F @ N5 ) )
% 5.45/5.73 => ( ( ord_less_eq_nat @ N2 @ N6 )
% 5.45/5.73 => ( ord_less_eq_int @ ( F @ N6 ) @ ( F @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % lift_Suc_antimono_le
% 5.45/5.73 thf(fact_4374_diff__less,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less
% 5.45/5.73 thf(fact_4375_power__Suc2,axiom,
% 5.45/5.73 ! [A: code_integer,N2: nat] :
% 5.45/5.73 ( ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc2
% 5.45/5.73 thf(fact_4376_power__Suc2,axiom,
% 5.45/5.73 ! [A: assn,N2: nat] :
% 5.45/5.73 ( ( power_power_assn @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_assn @ ( power_power_assn @ A @ N2 ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc2
% 5.45/5.73 thf(fact_4377_power__Suc2,axiom,
% 5.45/5.73 ! [A: rat,N2: nat] :
% 5.45/5.73 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_rat @ ( power_power_rat @ A @ N2 ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc2
% 5.45/5.73 thf(fact_4378_power__Suc2,axiom,
% 5.45/5.73 ! [A: nat,N2: nat] :
% 5.45/5.73 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc2
% 5.45/5.73 thf(fact_4379_power__Suc2,axiom,
% 5.45/5.73 ! [A: int,N2: nat] :
% 5.45/5.73 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc2
% 5.45/5.73 thf(fact_4380_power__Suc,axiom,
% 5.45/5.73 ! [A: code_integer,N2: nat] :
% 5.45/5.73 ( ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc
% 5.45/5.73 thf(fact_4381_power__Suc,axiom,
% 5.45/5.73 ! [A: assn,N2: nat] :
% 5.45/5.73 ( ( power_power_assn @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_assn @ A @ ( power_power_assn @ A @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc
% 5.45/5.73 thf(fact_4382_power__Suc,axiom,
% 5.45/5.73 ! [A: rat,N2: nat] :
% 5.45/5.73 ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc
% 5.45/5.73 thf(fact_4383_power__Suc,axiom,
% 5.45/5.73 ! [A: nat,N2: nat] :
% 5.45/5.73 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc
% 5.45/5.73 thf(fact_4384_power__Suc,axiom,
% 5.45/5.73 ! [A: int,N2: nat] :
% 5.45/5.73 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.45/5.73 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % power_Suc
% 5.45/5.73 thf(fact_4385_Ex__less__Suc2,axiom,
% 5.45/5.73 ! [N2: nat,P: nat > $o] :
% 5.45/5.73 ( ( ? [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N2 ) )
% 5.45/5.73 & ( P @ I4 ) ) )
% 5.45/5.73 = ( ( P @ zero_zero_nat )
% 5.45/5.73 | ? [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ N2 )
% 5.45/5.73 & ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Ex_less_Suc2
% 5.45/5.73 thf(fact_4386_gr0__conv__Suc,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 = ( ? [M3: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 = ( suc @ M3 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % gr0_conv_Suc
% 5.45/5.73 thf(fact_4387_All__less__Suc2,axiom,
% 5.45/5.73 ! [N2: nat,P: nat > $o] :
% 5.45/5.73 ( ( ! [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ ( suc @ N2 ) )
% 5.45/5.73 => ( P @ I4 ) ) )
% 5.45/5.73 = ( ( P @ zero_zero_nat )
% 5.45/5.73 & ! [I4: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I4 @ N2 )
% 5.45/5.73 => ( P @ ( suc @ I4 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % All_less_Suc2
% 5.45/5.73 thf(fact_4388_gr0__implies__Suc,axiom,
% 5.45/5.73 ! [N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.73 => ? [M5: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 = ( suc @ M5 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % gr0_implies_Suc
% 5.45/5.73 thf(fact_4389_less__Suc__eq__0__disj,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 = ( ( M = zero_zero_nat )
% 5.45/5.73 | ? [J3: nat] :
% 5.45/5.73 ( ( M
% 5.45/5.73 = ( suc @ J3 ) )
% 5.45/5.73 & ( ord_less_nat @ J3 @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_Suc_eq_0_disj
% 5.45/5.73 thf(fact_4390_diff__add__0,axiom,
% 5.45/5.73 ! [N2: nat,M: nat] :
% 5.45/5.73 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.45/5.73 = zero_zero_nat ) ).
% 5.45/5.73
% 5.45/5.73 % diff_add_0
% 5.45/5.73 thf(fact_4391_less__diff__iff,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.73 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.45/5.73 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_diff_iff
% 5.45/5.73 thf(fact_4392_diff__less__mono,axiom,
% 5.45/5.73 ! [A: nat,B: nat,C: nat] :
% 5.45/5.73 ( ( ord_less_nat @ A @ B )
% 5.45/5.73 => ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.73 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % diff_less_mono
% 5.45/5.73 thf(fact_4393_less__diff__conv,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.73 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.45/5.73 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_diff_conv
% 5.45/5.73 thf(fact_4394_add__diff__inverse__nat,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ~ ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.73 = M ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_diff_inverse_nat
% 5.45/5.73 thf(fact_4395_nat__compl__induct_H,axiom,
% 5.45/5.73 ! [P: nat > $o,N2: nat] :
% 5.45/5.73 ( ( P @ zero_zero_nat )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ! [Nn: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ Nn @ N5 )
% 5.45/5.73 => ( P @ Nn ) )
% 5.45/5.73 => ( P @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( P @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_compl_induct'
% 5.45/5.73 thf(fact_4396_nat__compl__induct,axiom,
% 5.45/5.73 ! [P: nat > $o,N2: nat] :
% 5.45/5.73 ( ( P @ zero_zero_nat )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ! [Nn: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ Nn @ N5 )
% 5.45/5.73 => ( P @ Nn ) )
% 5.45/5.73 => ( P @ ( suc @ N5 ) ) )
% 5.45/5.73 => ( P @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_compl_induct
% 5.45/5.73 thf(fact_4397_add__is__1,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ( plus_plus_nat @ M @ N2 )
% 5.45/5.73 = ( suc @ zero_zero_nat ) )
% 5.45/5.73 = ( ( ( M
% 5.45/5.73 = ( suc @ zero_zero_nat ) )
% 5.45/5.73 & ( N2 = zero_zero_nat ) )
% 5.45/5.73 | ( ( M = zero_zero_nat )
% 5.45/5.73 & ( N2
% 5.45/5.73 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % add_is_1
% 5.45/5.73 thf(fact_4398_one__is__add,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ( suc @ zero_zero_nat )
% 5.45/5.73 = ( plus_plus_nat @ M @ N2 ) )
% 5.45/5.73 = ( ( ( M
% 5.45/5.73 = ( suc @ zero_zero_nat ) )
% 5.45/5.73 & ( N2 = zero_zero_nat ) )
% 5.45/5.73 | ( ( M = zero_zero_nat )
% 5.45/5.73 & ( N2
% 5.45/5.73 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % one_is_add
% 5.45/5.73 thf(fact_4399_le__diff__conv,axiom,
% 5.45/5.73 ! [J: nat,K: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.45/5.73 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_diff_conv
% 5.45/5.73 thf(fact_4400_Nat_Ole__diff__conv2,axiom,
% 5.45/5.73 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.73 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.45/5.73 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.le_diff_conv2
% 5.45/5.73 thf(fact_4401_Nat_Odiff__add__assoc,axiom,
% 5.45/5.73 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.45/5.73 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.diff_add_assoc
% 5.45/5.73 thf(fact_4402_Nat_Odiff__add__assoc2,axiom,
% 5.45/5.73 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.73 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.45/5.73 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.diff_add_assoc2
% 5.45/5.73 thf(fact_4403_Nat_Ole__imp__diff__is__add,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.45/5.73 = K )
% 5.45/5.73 = ( J
% 5.45/5.73 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Nat.le_imp_diff_is_add
% 5.45/5.73 thf(fact_4404_Suc__leI,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_leI
% 5.45/5.73 thf(fact_4405_Suc__le__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_le_eq
% 5.45/5.73 thf(fact_4406_dec__induct,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,P: nat > $o] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ( P @ I2 )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ N5 )
% 5.45/5.73 => ( ( ord_less_nat @ N5 @ J )
% 5.45/5.73 => ( ( P @ N5 )
% 5.45/5.73 => ( P @ ( suc @ N5 ) ) ) ) )
% 5.45/5.73 => ( P @ J ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % dec_induct
% 5.45/5.73 thf(fact_4407_inc__induct,axiom,
% 5.45/5.73 ! [I2: nat,J: nat,P: nat > $o] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.73 => ( ( P @ J )
% 5.45/5.73 => ( ! [N5: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ I2 @ N5 )
% 5.45/5.73 => ( ( ord_less_nat @ N5 @ J )
% 5.45/5.73 => ( ( P @ ( suc @ N5 ) )
% 5.45/5.73 => ( P @ N5 ) ) ) )
% 5.45/5.73 => ( P @ I2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % inc_induct
% 5.45/5.73 thf(fact_4408_Suc__le__lessD,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_le_lessD
% 5.45/5.73 thf(fact_4409_le__less__Suc__eq,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.45/5.73 = ( N2 = M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_less_Suc_eq
% 5.45/5.73 thf(fact_4410_less__Suc__eq__le,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_Suc_eq_le
% 5.45/5.73 thf(fact_4411_less__eq__Suc__le,axiom,
% 5.45/5.73 ( ord_less_nat
% 5.45/5.73 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_eq_Suc_le
% 5.45/5.73 thf(fact_4412_le__imp__less__Suc,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.73 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % le_imp_less_Suc
% 5.45/5.73 thf(fact_4413_nat__in__between__eq_I2_J,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.73 & ( ord_less_nat @ B @ ( suc @ A ) ) )
% 5.45/5.73 = ( B = A ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_in_between_eq(2)
% 5.45/5.73 thf(fact_4414_nat__in__between__eq_I1_J,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ( ord_less_nat @ A @ B )
% 5.45/5.73 & ( ord_less_eq_nat @ B @ ( suc @ A ) ) )
% 5.45/5.73 = ( B
% 5.45/5.73 = ( suc @ A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % nat_in_between_eq(1)
% 5.45/5.73 thf(fact_4415_less__natE,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ~ ! [Q5: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 != ( suc @ ( plus_plus_nat @ M @ Q5 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_natE
% 5.45/5.73 thf(fact_4416_less__add__Suc1,axiom,
% 5.45/5.73 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_add_Suc1
% 5.45/5.73 thf(fact_4417_less__add__Suc2,axiom,
% 5.45/5.73 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_add_Suc2
% 5.45/5.73 thf(fact_4418_less__iff__Suc__add,axiom,
% 5.45/5.73 ( ord_less_nat
% 5.45/5.73 = ( ^ [M3: nat,N: nat] :
% 5.45/5.73 ? [K3: nat] :
% 5.45/5.73 ( N
% 5.45/5.73 = ( suc @ ( plus_plus_nat @ M3 @ K3 ) ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_iff_Suc_add
% 5.45/5.73 thf(fact_4419_less__imp__Suc__add,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.73 => ? [K2: nat] :
% 5.45/5.73 ( N2
% 5.45/5.73 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % less_imp_Suc_add
% 5.45/5.73 thf(fact_4420_Suc__mult__less__cancel1,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.45/5.73 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_mult_less_cancel1
% 5.45/5.73 thf(fact_4421_One__nat__def,axiom,
% 5.45/5.73 ( one_one_nat
% 5.45/5.73 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.73
% 5.45/5.73 % One_nat_def
% 5.45/5.73 thf(fact_4422_Suc__mult__le__cancel1,axiom,
% 5.45/5.73 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.45/5.73 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_mult_le_cancel1
% 5.45/5.73 thf(fact_4423_mult__Suc,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] :
% 5.45/5.73 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 5.45/5.73 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % mult_Suc
% 5.45/5.73 thf(fact_4424_Suc__eq__plus1,axiom,
% 5.45/5.73 ( suc
% 5.45/5.73 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_eq_plus1
% 5.45/5.73 thf(fact_4425_plus__1__eq__Suc,axiom,
% 5.45/5.73 ( ( plus_plus_nat @ one_one_nat )
% 5.45/5.73 = suc ) ).
% 5.45/5.73
% 5.45/5.73 % plus_1_eq_Suc
% 5.45/5.73 thf(fact_4426_Suc__eq__plus1__left,axiom,
% 5.45/5.73 ( suc
% 5.45/5.73 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_eq_plus1_left
% 5.45/5.73 thf(fact_4427_Suc__div__le__mono,axiom,
% 5.45/5.73 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.45/5.73
% 5.45/5.73 % Suc_div_le_mono
% 5.45/5.73 thf(fact_4428_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.45/5.73 ! [A: code_integer,B: code_integer] :
% 5.45/5.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.73 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.73 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.45/5.73 = A ) ) ) ).
% 5.45/5.73
% 5.45/5.73 % unique_euclidean_semiring_numeral_class.mod_less
% 5.45/5.73 thf(fact_4429_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.45/5.73 ! [A: nat,B: nat] :
% 5.45/5.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.73 => ( ( ord_less_nat @ A @ B )
% 5.45/5.73 => ( ( modulo_modulo_nat @ A @ B )
% 5.45/5.74 = A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.mod_less
% 5.45/5.74 thf(fact_4430_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_int @ A @ B )
% 5.45/5.74 => ( ( modulo_modulo_int @ A @ B )
% 5.45/5.74 = A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.mod_less
% 5.45/5.74 thf(fact_4431_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.45/5.74 ! [B: code_integer,A: code_integer] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.74 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.45/5.74 thf(fact_4432_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.45/5.74 ! [B: nat,A: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.45/5.74 thf(fact_4433_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.45/5.74 thf(fact_4434_cancel__div__mod__rules_I2_J,axiom,
% 5.45/5.74 ! [B: nat,A: nat,C: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_plus_nat @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(2)
% 5.45/5.74 thf(fact_4435_cancel__div__mod__rules_I2_J,axiom,
% 5.45/5.74 ! [B: int,A: int,C: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_plus_int @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(2)
% 5.45/5.74 thf(fact_4436_cancel__div__mod__rules_I2_J,axiom,
% 5.45/5.74 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(2)
% 5.45/5.74 thf(fact_4437_cancel__div__mod__rules_I2_J,axiom,
% 5.45/5.74 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(2)
% 5.45/5.74 thf(fact_4438_cancel__div__mod__rules_I1_J,axiom,
% 5.45/5.74 ! [A: nat,B: nat,C: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_plus_nat @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(1)
% 5.45/5.74 thf(fact_4439_cancel__div__mod__rules_I1_J,axiom,
% 5.45/5.74 ! [A: int,B: int,C: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_plus_int @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(1)
% 5.45/5.74 thf(fact_4440_cancel__div__mod__rules_I1_J,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(1)
% 5.45/5.74 thf(fact_4441_cancel__div__mod__rules_I1_J,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) @ C )
% 5.45/5.74 = ( plus_p4538020629002901425atural @ A @ C ) ) ).
% 5.45/5.74
% 5.45/5.74 % cancel_div_mod_rules(1)
% 5.45/5.74 thf(fact_4442_mod__div__decomp,axiom,
% 5.45/5.74 ! [A: nat,B: nat] :
% 5.45/5.74 ( A
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_decomp
% 5.45/5.74 thf(fact_4443_mod__div__decomp,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( A
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_decomp
% 5.45/5.74 thf(fact_4444_mod__div__decomp,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer] :
% 5.45/5.74 ( A
% 5.45/5.74 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_decomp
% 5.45/5.74 thf(fact_4445_mod__div__decomp,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural] :
% 5.45/5.74 ( A
% 5.45/5.74 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_decomp
% 5.45/5.74 thf(fact_4446_div__mult__mod__eq,axiom,
% 5.45/5.74 ! [A: nat,B: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult_mod_eq
% 5.45/5.74 thf(fact_4447_div__mult__mod__eq,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult_mod_eq
% 5.45/5.74 thf(fact_4448_div__mult__mod__eq,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult_mod_eq
% 5.45/5.74 thf(fact_4449_div__mult__mod__eq,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult_mod_eq
% 5.45/5.74 thf(fact_4450_mod__div__mult__eq,axiom,
% 5.45/5.74 ! [A: nat,B: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_mult_eq
% 5.45/5.74 thf(fact_4451_mod__div__mult__eq,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_mult_eq
% 5.45/5.74 thf(fact_4452_mod__div__mult__eq,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_mult_eq
% 5.45/5.74 thf(fact_4453_mod__div__mult__eq,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_div_mult_eq
% 5.45/5.74 thf(fact_4454_mod__mult__div__eq,axiom,
% 5.45/5.74 ! [A: nat,B: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_mult_div_eq
% 5.45/5.74 thf(fact_4455_mod__mult__div__eq,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_mult_div_eq
% 5.45/5.74 thf(fact_4456_mod__mult__div__eq,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_mult_div_eq
% 5.45/5.74 thf(fact_4457_mod__mult__div__eq,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ B ) @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mod_mult_div_eq
% 5.45/5.74 thf(fact_4458_mult__div__mod__eq,axiom,
% 5.45/5.74 ! [B: nat,A: nat] :
% 5.45/5.74 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mult_div_mod_eq
% 5.45/5.74 thf(fact_4459_mult__div__mod__eq,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mult_div_mod_eq
% 5.45/5.74 thf(fact_4460_mult__div__mod__eq,axiom,
% 5.45/5.74 ! [B: code_integer,A: code_integer] :
% 5.45/5.74 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mult_div_mod_eq
% 5.45/5.74 thf(fact_4461_mult__div__mod__eq,axiom,
% 5.45/5.74 ! [B: code_natural,A: code_natural] :
% 5.45/5.74 ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ A @ B ) ) @ ( modulo8411746178871703098atural @ A @ B ) )
% 5.45/5.74 = A ) ).
% 5.45/5.74
% 5.45/5.74 % mult_div_mod_eq
% 5.45/5.74 thf(fact_4462_div__mult1__eq,axiom,
% 5.45/5.74 ! [A: nat,B: nat,C: nat] :
% 5.45/5.74 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult1_eq
% 5.45/5.74 thf(fact_4463_div__mult1__eq,axiom,
% 5.45/5.74 ! [A: int,B: int,C: int] :
% 5.45/5.74 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult1_eq
% 5.45/5.74 thf(fact_4464_div__mult1__eq,axiom,
% 5.45/5.74 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.74 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.74 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult1_eq
% 5.45/5.74 thf(fact_4465_div__mult1__eq,axiom,
% 5.45/5.74 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.45/5.74 ( ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C )
% 5.45/5.74 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( modulo8411746178871703098atural @ B @ C ) ) @ C ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_mult1_eq
% 5.45/5.74 thf(fact_4466_le__add__iff1,axiom,
% 5.45/5.74 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.74 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff1
% 5.45/5.74 thf(fact_4467_le__add__iff1,axiom,
% 5.45/5.74 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.74 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff1
% 5.45/5.74 thf(fact_4468_le__add__iff1,axiom,
% 5.45/5.74 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff1
% 5.45/5.74 thf(fact_4469_le__add__iff2,axiom,
% 5.45/5.74 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.74 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_le3102999989581377725nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff2
% 5.45/5.74 thf(fact_4470_le__add__iff2,axiom,
% 5.45/5.74 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.74 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff2
% 5.45/5.74 thf(fact_4471_le__add__iff2,axiom,
% 5.45/5.74 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_add_iff2
% 5.45/5.74 thf(fact_4472_less__add__iff1,axiom,
% 5.45/5.74 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff1
% 5.45/5.74 thf(fact_4473_less__add__iff1,axiom,
% 5.45/5.74 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.74 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff1
% 5.45/5.74 thf(fact_4474_less__add__iff1,axiom,
% 5.45/5.74 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.74 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff1
% 5.45/5.74 thf(fact_4475_less__add__iff2,axiom,
% 5.45/5.74 ! [A: code_integer,E: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ E ) @ C ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_le6747313008572928689nteger @ C @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff2
% 5.45/5.74 thf(fact_4476_less__add__iff2,axiom,
% 5.45/5.74 ! [A: rat,E: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.74 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff2
% 5.45/5.74 thf(fact_4477_less__add__iff2,axiom,
% 5.45/5.74 ! [A: int,E: int,C: int,B: int,D2: int] :
% 5.45/5.74 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D2 ) )
% 5.45/5.74 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_add_iff2
% 5.45/5.74 thf(fact_4478_square__diff__one__factored,axiom,
% 5.45/5.74 ! [X: code_integer] :
% 5.45/5.74 ( ( minus_8373710615458151222nteger @ ( times_3573771949741848930nteger @ X @ X ) @ one_one_Code_integer )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ X @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % square_diff_one_factored
% 5.45/5.74 thf(fact_4479_square__diff__one__factored,axiom,
% 5.45/5.74 ! [X: rat] :
% 5.45/5.74 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.45/5.74 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % square_diff_one_factored
% 5.45/5.74 thf(fact_4480_square__diff__one__factored,axiom,
% 5.45/5.74 ! [X: int] :
% 5.45/5.74 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.45/5.74 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % square_diff_one_factored
% 5.45/5.74 thf(fact_4481_add__divide__eq__if__simps_I4_J,axiom,
% 5.45/5.74 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.74 ( ( ( Z = zero_zero_rat )
% 5.45/5.74 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.45/5.74 = A ) )
% 5.45/5.74 & ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.45/5.74 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % add_divide_eq_if_simps(4)
% 5.45/5.74 thf(fact_4482_diff__frac__eq,axiom,
% 5.45/5.74 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 5.45/5.74 ( ( Y != zero_zero_rat )
% 5.45/5.74 => ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.45/5.74 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % diff_frac_eq
% 5.45/5.74 thf(fact_4483_diff__divide__eq__iff,axiom,
% 5.45/5.74 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.74 ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.45/5.74 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % diff_divide_eq_iff
% 5.45/5.74 thf(fact_4484_divide__diff__eq__iff,axiom,
% 5.45/5.74 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.74 ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.45/5.74 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % divide_diff_eq_iff
% 5.45/5.74 thf(fact_4485_mod__le__divisor,axiom,
% 5.45/5.74 ! [N2: nat,M: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.74 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_le_divisor
% 5.45/5.74 thf(fact_4486_power__inject__base,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat,B: code_integer] :
% 5.45/5.74 ( ( ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( power_8256067586552552935nteger @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.74 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.74 => ( A = B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_inject_base
% 5.45/5.74 thf(fact_4487_power__inject__base,axiom,
% 5.45/5.74 ! [A: rat,N2: nat,B: rat] :
% 5.45/5.74 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.74 => ( A = B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_inject_base
% 5.45/5.74 thf(fact_4488_power__inject__base,axiom,
% 5.45/5.74 ! [A: nat,N2: nat,B: nat] :
% 5.45/5.74 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.74 => ( A = B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_inject_base
% 5.45/5.74 thf(fact_4489_power__inject__base,axiom,
% 5.45/5.74 ! [A: int,N2: nat,B: int] :
% 5.45/5.74 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.74 => ( A = B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_inject_base
% 5.45/5.74 thf(fact_4490_power__le__imp__le__base,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat,B: code_integer] :
% 5.45/5.74 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ ( power_8256067586552552935nteger @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.74 => ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_le_imp_le_base
% 5.45/5.74 thf(fact_4491_power__le__imp__le__base,axiom,
% 5.45/5.74 ! [A: rat,N2: nat,B: rat] :
% 5.45/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.74 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_le_imp_le_base
% 5.45/5.74 thf(fact_4492_power__le__imp__le__base,axiom,
% 5.45/5.74 ! [A: nat,N2: nat,B: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.45/5.74 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_le_imp_le_base
% 5.45/5.74 thf(fact_4493_power__le__imp__le__base,axiom,
% 5.45/5.74 ! [A: int,N2: nat,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_le_imp_le_base
% 5.45/5.74 thf(fact_4494_divide__eq__eq__numeral_I1_J,axiom,
% 5.45/5.74 ! [B: rat,C: rat,W2: num] :
% 5.45/5.74 ( ( ( divide_divide_rat @ B @ C )
% 5.45/5.74 = ( numeral_numeral_rat @ W2 ) )
% 5.45/5.74 = ( ( ( C != zero_zero_rat )
% 5.45/5.74 => ( B
% 5.45/5.74 = ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.45/5.74 & ( ( C = zero_zero_rat )
% 5.45/5.74 => ( ( numeral_numeral_rat @ W2 )
% 5.45/5.74 = zero_zero_rat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % divide_eq_eq_numeral(1)
% 5.45/5.74 thf(fact_4495_eq__divide__eq__numeral_I1_J,axiom,
% 5.45/5.74 ! [W2: num,B: rat,C: rat] :
% 5.45/5.74 ( ( ( numeral_numeral_rat @ W2 )
% 5.45/5.74 = ( divide_divide_rat @ B @ C ) )
% 5.45/5.74 = ( ( ( C != zero_zero_rat )
% 5.45/5.74 => ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C )
% 5.45/5.74 = B ) )
% 5.45/5.74 & ( ( C = zero_zero_rat )
% 5.45/5.74 => ( ( numeral_numeral_rat @ W2 )
% 5.45/5.74 = zero_zero_rat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % eq_divide_eq_numeral(1)
% 5.45/5.74 thf(fact_4496_mod__eq__nat1E,axiom,
% 5.45/5.74 ! [M: nat,Q6: nat,N2: nat] :
% 5.45/5.74 ( ( ( modulo_modulo_nat @ M @ Q6 )
% 5.45/5.74 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ~ ! [S7: nat] :
% 5.45/5.74 ( M
% 5.45/5.74 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q6 @ S7 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_eq_nat1E
% 5.45/5.74 thf(fact_4497_mod__eq__nat2E,axiom,
% 5.45/5.74 ! [M: nat,Q6: nat,N2: nat] :
% 5.45/5.74 ( ( ( modulo_modulo_nat @ M @ Q6 )
% 5.45/5.74 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 5.45/5.74 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.74 => ~ ! [S7: nat] :
% 5.45/5.74 ( N2
% 5.45/5.74 != ( plus_plus_nat @ M @ ( times_times_nat @ Q6 @ S7 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_eq_nat2E
% 5.45/5.74 thf(fact_4498_nat__mod__eq__lemma,axiom,
% 5.45/5.74 ! [X: nat,N2: nat,Y: nat] :
% 5.45/5.74 ( ( ( modulo_modulo_nat @ X @ N2 )
% 5.45/5.74 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.45/5.74 => ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.74 => ? [Q5: nat] :
% 5.45/5.74 ( X
% 5.45/5.74 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q5 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_mod_eq_lemma
% 5.45/5.74 thf(fact_4499_div__less__mono,axiom,
% 5.45/5.74 ! [A3: nat,B3: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.74 => ( ( ( modulo_modulo_nat @ A3 @ N2 )
% 5.45/5.74 = zero_zero_nat )
% 5.45/5.74 => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.45/5.74 = zero_zero_nat )
% 5.45/5.74 => ( ord_less_nat @ ( divide_divide_nat @ A3 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_less_mono
% 5.45/5.74 thf(fact_4500_power__gt1,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ A )
% 5.45/5.74 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_gt1
% 5.45/5.74 thf(fact_4501_power__gt1,axiom,
% 5.45/5.74 ! [A: rat,N2: nat] :
% 5.45/5.74 ( ( ord_less_rat @ one_one_rat @ A )
% 5.45/5.74 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_gt1
% 5.45/5.74 thf(fact_4502_power__gt1,axiom,
% 5.45/5.74 ! [A: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ one_one_nat @ A )
% 5.45/5.74 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_gt1
% 5.45/5.74 thf(fact_4503_power__gt1,axiom,
% 5.45/5.74 ! [A: int,N2: nat] :
% 5.45/5.74 ( ( ord_less_int @ one_one_int @ A )
% 5.45/5.74 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_gt1
% 5.45/5.74 thf(fact_4504_nat__diff__split,axiom,
% 5.45/5.74 ! [P: nat > $o,A: nat,B: nat] :
% 5.45/5.74 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.74 = ( ( ( ord_less_nat @ A @ B )
% 5.45/5.74 => ( P @ zero_zero_nat ) )
% 5.45/5.74 & ! [D5: nat] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_nat @ B @ D5 ) )
% 5.45/5.74 => ( P @ D5 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_diff_split
% 5.45/5.74 thf(fact_4505_nat__diff__split__asm,axiom,
% 5.45/5.74 ! [P: nat > $o,A: nat,B: nat] :
% 5.45/5.74 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.74 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.45/5.74 & ~ ( P @ zero_zero_nat ) )
% 5.45/5.74 | ? [D5: nat] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_nat @ B @ D5 ) )
% 5.45/5.74 & ~ ( P @ D5 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_diff_split_asm
% 5.45/5.74 thf(fact_4506_less__diff__conv2,axiom,
% 5.45/5.74 ! [K: nat,J: nat,I2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ K @ J )
% 5.45/5.74 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.45/5.74 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_diff_conv2
% 5.45/5.74 thf(fact_4507_ex__least__nat__less,axiom,
% 5.45/5.74 ! [P: nat > $o,N2: nat] :
% 5.45/5.74 ( ( P @ N2 )
% 5.45/5.74 => ( ~ ( P @ zero_zero_nat )
% 5.45/5.74 => ? [K2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ K2 @ N2 )
% 5.45/5.74 & ! [I: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I @ K2 )
% 5.45/5.74 => ~ ( P @ I ) )
% 5.45/5.74 & ( P @ ( suc @ K2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % ex_least_nat_less
% 5.45/5.74 thf(fact_4508_n__less__n__mult__m,axiom,
% 5.45/5.74 ! [N2: nat,M: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.74 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.45/5.74 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % n_less_n_mult_m
% 5.45/5.74 thf(fact_4509_n__less__m__mult__n,axiom,
% 5.45/5.74 ! [N2: nat,M: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.74 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.45/5.74 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % n_less_m_mult_n
% 5.45/5.74 thf(fact_4510_one__less__mult,axiom,
% 5.45/5.74 ! [N2: nat,M: nat] :
% 5.45/5.74 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.45/5.74 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.45/5.74 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % one_less_mult
% 5.45/5.74 thf(fact_4511_nat__induct__non__zero,axiom,
% 5.45/5.74 ! [N2: nat,P: nat > $o] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.74 => ( ( P @ one_one_nat )
% 5.45/5.74 => ( ! [N5: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.74 => ( ( P @ N5 )
% 5.45/5.74 => ( P @ ( suc @ N5 ) ) ) )
% 5.45/5.74 => ( P @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_induct_non_zero
% 5.45/5.74 thf(fact_4512_nat__eq__add__iff1,axiom,
% 5.45/5.74 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ J @ I2 )
% 5.45/5.74 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 5.45/5.74 = N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_eq_add_iff1
% 5.45/5.74 thf(fact_4513_nat__eq__add__iff2,axiom,
% 5.45/5.74 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.74 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( M
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_eq_add_iff2
% 5.45/5.74 thf(fact_4514_nat__le__add__iff1,axiom,
% 5.45/5.74 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ J @ I2 )
% 5.45/5.74 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_le_add_iff1
% 5.45/5.74 thf(fact_4515_nat__le__add__iff2,axiom,
% 5.45/5.74 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.74 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_le_add_iff2
% 5.45/5.74 thf(fact_4516_nat__diff__add__eq1,axiom,
% 5.45/5.74 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ J @ I2 )
% 5.45/5.74 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_diff_add_eq1
% 5.45/5.74 thf(fact_4517_nat__diff__add__eq2,axiom,
% 5.45/5.74 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.74 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_diff_add_eq2
% 5.45/5.74 thf(fact_4518_power__gt__expt,axiom,
% 5.45/5.74 ! [N2: nat,K: nat] :
% 5.45/5.74 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.45/5.74 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_gt_expt
% 5.45/5.74 thf(fact_4519_nat__one__le__power,axiom,
% 5.45/5.74 ! [I2: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I2 )
% 5.45/5.74 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I2 @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_one_le_power
% 5.45/5.74 thf(fact_4520_frac__le__eq,axiom,
% 5.45/5.74 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 5.45/5.74 ( ( Y != zero_zero_rat )
% 5.45/5.74 => ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.45/5.74 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % frac_le_eq
% 5.45/5.74 thf(fact_4521_frac__less__eq,axiom,
% 5.45/5.74 ! [Y: rat,Z: rat,X: rat,W2: rat] :
% 5.45/5.74 ( ( Y != zero_zero_rat )
% 5.45/5.74 => ( ( Z != zero_zero_rat )
% 5.45/5.74 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W2 @ Z ) )
% 5.45/5.74 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W2 @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % frac_less_eq
% 5.45/5.74 thf(fact_4522_split__mod,axiom,
% 5.45/5.74 ! [P: nat > $o,M: nat,N2: nat] :
% 5.45/5.74 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.45/5.74 = ( ( ( N2 = zero_zero_nat )
% 5.45/5.74 => ( P @ M ) )
% 5.45/5.74 & ( ( N2 != zero_zero_nat )
% 5.45/5.74 => ! [I4: nat,J3: nat] :
% 5.45/5.74 ( ( ord_less_nat @ J3 @ N2 )
% 5.45/5.74 => ( ( M
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I4 ) @ J3 ) )
% 5.45/5.74 => ( P @ J3 ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % split_mod
% 5.45/5.74 thf(fact_4523_divide__less__eq__numeral_I1_J,axiom,
% 5.45/5.74 ! [B: rat,C: rat,W2: num] :
% 5.45/5.74 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.74 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % divide_less_eq_numeral(1)
% 5.45/5.74 thf(fact_4524_less__divide__eq__numeral_I1_J,axiom,
% 5.45/5.74 ! [W2: num,B: rat,C: rat] :
% 5.45/5.74 ( ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.74 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_rat @ ( numeral_numeral_rat @ W2 ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % less_divide_eq_numeral(1)
% 5.45/5.74 thf(fact_4525_power__Suc__le__self,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat] :
% 5.45/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.74 => ( ( ord_le3102999989581377725nteger @ A @ one_one_Code_integer )
% 5.45/5.74 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_le_self
% 5.45/5.74 thf(fact_4526_power__Suc__le__self,axiom,
% 5.45/5.74 ! [A: rat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.74 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.45/5.74 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_le_self
% 5.45/5.74 thf(fact_4527_power__Suc__le__self,axiom,
% 5.45/5.74 ! [A: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.74 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.45/5.74 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_le_self
% 5.45/5.74 thf(fact_4528_power__Suc__le__self,axiom,
% 5.45/5.74 ! [A: int,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.45/5.74 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_le_self
% 5.45/5.74 thf(fact_4529_power__Suc__less__one,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.74 => ( ( ord_le6747313008572928689nteger @ A @ one_one_Code_integer )
% 5.45/5.74 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_less_one
% 5.45/5.74 thf(fact_4530_power__Suc__less__one,axiom,
% 5.45/5.74 ! [A: rat,N2: nat] :
% 5.45/5.74 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.74 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.45/5.74 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ one_one_rat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_less_one
% 5.45/5.74 thf(fact_4531_power__Suc__less__one,axiom,
% 5.45/5.74 ! [A: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.45/5.74 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.45/5.74 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ one_one_nat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_less_one
% 5.45/5.74 thf(fact_4532_power__Suc__less__one,axiom,
% 5.45/5.74 ! [A: int,N2: nat] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_int @ A @ one_one_int )
% 5.45/5.74 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ one_one_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_Suc_less_one
% 5.45/5.74 thf(fact_4533_power__diff,axiom,
% 5.45/5.74 ! [A: nat,N2: nat,M: nat] :
% 5.45/5.74 ( ( A != zero_zero_nat )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.74 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_diff
% 5.45/5.74 thf(fact_4534_power__diff,axiom,
% 5.45/5.74 ! [A: int,N2: nat,M: nat] :
% 5.45/5.74 ( ( A != zero_zero_int )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.74 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_diff
% 5.45/5.74 thf(fact_4535_power__diff,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat,M: nat] :
% 5.45/5.74 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.74 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_diff
% 5.45/5.74 thf(fact_4536_power__diff,axiom,
% 5.45/5.74 ! [A: rat,N2: nat,M: nat] :
% 5.45/5.74 ( ( A != zero_zero_rat )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.74 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_diff
% 5.45/5.74 thf(fact_4537_power__diff,axiom,
% 5.45/5.74 ! [A: code_natural,N2: nat,M: nat] :
% 5.45/5.74 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( power_7079662738309270450atural @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.74 = ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ A @ M ) @ ( power_7079662738309270450atural @ A @ N2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % power_diff
% 5.45/5.74 thf(fact_4538_nat__less__add__iff1,axiom,
% 5.45/5.74 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ J @ I2 )
% 5.45/5.74 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_less_add_iff1
% 5.45/5.74 thf(fact_4539_nat__less__add__iff2,axiom,
% 5.45/5.74 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.74 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.45/5.74 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_less_add_iff2
% 5.45/5.74 thf(fact_4540_mult__eq__if,axiom,
% 5.45/5.74 ( times_times_nat
% 5.45/5.74 = ( ^ [M3: nat,N: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mult_eq_if
% 5.45/5.74 thf(fact_4541_div__nat__eqI,axiom,
% 5.45/5.74 ! [N2: nat,Q6: nat,M: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q6 ) @ M )
% 5.45/5.74 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q6 ) ) )
% 5.45/5.74 => ( ( divide_divide_nat @ M @ N2 )
% 5.45/5.74 = Q6 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_nat_eqI
% 5.45/5.74 thf(fact_4542_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.45/5.74 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.74 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.45/5.74 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.74 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.45/5.74 thf(fact_4543_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.45/5.74 ! [C: nat,A: nat,B: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.45/5.74 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.74 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.45/5.74 thf(fact_4544_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.45/5.74 ! [C: int,A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.74 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.45/5.74 thf(fact_4545_scaling__mono,axiom,
% 5.45/5.74 ! [U: rat,V: rat,R3: rat,S2: rat] :
% 5.45/5.74 ( ( ord_less_eq_rat @ U @ V )
% 5.45/5.74 => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 5.45/5.74 => ( ( ord_less_eq_rat @ R3 @ S2 )
% 5.45/5.74 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S2 ) ) @ V ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % scaling_mono
% 5.45/5.74 thf(fact_4546_divide__le__eq__numeral_I1_J,axiom,
% 5.45/5.74 ! [B: rat,C: rat,W2: num] :
% 5.45/5.74 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.74 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.74 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ C ) @ B ) )
% 5.45/5.74 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % divide_le_eq_numeral(1)
% 5.45/5.74 thf(fact_4547_nat__approx__posE,axiom,
% 5.45/5.74 ! [E: rat] :
% 5.45/5.74 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.45/5.74 => ~ ! [N5: nat] :
% 5.45/5.74 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N5 ) ) ) @ E ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat_approx_posE
% 5.45/5.74 thf(fact_4548_ex__less__of__nat__mult,axiom,
% 5.45/5.74 ! [X: rat,Y: rat] :
% 5.45/5.74 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.74 => ? [N5: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N5 ) @ X ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % ex_less_of_nat_mult
% 5.45/5.74 thf(fact_4549_of__nat__code,axiom,
% 5.45/5.74 ( semiri681578069525770553at_rat
% 5.45/5.74 = ( ^ [N: nat] :
% 5.45/5.74 ( semiri7787848453975740701ux_rat
% 5.45/5.74 @ ^ [I4: rat] : ( plus_plus_rat @ I4 @ one_one_rat )
% 5.45/5.74 @ N
% 5.45/5.74 @ zero_zero_rat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % of_nat_code
% 5.45/5.74 thf(fact_4550_of__nat__code,axiom,
% 5.45/5.74 ( semiri1314217659103216013at_int
% 5.45/5.74 = ( ^ [N: nat] :
% 5.45/5.74 ( semiri8420488043553186161ux_int
% 5.45/5.74 @ ^ [I4: int] : ( plus_plus_int @ I4 @ one_one_int )
% 5.45/5.74 @ N
% 5.45/5.74 @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % of_nat_code
% 5.45/5.74 thf(fact_4551_of__nat__code,axiom,
% 5.45/5.74 ( semiri1316708129612266289at_nat
% 5.45/5.74 = ( ^ [N: nat] :
% 5.45/5.74 ( semiri8422978514062236437ux_nat
% 5.45/5.74 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ one_one_nat )
% 5.45/5.74 @ N
% 5.45/5.74 @ zero_zero_nat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % of_nat_code
% 5.45/5.74 thf(fact_4552_of__nat__code,axiom,
% 5.45/5.74 ( semiri4939895301339042750nteger
% 5.45/5.74 = ( ^ [N: nat] :
% 5.45/5.74 ( semiri4055485073559036834nteger
% 5.45/5.74 @ ^ [I4: code_integer] : ( plus_p5714425477246183910nteger @ I4 @ one_one_Code_integer )
% 5.45/5.74 @ N
% 5.45/5.74 @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % of_nat_code
% 5.45/5.74 thf(fact_4553_gcd__nat__induct,axiom,
% 5.45/5.74 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.45/5.74 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.45/5.74 => ( ! [M5: nat,N5: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.74 => ( ( P @ N5 @ ( modulo_modulo_nat @ M5 @ N5 ) )
% 5.45/5.74 => ( P @ M5 @ N5 ) ) )
% 5.45/5.74 => ( P @ M @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % gcd_nat_induct
% 5.45/5.74 thf(fact_4554_option_Osize__gen_I2_J,axiom,
% 5.45/5.74 ! [X: produc3260487557148687353it_nat > nat,X2: produc3260487557148687353it_nat] :
% 5.45/5.74 ( ( size_o1731029420616209814it_nat @ X @ ( some_P7913643980934408916it_nat @ X2 ) )
% 5.45/5.74 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % option.size_gen(2)
% 5.45/5.74 thf(fact_4555_option_Osize__gen_I2_J,axiom,
% 5.45/5.74 ! [X: num > nat,X2: num] :
% 5.45/5.74 ( ( size_option_num @ X @ ( some_num @ X2 ) )
% 5.45/5.74 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % option.size_gen(2)
% 5.45/5.74 thf(fact_4556_option_Osize__gen_I2_J,axiom,
% 5.45/5.74 ! [X: produc8664842809031399944it_nat > nat,X2: produc8664842809031399944it_nat] :
% 5.45/5.74 ( ( size_o29782932136985253it_nat @ X @ ( some_P1914260805536162275it_nat @ X2 ) )
% 5.45/5.74 = ( plus_plus_nat @ ( X @ X2 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % option.size_gen(2)
% 5.45/5.74 thf(fact_4557_pochhammer__code,axiom,
% 5.45/5.74 ( comm_s4028243227959126397er_rat
% 5.45/5.74 = ( ^ [A5: rat,N: nat] :
% 5.45/5.74 ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 5.45/5.74 @ ( set_fo1949268297981939178at_rat
% 5.45/5.74 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.45/5.74 @ zero_zero_nat
% 5.45/5.74 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.45/5.74 @ one_one_rat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_code
% 5.45/5.74 thf(fact_4558_pochhammer__code,axiom,
% 5.45/5.74 ( comm_s4660882817536571857er_int
% 5.45/5.74 = ( ^ [A5: int,N: nat] :
% 5.45/5.74 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 5.45/5.74 @ ( set_fo2581907887559384638at_int
% 5.45/5.74 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.45/5.74 @ zero_zero_nat
% 5.45/5.74 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.45/5.74 @ one_one_int ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_code
% 5.45/5.74 thf(fact_4559_pochhammer__code,axiom,
% 5.45/5.74 ( comm_s8582702949713902594nteger
% 5.45/5.74 = ( ^ [A5: code_integer,N: nat] :
% 5.45/5.74 ( if_Code_integer @ ( N = zero_zero_nat ) @ one_one_Code_integer
% 5.45/5.74 @ ( set_fo1084959871951514735nteger
% 5.45/5.74 @ ^ [O: nat] : ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ O ) ) )
% 5.45/5.74 @ zero_zero_nat
% 5.45/5.74 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.45/5.74 @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_code
% 5.45/5.74 thf(fact_4560_pochhammer__code,axiom,
% 5.45/5.74 ( comm_s4663373288045622133er_nat
% 5.45/5.74 = ( ^ [A5: nat,N: nat] :
% 5.45/5.74 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 5.45/5.74 @ ( set_fo2584398358068434914at_nat
% 5.45/5.74 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.45/5.74 @ zero_zero_nat
% 5.45/5.74 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.45/5.74 @ one_one_nat ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_code
% 5.45/5.74 thf(fact_4561_option_Osize__gen_I1_J,axiom,
% 5.45/5.74 ! [X: num > nat] :
% 5.45/5.74 ( ( size_option_num @ X @ none_num )
% 5.45/5.74 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % option.size_gen(1)
% 5.45/5.74 thf(fact_4562_Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ A3 @ A3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_cancel
% 5.45/5.74 thf(fact_4563_Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_o] :
% 5.45/5.74 ( ( minus_minus_set_o @ A3 @ A3 )
% 5.45/5.74 = bot_bot_set_o ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_cancel
% 5.45/5.74 thf(fact_4564_Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_int] :
% 5.45/5.74 ( ( minus_minus_set_int @ A3 @ A3 )
% 5.45/5.74 = bot_bot_set_int ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_cancel
% 5.45/5.74 thf(fact_4565_Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ A3 @ A3 )
% 5.45/5.74 = bot_bot_set_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_cancel
% 5.45/5.74 thf(fact_4566_empty__Diff,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ bot_bo2099793752762293965at_nat @ A3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.74
% 5.45/5.74 % empty_Diff
% 5.45/5.74 thf(fact_4567_empty__Diff,axiom,
% 5.45/5.74 ! [A3: set_o] :
% 5.45/5.74 ( ( minus_minus_set_o @ bot_bot_set_o @ A3 )
% 5.45/5.74 = bot_bot_set_o ) ).
% 5.45/5.74
% 5.45/5.74 % empty_Diff
% 5.45/5.74 thf(fact_4568_empty__Diff,axiom,
% 5.45/5.74 ! [A3: set_int] :
% 5.45/5.74 ( ( minus_minus_set_int @ bot_bot_set_int @ A3 )
% 5.45/5.74 = bot_bot_set_int ) ).
% 5.45/5.74
% 5.45/5.74 % empty_Diff
% 5.45/5.74 thf(fact_4569_empty__Diff,axiom,
% 5.45/5.74 ! [A3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A3 )
% 5.45/5.74 = bot_bot_set_nat ) ).
% 5.45/5.74
% 5.45/5.74 % empty_Diff
% 5.45/5.74 thf(fact_4570_Diff__empty,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ A3 @ bot_bo2099793752762293965at_nat )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_empty
% 5.45/5.74 thf(fact_4571_Diff__empty,axiom,
% 5.45/5.74 ! [A3: set_o] :
% 5.45/5.74 ( ( minus_minus_set_o @ A3 @ bot_bot_set_o )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_empty
% 5.45/5.74 thf(fact_4572_Diff__empty,axiom,
% 5.45/5.74 ! [A3: set_int] :
% 5.45/5.74 ( ( minus_minus_set_int @ A3 @ bot_bot_set_int )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_empty
% 5.45/5.74 thf(fact_4573_Diff__empty,axiom,
% 5.45/5.74 ! [A3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ A3 @ bot_bot_set_nat )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_empty
% 5.45/5.74 thf(fact_4574_Un__Diff__cancel2,axiom,
% 5.45/5.74 ! [B3: set_Pr8693737435421807431at_nat,A3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ B3 @ A3 ) @ A3 )
% 5.45/5.74 = ( sup_su718114333110466843at_nat @ B3 @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel2
% 5.45/5.74 thf(fact_4575_Un__Diff__cancel2,axiom,
% 5.45/5.74 ! [B3: set_Pr8551490117392284871at_nat,A3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ B3 @ A3 ) @ A3 )
% 5.45/5.74 = ( sup_su3035147773818789531at_nat @ B3 @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel2
% 5.45/5.74 thf(fact_4576_Un__Diff__cancel2,axiom,
% 5.45/5.74 ! [B3: set_Pr4329608150637261639at_nat,A3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ B3 @ A3 ) @ A3 )
% 5.45/5.74 = ( sup_su5525570899277871387at_nat @ B3 @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel2
% 5.45/5.74 thf(fact_4577_Un__Diff__cancel2,axiom,
% 5.45/5.74 ! [B3: set_nat,A3: set_nat] :
% 5.45/5.74 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ B3 @ A3 ) @ A3 )
% 5.45/5.74 = ( sup_sup_set_nat @ B3 @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel2
% 5.45/5.74 thf(fact_4578_Un__Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( sup_su718114333110466843at_nat @ A3 @ ( minus_8321449233255521966at_nat @ B3 @ A3 ) )
% 5.45/5.74 = ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel
% 5.45/5.74 thf(fact_4579_Un__Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( sup_su3035147773818789531at_nat @ A3 @ ( minus_5060654252129873198at_nat @ B3 @ A3 ) )
% 5.45/5.74 = ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel
% 5.45/5.74 thf(fact_4580_Un__Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( sup_su5525570899277871387at_nat @ A3 @ ( minus_3314409938677909166at_nat @ B3 @ A3 ) )
% 5.45/5.74 = ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel
% 5.45/5.74 thf(fact_4581_Un__Diff__cancel,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( sup_sup_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.74 = ( sup_sup_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_cancel
% 5.45/5.74 thf(fact_4582_Diff__eq__empty__iff,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat )
% 5.45/5.74 = ( ord_le3146513528884898305at_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_eq_empty_iff
% 5.45/5.74 thf(fact_4583_Diff__eq__empty__iff,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ( minus_minus_set_o @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_o )
% 5.45/5.74 = ( ord_less_eq_set_o @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_eq_empty_iff
% 5.45/5.74 thf(fact_4584_Diff__eq__empty__iff,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ( minus_minus_set_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_nat )
% 5.45/5.74 = ( ord_less_eq_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_eq_empty_iff
% 5.45/5.74 thf(fact_4585_Diff__eq__empty__iff,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ( minus_minus_set_int @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_int )
% 5.45/5.74 = ( ord_less_eq_set_int @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_eq_empty_iff
% 5.45/5.74 thf(fact_4586_Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_disjoint
% 5.45/5.74 thf(fact_4587_Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( inf_inf_set_o @ A3 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.74 = bot_bot_set_o ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_disjoint
% 5.45/5.74 thf(fact_4588_Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( inf_inf_set_int @ A3 @ ( minus_minus_set_int @ B3 @ A3 ) )
% 5.45/5.74 = bot_bot_set_int ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_disjoint
% 5.45/5.74 thf(fact_4589_Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.74 = bot_bot_set_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_disjoint
% 5.45/5.74 thf(fact_4590_mod__pos__pos__trivial,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ( ord_less_int @ K @ L )
% 5.45/5.74 => ( ( modulo_modulo_int @ K @ L )
% 5.45/5.74 = K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_pos_pos_trivial
% 5.45/5.74 thf(fact_4591_mod__neg__neg__trivial,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ L @ K )
% 5.45/5.74 => ( ( modulo_modulo_int @ K @ L )
% 5.45/5.74 = K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_neg_neg_trivial
% 5.45/5.74 thf(fact_4592_div__pos__pos__trivial,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ( ord_less_int @ K @ L )
% 5.45/5.74 => ( ( divide_divide_int @ K @ L )
% 5.45/5.74 = zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_pos_pos_trivial
% 5.45/5.74 thf(fact_4593_div__neg__neg__trivial,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ L @ K )
% 5.45/5.74 => ( ( divide_divide_int @ K @ L )
% 5.45/5.74 = zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_neg_neg_trivial
% 5.45/5.74 thf(fact_4594_div__pos__geq,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ( ord_less_eq_int @ L @ K )
% 5.45/5.74 => ( ( divide_divide_int @ K @ L )
% 5.45/5.74 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_pos_geq
% 5.45/5.74 thf(fact_4595_verit__le__mono__div__int,axiom,
% 5.45/5.74 ! [A3: int,B3: int,N2: int] :
% 5.45/5.74 ( ( ord_less_int @ A3 @ B3 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.45/5.74 => ( ord_less_eq_int
% 5.45/5.74 @ ( plus_plus_int @ ( divide_divide_int @ A3 @ N2 )
% 5.45/5.74 @ ( if_int
% 5.45/5.74 @ ( ( modulo_modulo_int @ B3 @ N2 )
% 5.45/5.74 = zero_zero_int )
% 5.45/5.74 @ one_one_int
% 5.45/5.74 @ zero_zero_int ) )
% 5.45/5.74 @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % verit_le_mono_div_int
% 5.45/5.74 thf(fact_4596_zdiv__mono__strict,axiom,
% 5.45/5.74 ! [A3: int,B3: int,N2: int] :
% 5.45/5.74 ( ( ord_less_int @ A3 @ B3 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.45/5.74 => ( ( ( modulo_modulo_int @ A3 @ N2 )
% 5.45/5.74 = zero_zero_int )
% 5.45/5.74 => ( ( ( modulo_modulo_int @ B3 @ N2 )
% 5.45/5.74 = zero_zero_int )
% 5.45/5.74 => ( ord_less_int @ ( divide_divide_int @ A3 @ N2 ) @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono_strict
% 5.45/5.74 thf(fact_4597_split__pos__lemma,axiom,
% 5.45/5.74 ! [K: int,P: int > int > $o,N2: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.45/5.74 = ( ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.45/5.74 & ( ord_less_int @ J3 @ K )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % split_pos_lemma
% 5.45/5.74 thf(fact_4598_split__neg__lemma,axiom,
% 5.45/5.74 ! [K: int,P: int > int > $o,N2: int] :
% 5.45/5.74 ( ( ord_less_int @ K @ zero_zero_int )
% 5.45/5.74 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.45/5.74 = ( ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_int @ K @ J3 )
% 5.45/5.74 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ I4 @ J3 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % split_neg_lemma
% 5.45/5.74 thf(fact_4599_zmod__zmult2__eq,axiom,
% 5.45/5.74 ! [C: int,A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.74 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zmod_zmult2_eq
% 5.45/5.74 thf(fact_4600_Euclidean__Division_Opos__mod__sign,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Euclidean_Division.pos_mod_sign
% 5.45/5.74 thf(fact_4601_neg__mod__sign,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ L @ zero_zero_int )
% 5.45/5.74 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % neg_mod_sign
% 5.45/5.74 thf(fact_4602_Euclidean__Division_Opos__mod__bound,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.45/5.74
% 5.45/5.74 % Euclidean_Division.pos_mod_bound
% 5.45/5.74 thf(fact_4603_neg__mod__bound,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ L @ zero_zero_int )
% 5.45/5.74 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % neg_mod_bound
% 5.45/5.74 thf(fact_4604_mod__pos__neg__trivial,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.45/5.74 => ( ( modulo_modulo_int @ K @ L )
% 5.45/5.74 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_pos_neg_trivial
% 5.45/5.74 thf(fact_4605_zmod__le__nonneg__dividend,axiom,
% 5.45/5.74 ! [M: int,K: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.45/5.74 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.45/5.74
% 5.45/5.74 % zmod_le_nonneg_dividend
% 5.45/5.74 thf(fact_4606_mod__pos__geq,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ( ord_less_eq_int @ L @ K )
% 5.45/5.74 => ( ( modulo_modulo_int @ K @ L )
% 5.45/5.74 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % mod_pos_geq
% 5.45/5.74 thf(fact_4607_neg__mod__conj,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.45/5.74 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % neg_mod_conj
% 5.45/5.74 thf(fact_4608_pos__mod__conj,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.45/5.74 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_mod_conj
% 5.45/5.74 thf(fact_4609_zmod__trivial__iff,axiom,
% 5.45/5.74 ! [I2: int,K: int] :
% 5.45/5.74 ( ( ( modulo_modulo_int @ I2 @ K )
% 5.45/5.74 = I2 )
% 5.45/5.74 = ( ( K = zero_zero_int )
% 5.45/5.74 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.45/5.74 & ( ord_less_int @ I2 @ K ) )
% 5.45/5.74 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.45/5.74 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zmod_trivial_iff
% 5.45/5.74 thf(fact_4610_plusinfinity,axiom,
% 5.45/5.74 ! [D2: int,P6: int > $o,P: int > $o] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.74 => ( ! [X3: int,K2: int] :
% 5.45/5.74 ( ( P6 @ X3 )
% 5.45/5.74 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.45/5.74 => ( ? [Z5: int] :
% 5.45/5.74 ! [X3: int] :
% 5.45/5.74 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.74 => ( ( P @ X3 )
% 5.45/5.74 = ( P6 @ X3 ) ) )
% 5.45/5.74 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.45/5.74 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % plusinfinity
% 5.45/5.74 thf(fact_4611_minusinfinity,axiom,
% 5.45/5.74 ! [D2: int,P1: int > $o,P: int > $o] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.74 => ( ! [X3: int,K2: int] :
% 5.45/5.74 ( ( P1 @ X3 )
% 5.45/5.74 = ( P1 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.45/5.74 => ( ? [Z5: int] :
% 5.45/5.74 ! [X3: int] :
% 5.45/5.74 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.74 => ( ( P @ X3 )
% 5.45/5.74 = ( P1 @ X3 ) ) )
% 5.45/5.74 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.45/5.74 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minusinfinity
% 5.45/5.74 thf(fact_4612_decr__mult__lemma,axiom,
% 5.45/5.74 ! [D2: int,P: int > $o,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.74 => ( ! [X3: int] :
% 5.45/5.74 ( ( P @ X3 )
% 5.45/5.74 => ( P @ ( minus_minus_int @ X3 @ D2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ! [X7: int] :
% 5.45/5.74 ( ( P @ X7 )
% 5.45/5.74 => ( P @ ( minus_minus_int @ X7 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % decr_mult_lemma
% 5.45/5.74 thf(fact_4613_int__mod__pos__eq,axiom,
% 5.45/5.74 ! [A: int,B: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.45/5.74 => ( ( ord_less_int @ R3 @ B )
% 5.45/5.74 => ( ( modulo_modulo_int @ A @ B )
% 5.45/5.74 = R3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_mod_pos_eq
% 5.45/5.74 thf(fact_4614_int__mod__neg__eq,axiom,
% 5.45/5.74 ! [A: int,B: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ B @ R3 )
% 5.45/5.74 => ( ( modulo_modulo_int @ A @ B )
% 5.45/5.74 = R3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_mod_neg_eq
% 5.45/5.74 thf(fact_4615_split__zmod,axiom,
% 5.45/5.74 ! [P: int > $o,N2: int,K: int] :
% 5.45/5.74 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 5.45/5.74 = ( ( ( K = zero_zero_int )
% 5.45/5.74 => ( P @ N2 ) )
% 5.45/5.74 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.45/5.74 & ( ord_less_int @ J3 @ K )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ J3 ) ) )
% 5.45/5.74 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.45/5.74 => ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_int @ K @ J3 )
% 5.45/5.74 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ J3 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % split_zmod
% 5.45/5.74 thf(fact_4616_q__pos__lemma,axiom,
% 5.45/5.74 ! [B2: int,Q8: int,R7: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q8 ) @ R7 ) )
% 5.45/5.74 => ( ( ord_less_int @ R7 @ B2 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.45/5.74 => ( ord_less_eq_int @ zero_zero_int @ Q8 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % q_pos_lemma
% 5.45/5.74 thf(fact_4617_zdiv__mono2__lemma,axiom,
% 5.45/5.74 ! [B: int,Q6: int,R3: int,B2: int,Q8: int,R7: int] :
% 5.45/5.74 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 )
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B2 @ Q8 ) @ R7 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q8 ) @ R7 ) )
% 5.45/5.74 => ( ( ord_less_int @ R7 @ B2 )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.45/5.74 => ( ( ord_less_eq_int @ B2 @ B )
% 5.45/5.74 => ( ord_less_eq_int @ Q6 @ Q8 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono2_lemma
% 5.45/5.74 thf(fact_4618_incr__mult__lemma,axiom,
% 5.45/5.74 ! [D2: int,P: int > $o,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.74 => ( ! [X3: int] :
% 5.45/5.74 ( ( P @ X3 )
% 5.45/5.74 => ( P @ ( plus_plus_int @ X3 @ D2 ) ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ! [X7: int] :
% 5.45/5.74 ( ( P @ X7 )
% 5.45/5.74 => ( P @ ( plus_plus_int @ X7 @ ( times_times_int @ K @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % incr_mult_lemma
% 5.45/5.74 thf(fact_4619_zdiv__mono2__neg__lemma,axiom,
% 5.45/5.74 ! [B: int,Q6: int,R3: int,B2: int,Q8: int,R7: int] :
% 5.45/5.74 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 )
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B2 @ Q8 ) @ R7 ) )
% 5.45/5.74 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B2 @ Q8 ) @ R7 ) @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ R3 @ B )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R7 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.45/5.74 => ( ( ord_less_eq_int @ B2 @ B )
% 5.45/5.74 => ( ord_less_eq_int @ Q8 @ Q6 ) ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono2_neg_lemma
% 5.45/5.74 thf(fact_4620_unique__quotient__lemma,axiom,
% 5.45/5.74 ! [B: int,Q8: int,R7: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q8 ) @ R7 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R7 )
% 5.45/5.74 => ( ( ord_less_int @ R7 @ B )
% 5.45/5.74 => ( ( ord_less_int @ R3 @ B )
% 5.45/5.74 => ( ord_less_eq_int @ Q8 @ Q6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_quotient_lemma
% 5.45/5.74 thf(fact_4621_unique__quotient__lemma__neg,axiom,
% 5.45/5.74 ! [B: int,Q8: int,R7: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q8 ) @ R7 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ B @ R3 )
% 5.45/5.74 => ( ( ord_less_int @ B @ R7 )
% 5.45/5.74 => ( ord_less_eq_int @ Q6 @ Q8 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % unique_quotient_lemma_neg
% 5.45/5.74 thf(fact_4622_imp__le__cong,axiom,
% 5.45/5.74 ! [X: int,X10: int,P: $o,P6: $o] :
% 5.45/5.74 ( ( X = X10 )
% 5.45/5.74 => ( ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 5.45/5.74 => ( P = P6 ) )
% 5.45/5.74 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.74 => P )
% 5.45/5.74 = ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 5.45/5.74 => P6 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % imp_le_cong
% 5.45/5.74 thf(fact_4623_conj__le__cong,axiom,
% 5.45/5.74 ! [X: int,X10: int,P: $o,P6: $o] :
% 5.45/5.74 ( ( X = X10 )
% 5.45/5.74 => ( ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 5.45/5.74 => ( P = P6 ) )
% 5.45/5.74 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.74 & P )
% 5.45/5.74 = ( ( ord_less_eq_int @ zero_zero_int @ X10 )
% 5.45/5.74 & P6 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % conj_le_cong
% 5.45/5.74 thf(fact_4624_verit__la__generic,axiom,
% 5.45/5.74 ! [A: int,X: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ A @ X )
% 5.45/5.74 | ( A = X )
% 5.45/5.74 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.45/5.74
% 5.45/5.74 % verit_la_generic
% 5.45/5.74 thf(fact_4625_split__zdiv,axiom,
% 5.45/5.74 ! [P: int > $o,N2: int,K: int] :
% 5.45/5.74 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 5.45/5.74 = ( ( ( K = zero_zero_int )
% 5.45/5.74 => ( P @ zero_zero_int ) )
% 5.45/5.74 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.45/5.74 & ( ord_less_int @ J3 @ K )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ I4 ) ) )
% 5.45/5.74 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.45/5.74 => ! [I4: int,J3: int] :
% 5.45/5.74 ( ( ( ord_less_int @ K @ J3 )
% 5.45/5.74 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.45/5.74 & ( N2
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ K @ I4 ) @ J3 ) ) )
% 5.45/5.74 => ( P @ I4 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % split_zdiv
% 5.45/5.74 thf(fact_4626_int__div__neg__eq,axiom,
% 5.45/5.74 ! [A: int,B: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ B @ R3 )
% 5.45/5.74 => ( ( divide_divide_int @ A @ B )
% 5.45/5.74 = Q6 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_div_neg_eq
% 5.45/5.74 thf(fact_4627_int__div__pos__eq,axiom,
% 5.45/5.74 ! [A: int,B: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( A
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ B @ Q6 ) @ R3 ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.45/5.74 => ( ( ord_less_int @ R3 @ B )
% 5.45/5.74 => ( ( divide_divide_int @ A @ B )
% 5.45/5.74 = Q6 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_div_pos_eq
% 5.45/5.74 thf(fact_4628_zdiv__zmult2__eq,axiom,
% 5.45/5.74 ! [C: int,A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.45/5.74 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.74 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_zmult2_eq
% 5.45/5.74 thf(fact_4629_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.45/5.74 = ( ( ord_less_eq_int @ B @ A )
% 5.45/5.74 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nonneg1_imp_zdiv_pos_iff
% 5.45/5.74 thf(fact_4630_pos__imp__zdiv__nonneg__iff,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.45/5.74 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_imp_zdiv_nonneg_iff
% 5.45/5.74 thf(fact_4631_neg__imp__zdiv__nonneg__iff,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.45/5.74 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % neg_imp_zdiv_nonneg_iff
% 5.45/5.74 thf(fact_4632_pos__imp__zdiv__pos__iff,axiom,
% 5.45/5.74 ! [K: int,I2: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 5.45/5.74 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_imp_zdiv_pos_iff
% 5.45/5.74 thf(fact_4633_div__nonpos__pos__le0,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_nonpos_pos_le0
% 5.45/5.74 thf(fact_4634_div__nonneg__neg__le0,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_nonneg_neg_le0
% 5.45/5.74 thf(fact_4635_div__positive__int,axiom,
% 5.45/5.74 ! [L: int,K: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ L @ K )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_positive_int
% 5.45/5.74 thf(fact_4636_div__int__pos__iff,axiom,
% 5.45/5.74 ! [K: int,L: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.45/5.74 = ( ( K = zero_zero_int )
% 5.45/5.74 | ( L = zero_zero_int )
% 5.45/5.74 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.45/5.74 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.45/5.74 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_int_pos_iff
% 5.45/5.74 thf(fact_4637_zdiv__mono2__neg,axiom,
% 5.45/5.74 ! [A: int,B2: int,B: int] :
% 5.45/5.74 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.45/5.74 => ( ( ord_less_eq_int @ B2 @ B )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B2 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono2_neg
% 5.45/5.74 thf(fact_4638_zdiv__mono1__neg,axiom,
% 5.45/5.74 ! [A: int,A2: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ A @ A2 )
% 5.45/5.74 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A2 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono1_neg
% 5.45/5.74 thf(fact_4639_zdiv__eq__0__iff,axiom,
% 5.45/5.74 ! [I2: int,K: int] :
% 5.45/5.74 ( ( ( divide_divide_int @ I2 @ K )
% 5.45/5.74 = zero_zero_int )
% 5.45/5.74 = ( ( K = zero_zero_int )
% 5.45/5.74 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.45/5.74 & ( ord_less_int @ I2 @ K ) )
% 5.45/5.74 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.45/5.74 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_eq_0_iff
% 5.45/5.74 thf(fact_4640_zdiv__mono2,axiom,
% 5.45/5.74 ! [A: int,B2: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B2 )
% 5.45/5.74 => ( ( ord_less_eq_int @ B2 @ B )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B2 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono2
% 5.45/5.74 thf(fact_4641_zdiv__mono1,axiom,
% 5.45/5.74 ! [A: int,A2: int,B: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ A @ A2 )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A2 @ B ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiv_mono1
% 5.45/5.74 thf(fact_4642_pos__imp__zdiv__neg__iff,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.45/5.74 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_imp_zdiv_neg_iff
% 5.45/5.74 thf(fact_4643_neg__imp__zdiv__neg__iff,axiom,
% 5.45/5.74 ! [B: int,A: int] :
% 5.45/5.74 ( ( ord_less_int @ B @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.45/5.74 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % neg_imp_zdiv_neg_iff
% 5.45/5.74 thf(fact_4644_int__div__less__self,axiom,
% 5.45/5.74 ! [X: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ X )
% 5.45/5.74 => ( ( ord_less_int @ one_one_int @ K )
% 5.45/5.74 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_div_less_self
% 5.45/5.74 thf(fact_4645_div__neg__pos__less0,axiom,
% 5.45/5.74 ! [A: int,B: int] :
% 5.45/5.74 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.74 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % div_neg_pos_less0
% 5.45/5.74 thf(fact_4646_Diff__mono,axiom,
% 5.45/5.74 ! [A3: set_nat,C3: set_nat,D3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.74 => ( ( ord_less_eq_set_nat @ D3 @ B3 )
% 5.45/5.74 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ C3 @ D3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_mono
% 5.45/5.74 thf(fact_4647_Diff__mono,axiom,
% 5.45/5.74 ! [A3: set_int,C3: set_int,D3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ord_less_eq_set_int @ A3 @ C3 )
% 5.45/5.74 => ( ( ord_less_eq_set_int @ D3 @ B3 )
% 5.45/5.74 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B3 ) @ ( minus_minus_set_int @ C3 @ D3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_mono
% 5.45/5.74 thf(fact_4648_Diff__subset,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset
% 5.45/5.74 thf(fact_4649_Diff__subset,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B3 ) @ A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset
% 5.45/5.74 thf(fact_4650_double__diff,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.74 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C3 @ A3 ) )
% 5.45/5.74 = A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % double_diff
% 5.45/5.74 thf(fact_4651_double__diff,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.74 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.74 => ( ( ord_less_eq_set_int @ B3 @ C3 )
% 5.45/5.74 => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C3 @ A3 ) )
% 5.45/5.74 = A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % double_diff
% 5.45/5.74 thf(fact_4652_int__ops_I6_J,axiom,
% 5.45/5.74 ! [A: nat,B: nat] :
% 5.45/5.74 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.45/5.74 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.74 = zero_zero_int ) )
% 5.45/5.74 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.45/5.74 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.45/5.74 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_ops(6)
% 5.45/5.74 thf(fact_4653_Diff__Int__distrib2,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C3 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int_distrib2
% 5.45/5.74 thf(fact_4654_Diff__Int__distrib2,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C3 ) @ ( inf_inf_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int_distrib2
% 5.45/5.74 thf(fact_4655_Diff__Int__distrib,axiom,
% 5.45/5.74 ! [C3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( inf_in2572325071724192079at_nat @ C3 @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ C3 @ A3 ) @ ( inf_in2572325071724192079at_nat @ C3 @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int_distrib
% 5.45/5.74 thf(fact_4656_Diff__Int__distrib,axiom,
% 5.45/5.74 ! [C3: set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( inf_inf_set_nat @ C3 @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ C3 @ A3 ) @ ( inf_inf_set_nat @ C3 @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int_distrib
% 5.45/5.74 thf(fact_4657_Diff__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ A3 @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Diff_Int
% 5.45/5.74 thf(fact_4658_Diff__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ A3 @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Diff_Int
% 5.45/5.74 thf(fact_4659_Diff__Int2,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C3 ) @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ C3 ) @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int2
% 5.45/5.74 thf(fact_4660_Diff__Int2,axiom,
% 5.45/5.74 ! [A3: set_nat,C3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C3 ) @ ( inf_inf_set_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ C3 ) @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int2
% 5.45/5.74 thf(fact_4661_Int__Diff,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( inf_in2572325071724192079at_nat @ A3 @ ( minus_1356011639430497352at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff
% 5.45/5.74 thf(fact_4662_Int__Diff,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( inf_inf_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff
% 5.45/5.74 thf(fact_4663_set__diff__diff__left,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( minus_8321449233255521966at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_8321449233255521966at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_diff_left
% 5.45/5.74 thf(fact_4664_set__diff__diff__left,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( minus_5060654252129873198at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_5060654252129873198at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_diff_left
% 5.45/5.74 thf(fact_4665_set__diff__diff__left,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( minus_3314409938677909166at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_3314409938677909166at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_diff_left
% 5.45/5.74 thf(fact_4666_set__diff__diff__left,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( minus_minus_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_diff_left
% 5.45/5.74 thf(fact_4667_Un__Diff,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( minus_8321449233255521966at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ C3 ) @ ( minus_8321449233255521966at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff
% 5.45/5.74 thf(fact_4668_Un__Diff,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( minus_5060654252129873198at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A3 @ C3 ) @ ( minus_5060654252129873198at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff
% 5.45/5.74 thf(fact_4669_Un__Diff,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( minus_3314409938677909166at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ C3 ) @ ( minus_3314409938677909166at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff
% 5.45/5.74 thf(fact_4670_Un__Diff,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ ( sup_sup_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ C3 ) @ ( minus_minus_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff
% 5.45/5.74 thf(fact_4671_psubset__imp__ex__mem,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ord_le7866589430770878221at_nat @ A3 @ B3 )
% 5.45/5.74 => ? [B4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B4 @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % psubset_imp_ex_mem
% 5.45/5.74 thf(fact_4672_psubset__imp__ex__mem,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ord_less_set_o @ A3 @ B3 )
% 5.45/5.74 => ? [B4: $o] : ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % psubset_imp_ex_mem
% 5.45/5.74 thf(fact_4673_psubset__imp__ex__mem,axiom,
% 5.45/5.74 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( ord_less_set_set_nat @ A3 @ B3 )
% 5.45/5.74 => ? [B4: set_nat] : ( member_set_nat @ B4 @ ( minus_2163939370556025621et_nat @ B3 @ A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % psubset_imp_ex_mem
% 5.45/5.74 thf(fact_4674_psubset__imp__ex__mem,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.74 => ? [B4: int] : ( member_int @ B4 @ ( minus_minus_set_int @ B3 @ A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % psubset_imp_ex_mem
% 5.45/5.74 thf(fact_4675_psubset__imp__ex__mem,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ord_less_set_nat @ A3 @ B3 )
% 5.45/5.74 => ? [B4: nat] : ( member_nat @ B4 @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % psubset_imp_ex_mem
% 5.45/5.74 thf(fact_4676_subset__minus__empty,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % subset_minus_empty
% 5.45/5.74 thf(fact_4677_subset__minus__empty,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.74 => ( ( minus_minus_set_o @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_o ) ) ).
% 5.45/5.74
% 5.45/5.74 % subset_minus_empty
% 5.45/5.74 thf(fact_4678_subset__minus__empty,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( minus_minus_set_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % subset_minus_empty
% 5.45/5.74 thf(fact_4679_subset__minus__empty,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.74 => ( ( minus_minus_set_int @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % subset_minus_empty
% 5.45/5.74 thf(fact_4680_disjoint__alt__simp2,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 5.45/5.74 != A3 )
% 5.45/5.74 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.74 != bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp2
% 5.45/5.74 thf(fact_4681_disjoint__alt__simp2,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ( minus_minus_set_o @ A3 @ B3 )
% 5.45/5.74 != A3 )
% 5.45/5.74 = ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_o ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp2
% 5.45/5.74 thf(fact_4682_disjoint__alt__simp2,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ( minus_minus_set_int @ A3 @ B3 )
% 5.45/5.74 != A3 )
% 5.45/5.74 = ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp2
% 5.45/5.74 thf(fact_4683_disjoint__alt__simp2,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ( minus_minus_set_nat @ A3 @ B3 )
% 5.45/5.74 != A3 )
% 5.45/5.74 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp2
% 5.45/5.74 thf(fact_4684_disjoint__alt__simp1,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 5.45/5.74 = A3 )
% 5.45/5.74 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp1
% 5.45/5.74 thf(fact_4685_disjoint__alt__simp1,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ( minus_minus_set_o @ A3 @ B3 )
% 5.45/5.74 = A3 )
% 5.45/5.74 = ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_o ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp1
% 5.45/5.74 thf(fact_4686_disjoint__alt__simp1,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ( minus_minus_set_int @ A3 @ B3 )
% 5.45/5.74 = A3 )
% 5.45/5.74 = ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp1
% 5.45/5.74 thf(fact_4687_disjoint__alt__simp1,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ( minus_minus_set_nat @ A3 @ B3 )
% 5.45/5.74 = A3 )
% 5.45/5.74 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp1
% 5.45/5.74 thf(fact_4688_Int__Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_disjoint
% 5.45/5.74 thf(fact_4689_Int__Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( inf_inf_set_o @ ( inf_inf_set_o @ A3 @ B3 ) @ ( minus_minus_set_o @ A3 @ B3 ) )
% 5.45/5.74 = bot_bot_set_o ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_disjoint
% 5.45/5.74 thf(fact_4690_Int__Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( inf_inf_set_int @ ( inf_inf_set_int @ A3 @ B3 ) @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.74 = bot_bot_set_int ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_disjoint
% 5.45/5.74 thf(fact_4691_Int__Diff__disjoint,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = bot_bot_set_nat ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_disjoint
% 5.45/5.74 thf(fact_4692_Diff__triv,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bo2099793752762293965at_nat )
% 5.45/5.74 => ( ( minus_1356011639430497352at_nat @ A3 @ B3 )
% 5.45/5.74 = A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_triv
% 5.45/5.74 thf(fact_4693_Diff__triv,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_o )
% 5.45/5.74 => ( ( minus_minus_set_o @ A3 @ B3 )
% 5.45/5.74 = A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_triv
% 5.45/5.74 thf(fact_4694_Diff__triv,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_int )
% 5.45/5.74 => ( ( minus_minus_set_int @ A3 @ B3 )
% 5.45/5.74 = A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_triv
% 5.45/5.74 thf(fact_4695_Diff__triv,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.74 = bot_bot_set_nat )
% 5.45/5.74 => ( ( minus_minus_set_nat @ A3 @ B3 )
% 5.45/5.74 = A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_triv
% 5.45/5.74 thf(fact_4696_Diff__partition,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( ord_le3000389064537975527at_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( sup_su718114333110466843at_nat @ A3 @ ( minus_8321449233255521966at_nat @ B3 @ A3 ) )
% 5.45/5.74 = B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_partition
% 5.45/5.74 thf(fact_4697_Diff__partition,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( ord_le8081472938463900775at_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( sup_su3035147773818789531at_nat @ A3 @ ( minus_5060654252129873198at_nat @ B3 @ A3 ) )
% 5.45/5.74 = B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_partition
% 5.45/5.74 thf(fact_4698_Diff__partition,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( ord_le1268244103169919719at_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( sup_su5525570899277871387at_nat @ A3 @ ( minus_3314409938677909166at_nat @ B3 @ A3 ) )
% 5.45/5.74 = B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_partition
% 5.45/5.74 thf(fact_4699_Diff__partition,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.74 => ( ( sup_sup_set_nat @ A3 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.74 = B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_partition
% 5.45/5.74 thf(fact_4700_Diff__partition,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.74 => ( ( sup_sup_set_int @ A3 @ ( minus_minus_set_int @ B3 @ A3 ) )
% 5.45/5.74 = B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_partition
% 5.45/5.74 thf(fact_4701_Diff__subset__conv,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( ord_le3000389064537975527at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( ord_le3000389064537975527at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset_conv
% 5.45/5.74 thf(fact_4702_Diff__subset__conv,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( ord_le8081472938463900775at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( ord_le8081472938463900775at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset_conv
% 5.45/5.74 thf(fact_4703_Diff__subset__conv,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( ord_le1268244103169919719at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( ord_le1268244103169919719at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset_conv
% 5.45/5.74 thf(fact_4704_Diff__subset__conv,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( ord_less_eq_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset_conv
% 5.45/5.74 thf(fact_4705_Diff__subset__conv,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int,C3: set_int] :
% 5.45/5.74 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A3 @ B3 ) @ C3 )
% 5.45/5.74 = ( ord_less_eq_set_int @ A3 @ ( sup_sup_set_int @ B3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_subset_conv
% 5.45/5.74 thf(fact_4706_pochhammer__pos,axiom,
% 5.45/5.74 ! [X: code_integer,N2: nat] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.74 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_pos
% 5.45/5.74 thf(fact_4707_pochhammer__pos,axiom,
% 5.45/5.74 ! [X: rat,N2: nat] :
% 5.45/5.74 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.74 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_pos
% 5.45/5.74 thf(fact_4708_pochhammer__pos,axiom,
% 5.45/5.74 ! [X: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.74 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_pos
% 5.45/5.74 thf(fact_4709_pochhammer__pos,axiom,
% 5.45/5.74 ! [X: int,N2: nat] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ X )
% 5.45/5.74 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_pos
% 5.45/5.74 thf(fact_4710_Un__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_Int
% 5.45/5.74 thf(fact_4711_Un__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_Int
% 5.45/5.74 thf(fact_4712_Un__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_Int
% 5.45/5.74 thf(fact_4713_Un__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_Int
% 5.45/5.74 thf(fact_4714_Un__Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Un_Diff_Int
% 5.45/5.74 thf(fact_4715_Int__Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( sup_su6327502436637775413at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_Un
% 5.45/5.74 thf(fact_4716_Int__Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( sup_su718114333110466843at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_Un
% 5.45/5.74 thf(fact_4717_Int__Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( sup_su3035147773818789531at_nat @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_Un
% 5.45/5.74 thf(fact_4718_Int__Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( sup_su5525570899277871387at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_Un
% 5.45/5.74 thf(fact_4719_Int__Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( sup_sup_set_nat @ ( inf_inf_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = A3 ) ).
% 5.45/5.74
% 5.45/5.74 % Int_Diff_Un
% 5.45/5.74 thf(fact_4720_Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ A3 @ ( inf_in2572325071724192079at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( sup_su6327502436637775413at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int
% 5.45/5.74 thf(fact_4721_Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( minus_8321449233255521966at_nat @ A3 @ ( inf_in4302113700860409141at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( sup_su718114333110466843at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) @ ( minus_8321449233255521966at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int
% 5.45/5.74 thf(fact_4722_Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( minus_5060654252129873198at_nat @ A3 @ ( inf_in1697001100524423349at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( sup_su3035147773818789531at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) @ ( minus_5060654252129873198at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int
% 5.45/5.74 thf(fact_4723_Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( minus_3314409938677909166at_nat @ A3 @ ( inf_in7913087082777306421at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( sup_su5525570899277871387at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) @ ( minus_3314409938677909166at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int
% 5.45/5.74 thf(fact_4724_Diff__Int,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ A3 @ ( inf_inf_set_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( sup_sup_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Int
% 5.45/5.74 thf(fact_4725_Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( minus_1356011639430497352at_nat @ A3 @ ( sup_su6327502436637775413at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( inf_in2572325071724192079at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ ( minus_1356011639430497352at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Un
% 5.45/5.74 thf(fact_4726_Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,C3: set_Pr8693737435421807431at_nat] :
% 5.45/5.74 ( ( minus_8321449233255521966at_nat @ A3 @ ( sup_su718114333110466843at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( inf_in4302113700860409141at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) @ ( minus_8321449233255521966at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Un
% 5.45/5.74 thf(fact_4727_Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,C3: set_Pr8551490117392284871at_nat] :
% 5.45/5.74 ( ( minus_5060654252129873198at_nat @ A3 @ ( sup_su3035147773818789531at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( inf_in1697001100524423349at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) @ ( minus_5060654252129873198at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Un
% 5.45/5.74 thf(fact_4728_Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,C3: set_Pr4329608150637261639at_nat] :
% 5.45/5.74 ( ( minus_3314409938677909166at_nat @ A3 @ ( sup_su5525570899277871387at_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( inf_in7913087082777306421at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) @ ( minus_3314409938677909166at_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Un
% 5.45/5.74 thf(fact_4729_Diff__Un,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat,C3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ A3 @ ( sup_sup_set_nat @ B3 @ C3 ) )
% 5.45/5.74 = ( inf_inf_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ ( minus_minus_set_nat @ A3 @ C3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_Un
% 5.45/5.74 thf(fact_4730_pochhammer__neq__0__mono,axiom,
% 5.45/5.74 ! [A: rat,M: nat,N2: nat] :
% 5.45/5.74 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.45/5.74 != zero_zero_rat )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.45/5.74 != zero_zero_rat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_neq_0_mono
% 5.45/5.74 thf(fact_4731_pochhammer__eq__0__mono,axiom,
% 5.45/5.74 ! [A: rat,N2: nat,M: nat] :
% 5.45/5.74 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.45/5.74 = zero_zero_rat )
% 5.45/5.74 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.74 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.45/5.74 = zero_zero_rat ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_eq_0_mono
% 5.45/5.74 thf(fact_4732_zdiff__int__split,axiom,
% 5.45/5.74 ! [P: int > $o,X: nat,Y: nat] :
% 5.45/5.74 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.45/5.74 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.45/5.74 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.45/5.74 & ( ( ord_less_nat @ X @ Y )
% 5.45/5.74 => ( P @ zero_zero_int ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zdiff_int_split
% 5.45/5.74 thf(fact_4733_pochhammer__nonneg,axiom,
% 5.45/5.74 ! [X: code_integer,N2: nat] :
% 5.45/5.74 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.74 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( comm_s8582702949713902594nteger @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_nonneg
% 5.45/5.74 thf(fact_4734_pochhammer__nonneg,axiom,
% 5.45/5.74 ! [X: rat,N2: nat] :
% 5.45/5.74 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.45/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_nonneg
% 5.45/5.74 thf(fact_4735_pochhammer__nonneg,axiom,
% 5.45/5.74 ! [X: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.45/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_nonneg
% 5.45/5.74 thf(fact_4736_pochhammer__nonneg,axiom,
% 5.45/5.74 ! [X: int,N2: nat] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ X )
% 5.45/5.74 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_nonneg
% 5.45/5.74 thf(fact_4737_disjoint__alt__simp3,axiom,
% 5.45/5.74 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( ord_le7866589430770878221at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) @ A3 )
% 5.45/5.74 = ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.74 != bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp3
% 5.45/5.74 thf(fact_4738_disjoint__alt__simp3,axiom,
% 5.45/5.74 ! [A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( ord_less_set_o @ ( minus_minus_set_o @ A3 @ B3 ) @ A3 )
% 5.45/5.74 = ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_o ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp3
% 5.45/5.74 thf(fact_4739_disjoint__alt__simp3,axiom,
% 5.45/5.74 ! [A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( ord_less_set_int @ ( minus_minus_set_int @ A3 @ B3 ) @ A3 )
% 5.45/5.74 = ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp3
% 5.45/5.74 thf(fact_4740_disjoint__alt__simp3,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( ord_less_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ A3 )
% 5.45/5.74 = ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.74 != bot_bot_set_nat ) ) ).
% 5.45/5.74
% 5.45/5.74 % disjoint_alt_simp3
% 5.45/5.74 thf(fact_4741_pochhammer__rec,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat] :
% 5.45/5.74 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_3573771949741848930nteger @ A @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec
% 5.45/5.74 thf(fact_4742_pochhammer__rec,axiom,
% 5.45/5.74 ! [A: rat,N2: nat] :
% 5.45/5.74 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec
% 5.45/5.74 thf(fact_4743_pochhammer__rec,axiom,
% 5.45/5.74 ! [A: nat,N2: nat] :
% 5.45/5.74 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec
% 5.45/5.74 thf(fact_4744_pochhammer__rec,axiom,
% 5.45/5.74 ! [A: int,N2: nat] :
% 5.45/5.74 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec
% 5.45/5.74 thf(fact_4745_pochhammer__rec_H,axiom,
% 5.45/5.74 ! [Z: rat,N2: nat] :
% 5.45/5.74 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec'
% 5.45/5.74 thf(fact_4746_pochhammer__rec_H,axiom,
% 5.45/5.74 ! [Z: int,N2: nat] :
% 5.45/5.74 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec'
% 5.45/5.74 thf(fact_4747_pochhammer__rec_H,axiom,
% 5.45/5.74 ! [Z: nat,N2: nat] :
% 5.45/5.74 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec'
% 5.45/5.74 thf(fact_4748_pochhammer__rec_H,axiom,
% 5.45/5.74 ! [Z: code_integer,N2: nat] :
% 5.45/5.74 ( ( comm_s8582702949713902594nteger @ Z @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ ( comm_s8582702949713902594nteger @ Z @ N2 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_rec'
% 5.45/5.74 thf(fact_4749_pochhammer__Suc,axiom,
% 5.45/5.74 ! [A: rat,N2: nat] :
% 5.45/5.74 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_Suc
% 5.45/5.74 thf(fact_4750_pochhammer__Suc,axiom,
% 5.45/5.74 ! [A: int,N2: nat] :
% 5.45/5.74 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_Suc
% 5.45/5.74 thf(fact_4751_pochhammer__Suc,axiom,
% 5.45/5.74 ! [A: nat,N2: nat] :
% 5.45/5.74 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_Suc
% 5.45/5.74 thf(fact_4752_pochhammer__Suc,axiom,
% 5.45/5.74 ! [A: code_integer,N2: nat] :
% 5.45/5.74 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ A @ N2 ) @ ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ N2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_Suc
% 5.45/5.74 thf(fact_4753_pochhammer__product_H,axiom,
% 5.45/5.74 ! [Z: rat,N2: nat,M: nat] :
% 5.45/5.74 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.45/5.74 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product'
% 5.45/5.74 thf(fact_4754_pochhammer__product_H,axiom,
% 5.45/5.74 ! [Z: int,N2: nat,M: nat] :
% 5.45/5.74 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.45/5.74 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product'
% 5.45/5.74 thf(fact_4755_pochhammer__product_H,axiom,
% 5.45/5.74 ! [Z: nat,N2: nat,M: nat] :
% 5.45/5.74 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.45/5.74 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product'
% 5.45/5.74 thf(fact_4756_pochhammer__product_H,axiom,
% 5.45/5.74 ! [Z: code_integer,N2: nat,M: nat] :
% 5.45/5.74 ( ( comm_s8582702949713902594nteger @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ N2 ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ N2 ) ) @ M ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product'
% 5.45/5.74 thf(fact_4757_pochhammer__product,axiom,
% 5.45/5.74 ! [M: nat,N2: nat,Z: rat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.74 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 5.45/5.74 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product
% 5.45/5.74 thf(fact_4758_pochhammer__product,axiom,
% 5.45/5.74 ! [M: nat,N2: nat,Z: int] :
% 5.45/5.74 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.74 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.45/5.74 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product
% 5.45/5.74 thf(fact_4759_pochhammer__product,axiom,
% 5.45/5.74 ! [M: nat,N2: nat,Z: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.74 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.45/5.74 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product
% 5.45/5.74 thf(fact_4760_pochhammer__product,axiom,
% 5.45/5.74 ! [M: nat,N2: nat,Z: code_integer] :
% 5.45/5.74 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.74 => ( ( comm_s8582702949713902594nteger @ Z @ N2 )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( comm_s8582702949713902594nteger @ Z @ M ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ Z @ ( semiri4939895301339042750nteger @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_product
% 5.45/5.74 thf(fact_4761_real__arch__simple,axiom,
% 5.45/5.74 ! [X: rat] :
% 5.45/5.74 ? [N5: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N5 ) ) ).
% 5.45/5.74
% 5.45/5.74 % real_arch_simple
% 5.45/5.74 thf(fact_4762_reals__Archimedean2,axiom,
% 5.45/5.74 ! [X: rat] :
% 5.45/5.74 ? [N5: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N5 ) ) ).
% 5.45/5.74
% 5.45/5.74 % reals_Archimedean2
% 5.45/5.74 thf(fact_4763_zle__diff1__eq,axiom,
% 5.45/5.74 ! [W2: int,Z: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ W2 @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.45/5.74 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.45/5.74
% 5.45/5.74 % zle_diff1_eq
% 5.45/5.74 thf(fact_4764_zle__add1__eq__le,axiom,
% 5.45/5.74 ! [W2: int,Z: int] :
% 5.45/5.74 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.45/5.74 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.45/5.74
% 5.45/5.74 % zle_add1_eq_le
% 5.45/5.74 thf(fact_4765_zero__less__imp__eq__int,axiom,
% 5.45/5.74 ! [K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ? [N5: nat] :
% 5.45/5.74 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.74 & ( K
% 5.45/5.74 = ( semiri1314217659103216013at_int @ N5 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zero_less_imp_eq_int
% 5.45/5.74 thf(fact_4766_pos__int__cases,axiom,
% 5.45/5.74 ! [K: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ~ ! [N5: nat] :
% 5.45/5.74 ( ( K
% 5.45/5.74 = ( semiri1314217659103216013at_int @ N5 ) )
% 5.45/5.74 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_int_cases
% 5.45/5.74 thf(fact_4767_zmult__zless__mono2__lemma,axiom,
% 5.45/5.74 ! [I2: int,J: int,K: nat] :
% 5.45/5.74 ( ( ord_less_int @ I2 @ J )
% 5.45/5.74 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.74 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zmult_zless_mono2_lemma
% 5.45/5.74 thf(fact_4768_nonneg__int__cases,axiom,
% 5.45/5.74 ! [K: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ~ ! [N5: nat] :
% 5.45/5.74 ( K
% 5.45/5.74 != ( semiri1314217659103216013at_int @ N5 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nonneg_int_cases
% 5.45/5.74 thf(fact_4769_zero__le__imp__eq__int,axiom,
% 5.45/5.74 ! [K: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.74 => ? [N5: nat] :
% 5.45/5.74 ( K
% 5.45/5.74 = ( semiri1314217659103216013at_int @ N5 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zero_le_imp_eq_int
% 5.45/5.74 thf(fact_4770_zle__int,axiom,
% 5.45/5.74 ! [M: nat,N2: nat] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.74 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.74
% 5.45/5.74 % zle_int
% 5.45/5.74 thf(fact_4771_Diff__idemp,axiom,
% 5.45/5.74 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A3 @ B3 ) @ B3 )
% 5.45/5.74 = ( minus_minus_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_idemp
% 5.45/5.74 thf(fact_4772_Diff__iff,axiom,
% 5.45/5.74 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.74 & ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_iff
% 5.45/5.74 thf(fact_4773_Diff__iff,axiom,
% 5.45/5.74 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B3 ) )
% 5.45/5.74 = ( ( member_o @ C @ A3 )
% 5.45/5.74 & ~ ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_iff
% 5.45/5.74 thf(fact_4774_Diff__iff,axiom,
% 5.45/5.74 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( ( member_set_nat @ C @ A3 )
% 5.45/5.74 & ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_iff
% 5.45/5.74 thf(fact_4775_Diff__iff,axiom,
% 5.45/5.74 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.74 = ( ( member_int @ C @ A3 )
% 5.45/5.74 & ~ ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_iff
% 5.45/5.74 thf(fact_4776_Diff__iff,axiom,
% 5.45/5.74 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 = ( ( member_nat @ C @ A3 )
% 5.45/5.74 & ~ ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % Diff_iff
% 5.45/5.74 thf(fact_4777_DiffI,axiom,
% 5.45/5.74 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.74 => ( ~ ( member8440522571783428010at_nat @ C @ B3 )
% 5.45/5.74 => ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffI
% 5.45/5.74 thf(fact_4778_DiffI,axiom,
% 5.45/5.74 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( member_o @ C @ A3 )
% 5.45/5.74 => ( ~ ( member_o @ C @ B3 )
% 5.45/5.74 => ( member_o @ C @ ( minus_minus_set_o @ A3 @ B3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffI
% 5.45/5.74 thf(fact_4779_DiffI,axiom,
% 5.45/5.74 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( member_set_nat @ C @ A3 )
% 5.45/5.74 => ( ~ ( member_set_nat @ C @ B3 )
% 5.45/5.74 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffI
% 5.45/5.74 thf(fact_4780_DiffI,axiom,
% 5.45/5.74 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( member_int @ C @ A3 )
% 5.45/5.74 => ( ~ ( member_int @ C @ B3 )
% 5.45/5.74 => ( member_int @ C @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffI
% 5.45/5.74 thf(fact_4781_DiffI,axiom,
% 5.45/5.74 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( member_nat @ C @ A3 )
% 5.45/5.74 => ( ~ ( member_nat @ C @ B3 )
% 5.45/5.74 => ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffI
% 5.45/5.74 thf(fact_4782_minus__set__def,axiom,
% 5.45/5.74 ( minus_1356011639430497352at_nat
% 5.45/5.74 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( collec3392354462482085612at_nat
% 5.45/5.74 @ ( minus_2270307095948843157_nat_o
% 5.45/5.74 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4783_minus__set__def,axiom,
% 5.45/5.74 ( minus_minus_set_o
% 5.45/5.74 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.74 ( collect_o
% 5.45/5.74 @ ( minus_minus_o_o
% 5.45/5.74 @ ^ [X4: $o] : ( member_o @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: $o] : ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4784_minus__set__def,axiom,
% 5.45/5.74 ( minus_1052850069191792384nt_int
% 5.45/5.74 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.74 ( collec213857154873943460nt_int
% 5.45/5.74 @ ( minus_711738161318947805_int_o
% 5.45/5.74 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4785_minus__set__def,axiom,
% 5.45/5.74 ( minus_7954133019191499631st_nat
% 5.45/5.74 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.74 ( collect_list_nat
% 5.45/5.74 @ ( minus_1139252259498527702_nat_o
% 5.45/5.74 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4786_minus__set__def,axiom,
% 5.45/5.74 ( minus_2163939370556025621et_nat
% 5.45/5.74 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.74 ( collect_set_nat
% 5.45/5.74 @ ( minus_6910147592129066416_nat_o
% 5.45/5.74 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4787_minus__set__def,axiom,
% 5.45/5.74 ( minus_minus_set_int
% 5.45/5.74 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.74 ( collect_int
% 5.45/5.74 @ ( minus_minus_int_o
% 5.45/5.74 @ ^ [X4: int] : ( member_int @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: int] : ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4788_minus__set__def,axiom,
% 5.45/5.74 ( minus_minus_set_nat
% 5.45/5.74 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.74 ( collect_nat
% 5.45/5.74 @ ( minus_minus_nat_o
% 5.45/5.74 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 )
% 5.45/5.74 @ ^ [X4: nat] : ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % minus_set_def
% 5.45/5.74 thf(fact_4789_DiffD2,axiom,
% 5.45/5.74 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( member8440522571783428010at_nat @ C @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD2
% 5.45/5.74 thf(fact_4790_DiffD2,axiom,
% 5.45/5.74 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( member_o @ C @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD2
% 5.45/5.74 thf(fact_4791_DiffD2,axiom,
% 5.45/5.74 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( member_set_nat @ C @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD2
% 5.45/5.74 thf(fact_4792_DiffD2,axiom,
% 5.45/5.74 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( member_int @ C @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD2
% 5.45/5.74 thf(fact_4793_DiffD2,axiom,
% 5.45/5.74 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( member_nat @ C @ B3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD2
% 5.45/5.74 thf(fact_4794_DiffD1,axiom,
% 5.45/5.74 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 => ( member8440522571783428010at_nat @ C @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD1
% 5.45/5.74 thf(fact_4795_DiffD1,axiom,
% 5.45/5.74 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B3 ) )
% 5.45/5.74 => ( member_o @ C @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD1
% 5.45/5.74 thf(fact_4796_DiffD1,axiom,
% 5.45/5.74 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) )
% 5.45/5.74 => ( member_set_nat @ C @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD1
% 5.45/5.74 thf(fact_4797_DiffD1,axiom,
% 5.45/5.74 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.74 => ( member_int @ C @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD1
% 5.45/5.74 thf(fact_4798_DiffD1,axiom,
% 5.45/5.74 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 => ( member_nat @ C @ A3 ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffD1
% 5.45/5.74 thf(fact_4799_DiffE,axiom,
% 5.45/5.74 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ C @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.74 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffE
% 5.45/5.74 thf(fact_4800_DiffE,axiom,
% 5.45/5.74 ! [C: $o,A3: set_o,B3: set_o] :
% 5.45/5.74 ( ( member_o @ C @ ( minus_minus_set_o @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( ( member_o @ C @ A3 )
% 5.45/5.74 => ( member_o @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffE
% 5.45/5.74 thf(fact_4801_DiffE,axiom,
% 5.45/5.74 ! [C: set_nat,A3: set_set_nat,B3: set_set_nat] :
% 5.45/5.74 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( ( member_set_nat @ C @ A3 )
% 5.45/5.74 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffE
% 5.45/5.74 thf(fact_4802_DiffE,axiom,
% 5.45/5.74 ! [C: int,A3: set_int,B3: set_int] :
% 5.45/5.74 ( ( member_int @ C @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( ( member_int @ C @ A3 )
% 5.45/5.74 => ( member_int @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffE
% 5.45/5.74 thf(fact_4803_DiffE,axiom,
% 5.45/5.74 ! [C: nat,A3: set_nat,B3: set_nat] :
% 5.45/5.74 ( ( member_nat @ C @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.74 => ~ ( ( member_nat @ C @ A3 )
% 5.45/5.74 => ( member_nat @ C @ B3 ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % DiffE
% 5.45/5.74 thf(fact_4804_set__diff__eq,axiom,
% 5.45/5.74 ( minus_1356011639430497352at_nat
% 5.45/5.74 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.45/5.74 ( collec3392354462482085612at_nat
% 5.45/5.74 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.74 ( ( member8440522571783428010at_nat @ X4 @ A6 )
% 5.45/5.74 & ~ ( member8440522571783428010at_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4805_set__diff__eq,axiom,
% 5.45/5.74 ( minus_minus_set_o
% 5.45/5.74 = ( ^ [A6: set_o,B6: set_o] :
% 5.45/5.74 ( collect_o
% 5.45/5.74 @ ^ [X4: $o] :
% 5.45/5.74 ( ( member_o @ X4 @ A6 )
% 5.45/5.74 & ~ ( member_o @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4806_set__diff__eq,axiom,
% 5.45/5.74 ( minus_1052850069191792384nt_int
% 5.45/5.74 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.45/5.74 ( collec213857154873943460nt_int
% 5.45/5.74 @ ^ [X4: product_prod_int_int] :
% 5.45/5.74 ( ( member5262025264175285858nt_int @ X4 @ A6 )
% 5.45/5.74 & ~ ( member5262025264175285858nt_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4807_set__diff__eq,axiom,
% 5.45/5.74 ( minus_7954133019191499631st_nat
% 5.45/5.74 = ( ^ [A6: set_list_nat,B6: set_list_nat] :
% 5.45/5.74 ( collect_list_nat
% 5.45/5.74 @ ^ [X4: list_nat] :
% 5.45/5.74 ( ( member_list_nat @ X4 @ A6 )
% 5.45/5.74 & ~ ( member_list_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4808_set__diff__eq,axiom,
% 5.45/5.74 ( minus_2163939370556025621et_nat
% 5.45/5.74 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.45/5.74 ( collect_set_nat
% 5.45/5.74 @ ^ [X4: set_nat] :
% 5.45/5.74 ( ( member_set_nat @ X4 @ A6 )
% 5.45/5.74 & ~ ( member_set_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4809_set__diff__eq,axiom,
% 5.45/5.74 ( minus_minus_set_int
% 5.45/5.74 = ( ^ [A6: set_int,B6: set_int] :
% 5.45/5.74 ( collect_int
% 5.45/5.74 @ ^ [X4: int] :
% 5.45/5.74 ( ( member_int @ X4 @ A6 )
% 5.45/5.74 & ~ ( member_int @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4810_set__diff__eq,axiom,
% 5.45/5.74 ( minus_minus_set_nat
% 5.45/5.74 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.45/5.74 ( collect_nat
% 5.45/5.74 @ ^ [X4: nat] :
% 5.45/5.74 ( ( member_nat @ X4 @ A6 )
% 5.45/5.74 & ~ ( member_nat @ X4 @ B6 ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % set_diff_eq
% 5.45/5.74 thf(fact_4811_int__ge__induct,axiom,
% 5.45/5.74 ! [K: int,I2: int,P: int > $o] :
% 5.45/5.74 ( ( ord_less_eq_int @ K @ I2 )
% 5.45/5.74 => ( ( P @ K )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ K @ I3 )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( P @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_ge_induct
% 5.45/5.74 thf(fact_4812_int__le__induct,axiom,
% 5.45/5.74 ! [I2: int,K: int,P: int > $o] :
% 5.45/5.74 ( ( ord_less_eq_int @ I2 @ K )
% 5.45/5.74 => ( ( P @ K )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ I3 @ K )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( P @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_le_induct
% 5.45/5.74 thf(fact_4813_int__induct,axiom,
% 5.45/5.74 ! [P: int > $o,K: int,I2: int] :
% 5.45/5.74 ( ( P @ K )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ K @ I3 )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ I3 @ K )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( P @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_induct
% 5.45/5.74 thf(fact_4814_int__gr__induct,axiom,
% 5.45/5.74 ! [K: int,I2: int,P: int > $o] :
% 5.45/5.74 ( ( ord_less_int @ K @ I2 )
% 5.45/5.74 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_int @ K @ I3 )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( P @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_gr_induct
% 5.45/5.74 thf(fact_4815_zless__add1__eq,axiom,
% 5.45/5.74 ! [W2: int,Z: int] :
% 5.45/5.74 ( ( ord_less_int @ W2 @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.45/5.74 = ( ( ord_less_int @ W2 @ Z )
% 5.45/5.74 | ( W2 = Z ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zless_add1_eq
% 5.45/5.74 thf(fact_4816_int__less__induct,axiom,
% 5.45/5.74 ! [I2: int,K: int,P: int > $o] :
% 5.45/5.74 ( ( ord_less_int @ I2 @ K )
% 5.45/5.74 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.45/5.74 => ( ! [I3: int] :
% 5.45/5.74 ( ( ord_less_int @ I3 @ K )
% 5.45/5.74 => ( ( P @ I3 )
% 5.45/5.74 => ( P @ ( minus_minus_int @ I3 @ one_one_int ) ) ) )
% 5.45/5.74 => ( P @ I2 ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_less_induct
% 5.45/5.74 thf(fact_4817_less__eq__int__code_I1_J,axiom,
% 5.45/5.74 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.45/5.74
% 5.45/5.74 % less_eq_int_code(1)
% 5.45/5.74 thf(fact_4818_odd__less__0__iff,axiom,
% 5.45/5.74 ! [Z: int] :
% 5.45/5.74 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.45/5.74 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.74
% 5.45/5.74 % odd_less_0_iff
% 5.45/5.74 thf(fact_4819_less__int__code_I1_J,axiom,
% 5.45/5.74 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.45/5.74
% 5.45/5.74 % less_int_code(1)
% 5.45/5.74 thf(fact_4820_zmult__zless__mono2,axiom,
% 5.45/5.74 ! [I2: int,J: int,K: int] :
% 5.45/5.74 ( ( ord_less_int @ I2 @ J )
% 5.45/5.74 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.74 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zmult_zless_mono2
% 5.45/5.74 thf(fact_4821_pos__zmult__eq__1__iff,axiom,
% 5.45/5.74 ! [M: int,N2: int] :
% 5.45/5.74 ( ( ord_less_int @ zero_zero_int @ M )
% 5.45/5.74 => ( ( ( times_times_int @ M @ N2 )
% 5.45/5.74 = one_one_int )
% 5.45/5.74 = ( ( M = one_one_int )
% 5.45/5.74 & ( N2 = one_one_int ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pos_zmult_eq_1_iff
% 5.45/5.74 thf(fact_4822_add1__zle__eq,axiom,
% 5.45/5.74 ! [W2: int,Z: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z )
% 5.45/5.74 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.45/5.74
% 5.45/5.74 % add1_zle_eq
% 5.45/5.74 thf(fact_4823_zless__imp__add1__zle,axiom,
% 5.45/5.74 ! [W2: int,Z: int] :
% 5.45/5.74 ( ( ord_less_int @ W2 @ Z )
% 5.45/5.74 => ( ord_less_eq_int @ ( plus_plus_int @ W2 @ one_one_int ) @ Z ) ) ).
% 5.45/5.74
% 5.45/5.74 % zless_imp_add1_zle
% 5.45/5.74 thf(fact_4824_zle__iff__zadd,axiom,
% 5.45/5.74 ( ord_less_eq_int
% 5.45/5.74 = ( ^ [W3: int,Z6: int] :
% 5.45/5.74 ? [N: nat] :
% 5.45/5.74 ( Z6
% 5.45/5.74 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zle_iff_zadd
% 5.45/5.74 thf(fact_4825_le__imp__0__less,axiom,
% 5.45/5.74 ! [Z: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.74 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % le_imp_0_less
% 5.45/5.74 thf(fact_4826_int__one__le__iff__zero__less,axiom,
% 5.45/5.74 ! [Z: int] :
% 5.45/5.74 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.45/5.74 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.74
% 5.45/5.74 % int_one_le_iff_zero_less
% 5.45/5.74 thf(fact_4827_zless__iff__Suc__zadd,axiom,
% 5.45/5.74 ( ord_less_int
% 5.45/5.74 = ( ^ [W3: int,Z6: int] :
% 5.45/5.74 ? [N: nat] :
% 5.45/5.74 ( Z6
% 5.45/5.74 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % zless_iff_Suc_zadd
% 5.45/5.74 thf(fact_4828_nat0__intermed__int__val,axiom,
% 5.45/5.74 ! [N2: nat,F: nat > int,K: int] :
% 5.45/5.74 ( ! [I3: nat] :
% 5.45/5.74 ( ( ord_less_nat @ I3 @ N2 )
% 5.45/5.74 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I3 @ one_one_nat ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.45/5.74 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.45/5.74 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.45/5.74 => ? [I3: nat] :
% 5.45/5.74 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.45/5.74 & ( ( F @ I3 )
% 5.45/5.74 = K ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % nat0_intermed_int_val
% 5.45/5.74 thf(fact_4829_eucl__rel__int__iff,axiom,
% 5.45/5.74 ! [K: int,L: int,Q6: int,R3: int] :
% 5.45/5.74 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.74 = ( ( K
% 5.45/5.74 = ( plus_plus_int @ ( times_times_int @ L @ Q6 ) @ R3 ) )
% 5.45/5.74 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.45/5.74 & ( ord_less_int @ R3 @ L ) ) )
% 5.45/5.74 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.45/5.74 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.45/5.74 => ( ( ord_less_int @ L @ R3 )
% 5.45/5.74 & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 5.45/5.74 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.45/5.74 => ( Q6 = zero_zero_int ) ) ) ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % eucl_rel_int_iff
% 5.45/5.74 thf(fact_4830_pochhammer__minus_H,axiom,
% 5.45/5.74 ! [B: rat,K: nat] :
% 5.45/5.74 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.45/5.74 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_minus'
% 5.45/5.74 thf(fact_4831_pochhammer__minus_H,axiom,
% 5.45/5.74 ! [B: int,K: nat] :
% 5.45/5.74 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.45/5.74 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_minus'
% 5.45/5.74 thf(fact_4832_pochhammer__minus_H,axiom,
% 5.45/5.74 ! [B: code_integer,K: nat] :
% 5.45/5.74 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.45/5.74 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.45/5.74
% 5.45/5.74 % pochhammer_minus'
% 5.45/5.74 thf(fact_4833_boolean__algebra__class_Oboolean__algebra_Odouble__compl,axiom,
% 5.45/5.74 ! [X: assn] :
% 5.45/5.74 ( ( uminus_uminus_assn @ ( uminus_uminus_assn @ X ) )
% 5.45/5.74 = X ) ).
% 5.45/5.74
% 5.45/5.74 % boolean_algebra_class.boolean_algebra.double_compl
% 5.45/5.74 thf(fact_4834_boolean__algebra__class_Oboolean__algebra_Odouble__compl,axiom,
% 5.45/5.74 ! [X: product_unit] :
% 5.45/5.74 ( ( uminus2952777764628376836t_unit @ ( uminus2952777764628376836t_unit @ X ) )
% 5.45/5.74 = X ) ).
% 5.45/5.74
% 5.45/5.74 % boolean_algebra_class.boolean_algebra.double_compl
% 5.45/5.74 thf(fact_4835_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff,axiom,
% 5.45/5.74 ! [X: assn,Y: assn] :
% 5.45/5.74 ( ( ( uminus_uminus_assn @ X )
% 5.45/5.74 = ( uminus_uminus_assn @ Y ) )
% 5.45/5.74 = ( X = Y ) ) ).
% 5.45/5.74
% 5.45/5.74 % boolean_algebra_class.boolean_algebra.compl_eq_compl_iff
% 5.45/5.74 thf(fact_4836_boolean__algebra__class_Oboolean__algebra_Ocompl__eq__compl__iff,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( ( uminus2952777764628376836t_unit @ X )
% 5.45/5.75 = ( uminus2952777764628376836t_unit @ Y ) )
% 5.45/5.75 = ( X = Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra_class.boolean_algebra.compl_eq_compl_iff
% 5.45/5.75 thf(fact_4837_Compl__anti__mono,axiom,
% 5.45/5.75 ! [A3: set_int,B3: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.75 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_anti_mono
% 5.45/5.75 thf(fact_4838_Compl__subset__Compl__iff,axiom,
% 5.45/5.75 ! [A3: set_int,B3: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 5.45/5.75 = ( ord_less_eq_set_int @ B3 @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_subset_Compl_iff
% 5.45/5.75 thf(fact_4839_neg__le__iff__le,axiom,
% 5.45/5.75 ! [B: code_integer,A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_iff_le
% 5.45/5.75 thf(fact_4840_neg__le__iff__le,axiom,
% 5.45/5.75 ! [B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_iff_le
% 5.45/5.75 thf(fact_4841_neg__le__iff__le,axiom,
% 5.45/5.75 ! [B: int,A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_iff_le
% 5.45/5.75 thf(fact_4842_compl__le__compl__iff,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 5.45/5.75 = ( ord_less_eq_assn @ Y @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_compl_iff
% 5.45/5.75 thf(fact_4843_compl__le__compl__iff,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 5.45/5.75 = ( ord_le3221252021190050221t_unit @ Y @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_compl_iff
% 5.45/5.75 thf(fact_4844_compl__le__compl__iff,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 5.45/5.75 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_compl_iff
% 5.45/5.75 thf(fact_4845_neg__less__iff__less,axiom,
% 5.45/5.75 ! [B: int,A: int] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_int @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_iff_less
% 5.45/5.75 thf(fact_4846_neg__less__iff__less,axiom,
% 5.45/5.75 ! [B: code_integer,A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_iff_less
% 5.45/5.75 thf(fact_4847_neg__less__iff__less,axiom,
% 5.45/5.75 ! [B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_iff_less
% 5.45/5.75 thf(fact_4848_compl__less__compl__iff,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) )
% 5.45/5.75 = ( ord_less_assn @ Y @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_compl_iff
% 5.45/5.75 thf(fact_4849_compl__less__compl__iff,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) )
% 5.45/5.75 = ( ord_le361264281704409273t_unit @ Y @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_compl_iff
% 5.45/5.75 thf(fact_4850_mult__minus__left,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.45/5.75 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_left
% 5.45/5.75 thf(fact_4851_mult__minus__left,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_left
% 5.45/5.75 thf(fact_4852_mult__minus__left,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.45/5.75 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_left
% 5.45/5.75 thf(fact_4853_minus__mult__minus,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.45/5.75 = ( times_times_int @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_minus
% 5.45/5.75 thf(fact_4854_minus__mult__minus,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_minus
% 5.45/5.75 thf(fact_4855_minus__mult__minus,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.45/5.75 = ( times_times_rat @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_minus
% 5.45/5.75 thf(fact_4856_mult__minus__right,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.45/5.75 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_right
% 5.45/5.75 thf(fact_4857_mult__minus__right,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_right
% 5.45/5.75 thf(fact_4858_mult__minus__right,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.45/5.75 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus_right
% 5.45/5.75 thf(fact_4859_Compl__disjoint2,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ A3 )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint2
% 5.45/5.75 thf(fact_4860_Compl__disjoint2,axiom,
% 5.45/5.75 ! [A3: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ A3 ) @ A3 )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint2
% 5.45/5.75 thf(fact_4861_Compl__disjoint2,axiom,
% 5.45/5.75 ! [A3: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ A3 )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint2
% 5.45/5.75 thf(fact_4862_Compl__disjoint2,axiom,
% 5.45/5.75 ! [A3: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ A3 ) @ A3 )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint2
% 5.45/5.75 thf(fact_4863_Compl__disjoint,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ A3 @ ( uminus6524753893492686040at_nat @ A3 ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint
% 5.45/5.75 thf(fact_4864_Compl__disjoint,axiom,
% 5.45/5.75 ! [A3: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint
% 5.45/5.75 thf(fact_4865_Compl__disjoint,axiom,
% 5.45/5.75 ! [A3: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint
% 5.45/5.75 thf(fact_4866_Compl__disjoint,axiom,
% 5.45/5.75 ! [A3: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_disjoint
% 5.45/5.75 thf(fact_4867_abs__mult__self__eq,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_self_eq
% 5.45/5.75 thf(fact_4868_abs__mult__self__eq,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.45/5.75 = ( times_times_rat @ A @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_self_eq
% 5.45/5.75 thf(fact_4869_abs__mult__self__eq,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.45/5.75 = ( times_times_int @ A @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_self_eq
% 5.45/5.75 thf(fact_4870_inter__compl__diff__conv,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) )
% 5.45/5.75 = ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % inter_compl_diff_conv
% 5.45/5.75 thf(fact_4871_inter__compl__diff__conv,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) )
% 5.45/5.75 = ( minus_minus_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % inter_compl_diff_conv
% 5.45/5.75 thf(fact_4872_Diff__Compl,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( minus_1356011639430497352at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) )
% 5.45/5.75 = ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Diff_Compl
% 5.45/5.75 thf(fact_4873_Diff__Compl,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( minus_minus_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) )
% 5.45/5.75 = ( inf_inf_set_nat @ A3 @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Diff_Compl
% 5.45/5.75 thf(fact_4874_abs__of__nat,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.75 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nat
% 5.45/5.75 thf(fact_4875_abs__of__nat,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.75 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nat
% 5.45/5.75 thf(fact_4876_abs__of__nat,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.75 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nat
% 5.45/5.75 thf(fact_4877_Compl__Diff__eq,axiom,
% 5.45/5.75 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( uminus4384627049435823934at_nat @ ( minus_8321449233255521966at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Diff_eq
% 5.45/5.75 thf(fact_4878_Compl__Diff__eq,axiom,
% 5.45/5.75 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( uminus2330091110623919550at_nat @ ( minus_5060654252129873198at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A3 ) @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Diff_eq
% 5.45/5.75 thf(fact_4879_Compl__Diff__eq,axiom,
% 5.45/5.75 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( uminus935396558254630718at_nat @ ( minus_3314409938677909166at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Diff_eq
% 5.45/5.75 thf(fact_4880_Compl__Diff__eq,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( uminus5710092332889474511et_nat @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ B3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Diff_eq
% 5.45/5.75 thf(fact_4881_negative__zle,axiom,
% 5.45/5.75 ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % negative_zle
% 5.45/5.75 thf(fact_4882_mod__not__dist,axiom,
% 5.45/5.75 ! [P: assn,H: produc3658429121746597890et_nat] :
% 5.45/5.75 ( ( rep_assn @ ( uminus_uminus_assn @ P ) @ H )
% 5.45/5.75 = ( ( in_range @ H )
% 5.45/5.75 & ~ ( rep_assn @ P @ H ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mod_not_dist
% 5.45/5.75 thf(fact_4883_neg__less__eq__nonneg,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_eq_nonneg
% 5.45/5.75 thf(fact_4884_neg__less__eq__nonneg,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.45/5.75 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_eq_nonneg
% 5.45/5.75 thf(fact_4885_neg__less__eq__nonneg,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.45/5.75 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_eq_nonneg
% 5.45/5.75 thf(fact_4886_less__eq__neg__nonpos,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_eq_neg_nonpos
% 5.45/5.75 thf(fact_4887_less__eq__neg__nonpos,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_eq_neg_nonpos
% 5.45/5.75 thf(fact_4888_less__eq__neg__nonpos,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_eq_neg_nonpos
% 5.45/5.75 thf(fact_4889_neg__le__0__iff__le,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_0_iff_le
% 5.45/5.75 thf(fact_4890_neg__le__0__iff__le,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.45/5.75 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_0_iff_le
% 5.45/5.75 thf(fact_4891_neg__le__0__iff__le,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.45/5.75 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_0_iff_le
% 5.45/5.75 thf(fact_4892_neg__0__le__iff__le,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_le_iff_le
% 5.45/5.75 thf(fact_4893_neg__0__le__iff__le,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_le_iff_le
% 5.45/5.75 thf(fact_4894_neg__0__le__iff__le,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_le_iff_le
% 5.45/5.75 thf(fact_4895_neg__less__0__iff__less,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.45/5.75 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_0_iff_less
% 5.45/5.75 thf(fact_4896_neg__less__0__iff__less,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_0_iff_less
% 5.45/5.75 thf(fact_4897_neg__less__0__iff__less,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.45/5.75 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_0_iff_less
% 5.45/5.75 thf(fact_4898_neg__0__less__iff__less,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_less_iff_less
% 5.45/5.75 thf(fact_4899_neg__0__less__iff__less,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_less_iff_less
% 5.45/5.75 thf(fact_4900_neg__0__less__iff__less,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_0_less_iff_less
% 5.45/5.75 thf(fact_4901_neg__less__pos,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.45/5.75 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_pos
% 5.45/5.75 thf(fact_4902_neg__less__pos,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_pos
% 5.45/5.75 thf(fact_4903_neg__less__pos,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.45/5.75 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_pos
% 5.45/5.75 thf(fact_4904_less__neg__neg,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.45/5.75 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_neg_neg
% 5.45/5.75 thf(fact_4905_less__neg__neg,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_neg_neg
% 5.45/5.75 thf(fact_4906_less__neg__neg,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.45/5.75 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_neg_neg
% 5.45/5.75 thf(fact_4907_mult__minus1__right,axiom,
% 5.45/5.75 ! [Z: int] :
% 5.45/5.75 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.45/5.75 = ( uminus_uminus_int @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1_right
% 5.45/5.75 thf(fact_4908_mult__minus1__right,axiom,
% 5.45/5.75 ! [Z: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1_right
% 5.45/5.75 thf(fact_4909_mult__minus1__right,axiom,
% 5.45/5.75 ! [Z: rat] :
% 5.45/5.75 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.45/5.75 = ( uminus_uminus_rat @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1_right
% 5.45/5.75 thf(fact_4910_mult__minus1,axiom,
% 5.45/5.75 ! [Z: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.45/5.75 = ( uminus_uminus_int @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1
% 5.45/5.75 thf(fact_4911_mult__minus1,axiom,
% 5.45/5.75 ! [Z: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1
% 5.45/5.75 thf(fact_4912_mult__minus1,axiom,
% 5.45/5.75 ! [Z: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.45/5.75 = ( uminus_uminus_rat @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_minus1
% 5.45/5.75 thf(fact_4913_abs__of__nonneg,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.75 => ( ( abs_abs_Code_integer @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonneg
% 5.45/5.75 thf(fact_4914_abs__of__nonneg,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.75 => ( ( abs_abs_rat @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonneg
% 5.45/5.75 thf(fact_4915_abs__of__nonneg,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.75 => ( ( abs_abs_int @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonneg
% 5.45/5.75 thf(fact_4916_abs__le__self__iff,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_self_iff
% 5.45/5.75 thf(fact_4917_abs__le__self__iff,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.45/5.75 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_self_iff
% 5.45/5.75 thf(fact_4918_abs__le__self__iff,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.45/5.75 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_self_iff
% 5.45/5.75 thf(fact_4919_abs__le__zero__iff,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.75 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_zero_iff
% 5.45/5.75 thf(fact_4920_abs__le__zero__iff,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.45/5.75 = ( A = zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_zero_iff
% 5.45/5.75 thf(fact_4921_abs__le__zero__iff,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.45/5.75 = ( A = zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_zero_iff
% 5.45/5.75 thf(fact_4922_zero__less__abs__iff,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.45/5.75 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_abs_iff
% 5.45/5.75 thf(fact_4923_zero__less__abs__iff,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.45/5.75 = ( A != zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_abs_iff
% 5.45/5.75 thf(fact_4924_zero__less__abs__iff,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.45/5.75 = ( A != zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_abs_iff
% 5.45/5.75 thf(fact_4925_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ X ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4926_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ X @ ( uminus_uminus_set_o @ X ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4927_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ X ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4928_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ X ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4929_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ X @ ( uminus_uminus_assn @ X ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4930_boolean__algebra_Oconj__cancel__right,axiom,
% 5.45/5.75 ! [X: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ X ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_right
% 5.45/5.75 thf(fact_4931_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ X )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4932_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ X )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4933_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ X )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4934_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ X )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4935_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ X )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4936_boolean__algebra_Oconj__cancel__left,axiom,
% 5.45/5.75 ! [X: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ X )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.conj_cancel_left
% 5.45/5.75 thf(fact_4937_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ Y @ ( uminus6524753893492686040at_nat @ X ) ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4938_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: set_o,Y: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ Y @ ( uminus_uminus_set_o @ X ) ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4939_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ Y @ ( uminus5710092332889474511et_nat @ X ) ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4940_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4941_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ Y @ ( uminus_uminus_assn @ X ) ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4942_inf__compl__bot__right,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_right
% 5.45/5.75 thf(fact_4943_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ X @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ Y ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4944_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: set_o,Y: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ X @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ Y ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4945_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ X @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ Y ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4946_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ X @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4947_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ X @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ Y ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4948_inf__compl__bot__left2,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ X @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left2
% 5.45/5.75 thf(fact_4949_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4950_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: set_o,Y: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ ( inf_inf_set_o @ X @ Y ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4951_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( inf_inf_set_nat @ X @ Y ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4952_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( inf_inf_set_int @ X @ Y ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4953_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( inf_inf_assn @ X @ Y ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4954_inf__compl__bot__left1,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( inf_inf_Product_unit @ X @ Y ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % inf_compl_bot_left1
% 5.45/5.75 thf(fact_4955_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ X @ Y ) )
% 5.45/5.75 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4956_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( uminus4384627049435823934at_nat @ ( sup_su718114333110466843at_nat @ X @ Y ) )
% 5.45/5.75 = ( inf_in4302113700860409141at_nat @ ( uminus4384627049435823934at_nat @ X ) @ ( uminus4384627049435823934at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4957_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ X @ Y ) )
% 5.45/5.75 = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4958_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ X @ Y ) )
% 5.45/5.75 = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4959_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ X @ Y ) )
% 5.45/5.75 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4960_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( uminus_uminus_assn @ ( sup_sup_assn @ X @ Y ) )
% 5.45/5.75 = ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4961_boolean__algebra_Ode__Morgan__disj,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( uminus2952777764628376836t_unit @ ( sup_sup_Product_unit @ X @ Y ) )
% 5.45/5.75 = ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_disj
% 5.45/5.75 thf(fact_4962_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) )
% 5.45/5.75 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ X ) @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4963_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( uminus4384627049435823934at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) )
% 5.45/5.75 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ X ) @ ( uminus4384627049435823934at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4964_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) )
% 5.45/5.75 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ X ) @ ( uminus2330091110623919550at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4965_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) )
% 5.45/5.75 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ X ) @ ( uminus935396558254630718at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4966_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ X @ Y ) )
% 5.45/5.75 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4967_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( uminus_uminus_assn @ ( inf_inf_assn @ X @ Y ) )
% 5.45/5.75 = ( sup_sup_assn @ ( uminus_uminus_assn @ X ) @ ( uminus_uminus_assn @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4968_boolean__algebra_Ode__Morgan__conj,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( uminus2952777764628376836t_unit @ ( inf_inf_Product_unit @ X @ Y ) )
% 5.45/5.75 = ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % boolean_algebra.de_Morgan_conj
% 5.45/5.75 thf(fact_4969_negative__zless,axiom,
% 5.45/5.75 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % negative_zless
% 5.45/5.75 thf(fact_4970_abs__of__nonpos,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.75 => ( ( abs_abs_Code_integer @ A )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonpos
% 5.45/5.75 thf(fact_4971_abs__of__nonpos,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.75 => ( ( abs_abs_rat @ A )
% 5.45/5.75 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonpos
% 5.45/5.75 thf(fact_4972_abs__of__nonpos,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.75 => ( ( abs_abs_int @ A )
% 5.45/5.75 = ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_nonpos
% 5.45/5.75 thf(fact_4973_zero__le__divide__abs__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.45/5.75 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.75 | ( B = zero_zero_rat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_le_divide_abs_iff
% 5.45/5.75 thf(fact_4974_divide__le__0__abs__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.45/5.75 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.45/5.75 | ( B = zero_zero_rat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_le_0_abs_iff
% 5.45/5.75 thf(fact_4975_left__minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat,A: int] :
% 5.45/5.75 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 5.45/5.75 = A ) ).
% 5.45/5.75
% 5.45/5.75 % left_minus_one_mult_self
% 5.45/5.75 thf(fact_4976_left__minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat,A: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.45/5.75 = A ) ).
% 5.45/5.75
% 5.45/5.75 % left_minus_one_mult_self
% 5.45/5.75 thf(fact_4977_left__minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat,A: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 5.45/5.75 = A ) ).
% 5.45/5.75
% 5.45/5.75 % left_minus_one_mult_self
% 5.45/5.75 thf(fact_4978_minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.45/5.75 = one_one_int ) ).
% 5.45/5.75
% 5.45/5.75 % minus_one_mult_self
% 5.45/5.75 thf(fact_4979_minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.45/5.75 = one_one_Code_integer ) ).
% 5.45/5.75
% 5.45/5.75 % minus_one_mult_self
% 5.45/5.75 thf(fact_4980_minus__one__mult__self,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 5.45/5.75 = one_one_rat ) ).
% 5.45/5.75
% 5.45/5.75 % minus_one_mult_self
% 5.45/5.75 thf(fact_4981_semiring__norm_I172_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(172)
% 5.45/5.75 thf(fact_4982_semiring__norm_I172_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(172)
% 5.45/5.75 thf(fact_4983_semiring__norm_I172_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(172)
% 5.45/5.75 thf(fact_4984_semiring__norm_I171_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: int] :
% 5.45/5.75 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(171)
% 5.45/5.75 thf(fact_4985_semiring__norm_I171_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(171)
% 5.45/5.75 thf(fact_4986_semiring__norm_I171_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ Y ) )
% 5.45/5.75 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(171)
% 5.45/5.75 thf(fact_4987_semiring__norm_I170_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W2 ) @ Y ) )
% 5.45/5.75 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(170)
% 5.45/5.75 thf(fact_4988_semiring__norm_I170_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ Y ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(170)
% 5.45/5.75 thf(fact_4989_semiring__norm_I170_J,axiom,
% 5.45/5.75 ! [V: num,W2: num,Y: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ Y ) )
% 5.45/5.75 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W2 ) ) ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % semiring_norm(170)
% 5.45/5.75 thf(fact_4990_mult__neg__numeral__simps_I3_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.45/5.75 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(3)
% 5.45/5.75 thf(fact_4991_mult__neg__numeral__simps_I3_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(3)
% 5.45/5.75 thf(fact_4992_mult__neg__numeral__simps_I3_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.45/5.75 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(3)
% 5.45/5.75 thf(fact_4993_mult__neg__numeral__simps_I2_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.75 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(2)
% 5.45/5.75 thf(fact_4994_mult__neg__numeral__simps_I2_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(2)
% 5.45/5.75 thf(fact_4995_mult__neg__numeral__simps_I2_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.75 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(2)
% 5.45/5.75 thf(fact_4996_mult__neg__numeral__simps_I1_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.45/5.75 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(1)
% 5.45/5.75 thf(fact_4997_mult__neg__numeral__simps_I1_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.45/5.75 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(1)
% 5.45/5.75 thf(fact_4998_mult__neg__numeral__simps_I1_J,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.45/5.75 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % mult_neg_numeral_simps(1)
% 5.45/5.75 thf(fact_4999_zabs__less__one__iff,axiom,
% 5.45/5.75 ! [Z: int] :
% 5.45/5.75 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.45/5.75 = ( Z = zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % zabs_less_one_iff
% 5.45/5.75 thf(fact_5000_neg__numeral__le__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.45/5.75 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_iff
% 5.45/5.75 thf(fact_5001_neg__numeral__le__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.45/5.75 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_iff
% 5.45/5.75 thf(fact_5002_neg__numeral__le__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.45/5.75 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_iff
% 5.45/5.75 thf(fact_5003_neg__numeral__less__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.45/5.75 = ( ord_less_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_iff
% 5.45/5.75 thf(fact_5004_neg__numeral__less__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.45/5.75 = ( ord_less_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_iff
% 5.45/5.75 thf(fact_5005_neg__numeral__less__iff,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.45/5.75 = ( ord_less_num @ N2 @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_iff
% 5.45/5.75 thf(fact_5006_divide__le__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [B: rat,W2: num,A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.45/5.75 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_le_eq_numeral1(2)
% 5.45/5.75 thf(fact_5007_le__divide__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [A: rat,B: rat,W2: num] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.45/5.75 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_divide_eq_numeral1(2)
% 5.45/5.75 thf(fact_5008_eq__divide__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [A: rat,B: rat,W2: num] :
% 5.45/5.75 ( ( A
% 5.45/5.75 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.45/5.75 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 != zero_zero_rat )
% 5.45/5.75 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.75 = B ) )
% 5.45/5.75 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 = zero_zero_rat )
% 5.45/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_divide_eq_numeral1(2)
% 5.45/5.75 thf(fact_5009_divide__eq__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [B: rat,W2: num,A: rat] :
% 5.45/5.75 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.75 = A )
% 5.45/5.75 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 != zero_zero_rat )
% 5.45/5.75 => ( B
% 5.45/5.75 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) )
% 5.45/5.75 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 = zero_zero_rat )
% 5.45/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_eq_eq_numeral1(2)
% 5.45/5.75 thf(fact_5010_less__divide__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [A: rat,B: rat,W2: num] :
% 5.45/5.75 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) )
% 5.45/5.75 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_divide_eq_numeral1(2)
% 5.45/5.75 thf(fact_5011_divide__less__eq__numeral1_I2_J,axiom,
% 5.45/5.75 ! [B: rat,W2: num,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ A )
% 5.45/5.75 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_less_eq_numeral1(2)
% 5.45/5.75 thf(fact_5012_zero__less__power__abs__iff,axiom,
% 5.45/5.75 ! [A: code_integer,N2: nat] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 5.45/5.75 = ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.75 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_power_abs_iff
% 5.45/5.75 thf(fact_5013_zero__less__power__abs__iff,axiom,
% 5.45/5.75 ! [A: rat,N2: nat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 5.45/5.75 = ( ( A != zero_zero_rat )
% 5.45/5.75 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_power_abs_iff
% 5.45/5.75 thf(fact_5014_zero__less__power__abs__iff,axiom,
% 5.45/5.75 ! [A: int,N2: nat] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.45/5.75 = ( ( A != zero_zero_int )
% 5.45/5.75 | ( N2 = zero_zero_nat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_power_abs_iff
% 5.45/5.75 thf(fact_5015_small__lazy_H_Ocases,axiom,
% 5.45/5.75 ! [X: product_prod_int_int] :
% 5.45/5.75 ~ ! [D: int,I3: int] :
% 5.45/5.75 ( X
% 5.45/5.75 != ( product_Pair_int_int @ D @ I3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % small_lazy'.cases
% 5.45/5.75 thf(fact_5016_exhaustive__int_H_Ocases,axiom,
% 5.45/5.75 ! [X: produc7773217078559923341nt_int] :
% 5.45/5.75 ~ ! [F2: int > option6357759511663192854e_term,D: int,I3: int] :
% 5.45/5.75 ( X
% 5.45/5.75 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D @ I3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % exhaustive_int'.cases
% 5.45/5.75 thf(fact_5017_full__exhaustive__int_H_Ocases,axiom,
% 5.45/5.75 ! [X: produc2285326912895808259nt_int] :
% 5.45/5.75 ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D: int,I3: int] :
% 5.45/5.75 ( X
% 5.45/5.75 != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D @ I3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % full_exhaustive_int'.cases
% 5.45/5.75 thf(fact_5018_unique__remainder,axiom,
% 5.45/5.75 ! [A: int,B: int,Q6: int,R3: int,Q8: int,R7: int] :
% 5.45/5.75 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.75 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q8 @ R7 ) )
% 5.45/5.75 => ( R3 = R7 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % unique_remainder
% 5.45/5.75 thf(fact_5019_unique__quotient,axiom,
% 5.45/5.75 ! [A: int,B: int,Q6: int,R3: int,Q8: int,R7: int] :
% 5.45/5.75 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.75 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q8 @ R7 ) )
% 5.45/5.75 => ( Q6 = Q8 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % unique_quotient
% 5.45/5.75 thf(fact_5020_abs__ge__minus__self,axiom,
% 5.45/5.75 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_minus_self
% 5.45/5.75 thf(fact_5021_abs__ge__minus__self,axiom,
% 5.45/5.75 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_minus_self
% 5.45/5.75 thf(fact_5022_abs__ge__minus__self,axiom,
% 5.45/5.75 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_minus_self
% 5.45/5.75 thf(fact_5023_abs__le__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.45/5.75 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.75 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_iff
% 5.45/5.75 thf(fact_5024_abs__le__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.45/5.75 = ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.75 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_iff
% 5.45/5.75 thf(fact_5025_abs__le__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.45/5.75 = ( ( ord_less_eq_int @ A @ B )
% 5.45/5.75 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_iff
% 5.45/5.75 thf(fact_5026_abs__le__D2,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.45/5.75 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D2
% 5.45/5.75 thf(fact_5027_abs__le__D2,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D2
% 5.45/5.75 thf(fact_5028_abs__le__D2,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D2
% 5.45/5.75 thf(fact_5029_abs__leI,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.75 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.45/5.75 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_leI
% 5.45/5.75 thf(fact_5030_abs__leI,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.75 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_leI
% 5.45/5.75 thf(fact_5031_abs__leI,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.75 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_leI
% 5.45/5.75 thf(fact_5032_abs__less__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.45/5.75 = ( ( ord_less_int @ A @ B )
% 5.45/5.75 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_less_iff
% 5.45/5.75 thf(fact_5033_abs__less__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.45/5.75 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.75 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_less_iff
% 5.45/5.75 thf(fact_5034_abs__less__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.45/5.75 = ( ( ord_less_rat @ A @ B )
% 5.45/5.75 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_less_iff
% 5.45/5.75 thf(fact_5035_abs__eq__iff_H,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ( abs_abs_Code_integer @ A )
% 5.45/5.75 = B )
% 5.45/5.75 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.75 & ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_iff'
% 5.45/5.75 thf(fact_5036_abs__eq__iff_H,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ( abs_abs_rat @ A )
% 5.45/5.75 = B )
% 5.45/5.75 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.75 & ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_iff'
% 5.45/5.75 thf(fact_5037_abs__eq__iff_H,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ( abs_abs_int @ A )
% 5.45/5.75 = B )
% 5.45/5.75 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.75 & ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_iff'
% 5.45/5.75 thf(fact_5038_eq__abs__iff_H,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( A
% 5.45/5.75 = ( abs_abs_Code_integer @ B ) )
% 5.45/5.75 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.75 & ( ( B = A )
% 5.45/5.75 | ( B
% 5.45/5.75 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_abs_iff'
% 5.45/5.75 thf(fact_5039_eq__abs__iff_H,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( A
% 5.45/5.75 = ( abs_abs_rat @ B ) )
% 5.45/5.75 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.75 & ( ( B = A )
% 5.45/5.75 | ( B
% 5.45/5.75 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_abs_iff'
% 5.45/5.75 thf(fact_5040_eq__abs__iff_H,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( A
% 5.45/5.75 = ( abs_abs_int @ B ) )
% 5.45/5.75 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.75 & ( ( B = A )
% 5.45/5.75 | ( B
% 5.45/5.75 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_abs_iff'
% 5.45/5.75 thf(fact_5041_abs__minus__le__zero,axiom,
% 5.45/5.75 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.75
% 5.45/5.75 % abs_minus_le_zero
% 5.45/5.75 thf(fact_5042_abs__minus__le__zero,axiom,
% 5.45/5.75 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.45/5.75
% 5.45/5.75 % abs_minus_le_zero
% 5.45/5.75 thf(fact_5043_abs__minus__le__zero,axiom,
% 5.45/5.75 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % abs_minus_le_zero
% 5.45/5.75 thf(fact_5044_abs__if,axiom,
% 5.45/5.75 ( abs_abs_int
% 5.45/5.75 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if
% 5.45/5.75 thf(fact_5045_abs__if,axiom,
% 5.45/5.75 ( abs_abs_Code_integer
% 5.45/5.75 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if
% 5.45/5.75 thf(fact_5046_abs__if,axiom,
% 5.45/5.75 ( abs_abs_rat
% 5.45/5.75 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if
% 5.45/5.75 thf(fact_5047_abs__if__raw,axiom,
% 5.45/5.75 ( abs_abs_int
% 5.45/5.75 = ( ^ [A5: int] : ( if_int @ ( ord_less_int @ A5 @ zero_zero_int ) @ ( uminus_uminus_int @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if_raw
% 5.45/5.75 thf(fact_5048_abs__if__raw,axiom,
% 5.45/5.75 ( abs_abs_Code_integer
% 5.45/5.75 = ( ^ [A5: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A5 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if_raw
% 5.45/5.75 thf(fact_5049_abs__if__raw,axiom,
% 5.45/5.75 ( abs_abs_rat
% 5.45/5.75 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_if_raw
% 5.45/5.75 thf(fact_5050_abs__of__neg,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.75 => ( ( abs_abs_int @ A )
% 5.45/5.75 = ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_neg
% 5.45/5.75 thf(fact_5051_abs__of__neg,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.75 => ( ( abs_abs_Code_integer @ A )
% 5.45/5.75 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_neg
% 5.45/5.75 thf(fact_5052_abs__of__neg,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.75 => ( ( abs_abs_rat @ A )
% 5.45/5.75 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_neg
% 5.45/5.75 thf(fact_5053_zabs__def,axiom,
% 5.45/5.75 ( abs_abs_int
% 5.45/5.75 = ( ^ [I4: int] : ( if_int @ ( ord_less_int @ I4 @ zero_zero_int ) @ ( uminus_uminus_int @ I4 ) @ I4 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zabs_def
% 5.45/5.75 thf(fact_5054_abs__le__D1,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.45/5.75 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D1
% 5.45/5.75 thf(fact_5055_abs__le__D1,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D1
% 5.45/5.75 thf(fact_5056_abs__le__D1,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.45/5.75 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_le_D1
% 5.45/5.75 thf(fact_5057_abs__ge__self,axiom,
% 5.45/5.75 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_self
% 5.45/5.75 thf(fact_5058_abs__ge__self,axiom,
% 5.45/5.75 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_self
% 5.45/5.75 thf(fact_5059_abs__ge__self,axiom,
% 5.45/5.75 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_self
% 5.45/5.75 thf(fact_5060_abs__mult,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult
% 5.45/5.75 thf(fact_5061_abs__mult,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.75 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult
% 5.45/5.75 thf(fact_5062_abs__mult,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.45/5.75 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult
% 5.45/5.75 thf(fact_5063_le__imp__neg__le,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.75 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_imp_neg_le
% 5.45/5.75 thf(fact_5064_le__imp__neg__le,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.75 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_imp_neg_le
% 5.45/5.75 thf(fact_5065_le__imp__neg__le,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A @ B )
% 5.45/5.75 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_imp_neg_le
% 5.45/5.75 thf(fact_5066_minus__le__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_le_iff
% 5.45/5.75 thf(fact_5067_minus__le__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.45/5.75 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_le_iff
% 5.45/5.75 thf(fact_5068_minus__le__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.45/5.75 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_le_iff
% 5.45/5.75 thf(fact_5069_le__minus__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.45/5.75 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_iff
% 5.45/5.75 thf(fact_5070_le__minus__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.45/5.75 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_iff
% 5.45/5.75 thf(fact_5071_le__minus__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.45/5.75 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_iff
% 5.45/5.75 thf(fact_5072_compl__le__swap2,axiom,
% 5.45/5.75 ! [Y: assn,X: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 5.45/5.75 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap2
% 5.45/5.75 thf(fact_5073_compl__le__swap2,axiom,
% 5.45/5.75 ! [Y: product_unit,X: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 5.45/5.75 => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap2
% 5.45/5.75 thf(fact_5074_compl__le__swap2,axiom,
% 5.45/5.75 ! [Y: set_int,X: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 5.45/5.75 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap2
% 5.45/5.75 thf(fact_5075_compl__le__swap1,axiom,
% 5.45/5.75 ! [Y: assn,X: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 5.45/5.75 => ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap1
% 5.45/5.75 thf(fact_5076_compl__le__swap1,axiom,
% 5.45/5.75 ! [Y: product_unit,X: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 5.45/5.75 => ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap1
% 5.45/5.75 thf(fact_5077_compl__le__swap1,axiom,
% 5.45/5.75 ! [Y: set_int,X: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 5.45/5.75 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_le_swap1
% 5.45/5.75 thf(fact_5078_compl__mono,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ X @ Y )
% 5.45/5.75 => ( ord_less_eq_assn @ ( uminus_uminus_assn @ Y ) @ ( uminus_uminus_assn @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_mono
% 5.45/5.75 thf(fact_5079_compl__mono,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ X @ Y )
% 5.45/5.75 => ( ord_le3221252021190050221t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ ( uminus2952777764628376836t_unit @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_mono
% 5.45/5.75 thf(fact_5080_compl__mono,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ X @ Y )
% 5.45/5.75 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_mono
% 5.45/5.75 thf(fact_5081_minus__less__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.45/5.75 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_less_iff
% 5.45/5.75 thf(fact_5082_minus__less__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_less_iff
% 5.45/5.75 thf(fact_5083_minus__less__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.45/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_less_iff
% 5.45/5.75 thf(fact_5084_less__minus__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.45/5.75 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_iff
% 5.45/5.75 thf(fact_5085_less__minus__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.45/5.75 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_iff
% 5.45/5.75 thf(fact_5086_less__minus__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.45/5.75 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_iff
% 5.45/5.75 thf(fact_5087_verit__negate__coefficient_I2_J,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ord_less_int @ A @ B )
% 5.45/5.75 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % verit_negate_coefficient(2)
% 5.45/5.75 thf(fact_5088_verit__negate__coefficient_I2_J,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.75 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % verit_negate_coefficient(2)
% 5.45/5.75 thf(fact_5089_verit__negate__coefficient_I2_J,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ A @ B )
% 5.45/5.75 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % verit_negate_coefficient(2)
% 5.45/5.75 thf(fact_5090_compl__less__swap1,axiom,
% 5.45/5.75 ! [Y: assn,X: assn] :
% 5.45/5.75 ( ( ord_less_assn @ Y @ ( uminus_uminus_assn @ X ) )
% 5.45/5.75 => ( ord_less_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_swap1
% 5.45/5.75 thf(fact_5091_compl__less__swap1,axiom,
% 5.45/5.75 ! [Y: product_unit,X: product_unit] :
% 5.45/5.75 ( ( ord_le361264281704409273t_unit @ Y @ ( uminus2952777764628376836t_unit @ X ) )
% 5.45/5.75 => ( ord_le361264281704409273t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_swap1
% 5.45/5.75 thf(fact_5092_compl__less__swap2,axiom,
% 5.45/5.75 ! [Y: assn,X: assn] :
% 5.45/5.75 ( ( ord_less_assn @ ( uminus_uminus_assn @ Y ) @ X )
% 5.45/5.75 => ( ord_less_assn @ ( uminus_uminus_assn @ X ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_swap2
% 5.45/5.75 thf(fact_5093_compl__less__swap2,axiom,
% 5.45/5.75 ! [Y: product_unit,X: product_unit] :
% 5.45/5.75 ( ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ Y ) @ X )
% 5.45/5.75 => ( ord_le361264281704409273t_unit @ ( uminus2952777764628376836t_unit @ X ) @ Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % compl_less_swap2
% 5.45/5.75 thf(fact_5094_square__eq__iff,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ( times_times_int @ A @ A )
% 5.45/5.75 = ( times_times_int @ B @ B ) )
% 5.45/5.75 = ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_iff
% 5.45/5.75 thf(fact_5095_square__eq__iff,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.45/5.75 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.45/5.75 = ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_iff
% 5.45/5.75 thf(fact_5096_square__eq__iff,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ( times_times_rat @ A @ A )
% 5.45/5.75 = ( times_times_rat @ B @ B ) )
% 5.45/5.75 = ( ( A = B )
% 5.45/5.75 | ( A
% 5.45/5.75 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_iff
% 5.45/5.75 thf(fact_5097_minus__mult__commute,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.45/5.75 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_commute
% 5.45/5.75 thf(fact_5098_minus__mult__commute,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.45/5.75 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_commute
% 5.45/5.75 thf(fact_5099_minus__mult__commute,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.45/5.75 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mult_commute
% 5.45/5.75 thf(fact_5100_minus__assn__def,axiom,
% 5.45/5.75 ( minus_minus_assn
% 5.45/5.75 = ( ^ [A5: assn,B5: assn] : ( inf_inf_assn @ A5 @ ( uminus_uminus_assn @ B5 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_assn_def
% 5.45/5.75 thf(fact_5101_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.75 ( ( collec213857154873943460nt_int
% 5.45/5.75 @ ^ [X4: product_prod_int_int] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_su6024340866399070445nt_int @ ( uminus6221592323253981072nt_int @ ( collec213857154873943460nt_int @ P ) ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5102_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.75 ( ( collect_list_nat
% 5.45/5.75 @ ^ [X4: list_nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_sup_set_list_nat @ ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5103_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.75 ( ( collect_set_nat
% 5.45/5.75 @ ^ [X4: set_nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_sup_set_set_nat @ ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5104_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: int > $o,Q: int > $o] :
% 5.45/5.75 ( ( collect_int
% 5.45/5.75 @ ^ [X4: int] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) @ ( collect_int @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5105_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: produc859450856879609959at_nat > $o,Q: produc859450856879609959at_nat > $o] :
% 5.45/5.75 ( ( collec7088162979684241874at_nat
% 5.45/5.75 @ ^ [X4: produc859450856879609959at_nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ ( collec7088162979684241874at_nat @ P ) ) @ ( collec7088162979684241874at_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5106_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: produc4166570645942440679at_nat > $o,Q: produc4166570645942440679at_nat > $o] :
% 5.45/5.75 ( ( collec5204685387357076818at_nat
% 5.45/5.75 @ ^ [X4: produc4166570645942440679at_nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ ( collec5204685387357076818at_nat @ P ) ) @ ( collec5204685387357076818at_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5107_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: produc3843707927480180839at_nat > $o,Q: produc3843707927480180839at_nat > $o] :
% 5.45/5.75 ( ( collec6321179662152712658at_nat
% 5.45/5.75 @ ^ [X4: produc3843707927480180839at_nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ ( collec6321179662152712658at_nat @ P ) ) @ ( collec6321179662152712658at_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5108_Collect__imp__eq,axiom,
% 5.45/5.75 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.75 ( ( collect_nat
% 5.45/5.75 @ ^ [X4: nat] :
% 5.45/5.75 ( ( P @ X4 )
% 5.45/5.75 => ( Q @ X4 ) ) )
% 5.45/5.75 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) @ ( collect_nat @ Q ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_imp_eq
% 5.45/5.75 thf(fact_5109_eucl__rel__int__by0,axiom,
% 5.45/5.75 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.45/5.75
% 5.45/5.75 % eucl_rel_int_by0
% 5.45/5.75 thf(fact_5110_div__int__unique,axiom,
% 5.45/5.75 ! [K: int,L: int,Q6: int,R3: int] :
% 5.45/5.75 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.75 => ( ( divide_divide_int @ K @ L )
% 5.45/5.75 = Q6 ) ) ).
% 5.45/5.75
% 5.45/5.75 % div_int_unique
% 5.45/5.75 thf(fact_5111_zminus1__lemma,axiom,
% 5.45/5.75 ! [A: int,B: int,Q6: int,R3: int] :
% 5.45/5.75 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.75 => ( ( B != zero_zero_int )
% 5.45/5.75 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q6 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q6 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zminus1_lemma
% 5.45/5.75 thf(fact_5112_mod__int__unique,axiom,
% 5.45/5.75 ! [K: int,L: int,Q6: int,R3: int] :
% 5.45/5.75 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.75 => ( ( modulo_modulo_int @ K @ L )
% 5.45/5.75 = R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % mod_int_unique
% 5.45/5.75 thf(fact_5113_abs__ge__zero,axiom,
% 5.45/5.75 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_zero
% 5.45/5.75 thf(fact_5114_abs__ge__zero,axiom,
% 5.45/5.75 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_zero
% 5.45/5.75 thf(fact_5115_abs__ge__zero,axiom,
% 5.45/5.75 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_ge_zero
% 5.45/5.75 thf(fact_5116_abs__of__pos,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.75 => ( ( abs_abs_Code_integer @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_pos
% 5.45/5.75 thf(fact_5117_abs__of__pos,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.75 => ( ( abs_abs_rat @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_pos
% 5.45/5.75 thf(fact_5118_abs__of__pos,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.75 => ( ( abs_abs_int @ A )
% 5.45/5.75 = A ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_of_pos
% 5.45/5.75 thf(fact_5119_abs__not__less__zero,axiom,
% 5.45/5.75 ! [A: code_integer] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.75
% 5.45/5.75 % abs_not_less_zero
% 5.45/5.75 thf(fact_5120_abs__not__less__zero,axiom,
% 5.45/5.75 ! [A: rat] :
% 5.45/5.75 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.45/5.75
% 5.45/5.75 % abs_not_less_zero
% 5.45/5.75 thf(fact_5121_abs__not__less__zero,axiom,
% 5.45/5.75 ! [A: int] :
% 5.45/5.75 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % abs_not_less_zero
% 5.45/5.75 thf(fact_5122_abs__triangle__ineq,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq
% 5.45/5.75 thf(fact_5123_abs__triangle__ineq,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq
% 5.45/5.75 thf(fact_5124_abs__triangle__ineq,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq
% 5.45/5.75 thf(fact_5125_abs__triangle__ineq2,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2
% 5.45/5.75 thf(fact_5126_abs__triangle__ineq2,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2
% 5.45/5.75 thf(fact_5127_abs__triangle__ineq2,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2
% 5.45/5.75 thf(fact_5128_abs__triangle__ineq3,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq3
% 5.45/5.75 thf(fact_5129_abs__triangle__ineq3,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq3
% 5.45/5.75 thf(fact_5130_abs__triangle__ineq3,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq3
% 5.45/5.75 thf(fact_5131_abs__triangle__ineq2__sym,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2_sym
% 5.45/5.75 thf(fact_5132_abs__triangle__ineq2__sym,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2_sym
% 5.45/5.75 thf(fact_5133_abs__triangle__ineq2__sym,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq2_sym
% 5.45/5.75 thf(fact_5134_abs__mult__less,axiom,
% 5.45/5.75 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.45/5.75 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D2 )
% 5.45/5.75 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_less
% 5.45/5.75 thf(fact_5135_abs__mult__less,axiom,
% 5.45/5.75 ! [A: rat,C: rat,B: rat,D2: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.45/5.75 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D2 )
% 5.45/5.75 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_less
% 5.45/5.75 thf(fact_5136_abs__mult__less,axiom,
% 5.45/5.75 ! [A: int,C: int,B: int,D2: int] :
% 5.45/5.75 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.45/5.75 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D2 )
% 5.45/5.75 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_less
% 5.45/5.75 thf(fact_5137_neg__numeral__le__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_numeral
% 5.45/5.75 thf(fact_5138_neg__numeral__le__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_numeral
% 5.45/5.75 thf(fact_5139_neg__numeral__le__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_numeral
% 5.45/5.75 thf(fact_5140_not__numeral__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_numeral
% 5.45/5.75 thf(fact_5141_not__numeral__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_numeral
% 5.45/5.75 thf(fact_5142_not__numeral__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_numeral
% 5.45/5.75 thf(fact_5143_le__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(2)
% 5.45/5.75 thf(fact_5144_le__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(2)
% 5.45/5.75 thf(fact_5145_le__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(2)
% 5.45/5.75 thf(fact_5146_le__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(4)
% 5.45/5.75 thf(fact_5147_le__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(4)
% 5.45/5.75 thf(fact_5148_le__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(4)
% 5.45/5.75 thf(fact_5149_neg__numeral__less__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_numeral
% 5.45/5.75 thf(fact_5150_neg__numeral__less__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_numeral
% 5.45/5.75 thf(fact_5151_neg__numeral__less__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_numeral
% 5.45/5.75 thf(fact_5152_not__numeral__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_numeral
% 5.45/5.75 thf(fact_5153_not__numeral__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_numeral
% 5.45/5.75 thf(fact_5154_not__numeral__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num,N2: num] :
% 5.45/5.75 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_numeral
% 5.45/5.75 thf(fact_5155_less__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(2)
% 5.45/5.75 thf(fact_5156_less__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(2)
% 5.45/5.75 thf(fact_5157_less__minus__one__simps_I2_J,axiom,
% 5.45/5.75 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(2)
% 5.45/5.75 thf(fact_5158_less__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(4)
% 5.45/5.75 thf(fact_5159_less__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(4)
% 5.45/5.75 thf(fact_5160_less__minus__one__simps_I4_J,axiom,
% 5.45/5.75 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(4)
% 5.45/5.75 thf(fact_5161_numeral__times__minus__swap,axiom,
% 5.45/5.75 ! [W2: num,X: int] :
% 5.45/5.75 ( ( times_times_int @ ( numeral_numeral_int @ W2 ) @ ( uminus_uminus_int @ X ) )
% 5.45/5.75 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % numeral_times_minus_swap
% 5.45/5.75 thf(fact_5162_numeral__times__minus__swap,axiom,
% 5.45/5.75 ! [W2: num,X: code_integer] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W2 ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % numeral_times_minus_swap
% 5.45/5.75 thf(fact_5163_numeral__times__minus__swap,axiom,
% 5.45/5.75 ! [W2: num,X: rat] :
% 5.45/5.75 ( ( times_times_rat @ ( numeral_numeral_rat @ W2 ) @ ( uminus_uminus_rat @ X ) )
% 5.45/5.75 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % numeral_times_minus_swap
% 5.45/5.75 thf(fact_5164_square__eq__1__iff,axiom,
% 5.45/5.75 ! [X: int] :
% 5.45/5.75 ( ( ( times_times_int @ X @ X )
% 5.45/5.75 = one_one_int )
% 5.45/5.75 = ( ( X = one_one_int )
% 5.45/5.75 | ( X
% 5.45/5.75 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_1_iff
% 5.45/5.75 thf(fact_5165_square__eq__1__iff,axiom,
% 5.45/5.75 ! [X: code_integer] :
% 5.45/5.75 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.45/5.75 = one_one_Code_integer )
% 5.45/5.75 = ( ( X = one_one_Code_integer )
% 5.45/5.75 | ( X
% 5.45/5.75 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_1_iff
% 5.45/5.75 thf(fact_5166_square__eq__1__iff,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ( times_times_rat @ X @ X )
% 5.45/5.75 = one_one_rat )
% 5.45/5.75 = ( ( X = one_one_rat )
% 5.45/5.75 | ( X
% 5.45/5.75 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % square_eq_1_iff
% 5.45/5.75 thf(fact_5167_diff__eq,axiom,
% 5.45/5.75 ( minus_1356011639430497352at_nat
% 5.45/5.75 = ( ^ [X4: set_Pr1261947904930325089at_nat,Y4: set_Pr1261947904930325089at_nat] : ( inf_in2572325071724192079at_nat @ X4 @ ( uminus6524753893492686040at_nat @ Y4 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % diff_eq
% 5.45/5.75 thf(fact_5168_diff__eq,axiom,
% 5.45/5.75 ( minus_minus_set_nat
% 5.45/5.75 = ( ^ [X4: set_nat,Y4: set_nat] : ( inf_inf_set_nat @ X4 @ ( uminus5710092332889474511et_nat @ Y4 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % diff_eq
% 5.45/5.75 thf(fact_5169_diff__eq,axiom,
% 5.45/5.75 ( minus_minus_assn
% 5.45/5.75 = ( ^ [X4: assn,Y4: assn] : ( inf_inf_assn @ X4 @ ( uminus_uminus_assn @ Y4 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % diff_eq
% 5.45/5.75 thf(fact_5170_diff__eq,axiom,
% 5.45/5.75 ( minus_3524152463667985524t_unit
% 5.45/5.75 = ( ^ [X4: product_unit,Y4: product_unit] : ( inf_inf_Product_unit @ X4 @ ( uminus2952777764628376836t_unit @ Y4 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % diff_eq
% 5.45/5.75 thf(fact_5171_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ A ) @ ( inf_in2572325071724192079at_nat @ X @ B ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5172_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: set_o,A: set_o,B: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ A ) @ ( inf_inf_set_o @ X @ B ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5173_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ A ) @ ( inf_inf_set_nat @ X @ B ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5174_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: set_int,A: set_int,B: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ A ) @ ( inf_inf_set_int @ X @ B ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5175_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: assn,A: assn,B: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ A ) @ ( inf_inf_assn @ X @ B ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5176_inf__cancel__left2,axiom,
% 5.45/5.75 ! [X: product_unit,A: product_unit,B: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ A ) @ ( inf_inf_Product_unit @ X @ B ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left2
% 5.45/5.75 thf(fact_5177_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,A: set_Pr1261947904930325089at_nat,B: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( inf_in2572325071724192079at_nat @ ( inf_in2572325071724192079at_nat @ X @ A ) @ ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ X ) @ B ) )
% 5.45/5.75 = bot_bo2099793752762293965at_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5178_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: set_o,A: set_o,B: set_o] :
% 5.45/5.75 ( ( inf_inf_set_o @ ( inf_inf_set_o @ X @ A ) @ ( inf_inf_set_o @ ( uminus_uminus_set_o @ X ) @ B ) )
% 5.45/5.75 = bot_bot_set_o ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5179_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: set_nat,A: set_nat,B: set_nat] :
% 5.45/5.75 ( ( inf_inf_set_nat @ ( inf_inf_set_nat @ X @ A ) @ ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ X ) @ B ) )
% 5.45/5.75 = bot_bot_set_nat ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5180_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: set_int,A: set_int,B: set_int] :
% 5.45/5.75 ( ( inf_inf_set_int @ ( inf_inf_set_int @ X @ A ) @ ( inf_inf_set_int @ ( uminus1532241313380277803et_int @ X ) @ B ) )
% 5.45/5.75 = bot_bot_set_int ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5181_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: assn,A: assn,B: assn] :
% 5.45/5.75 ( ( inf_inf_assn @ ( inf_inf_assn @ X @ A ) @ ( inf_inf_assn @ ( uminus_uminus_assn @ X ) @ B ) )
% 5.45/5.75 = bot_bot_assn ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5182_inf__cancel__left1,axiom,
% 5.45/5.75 ! [X: product_unit,A: product_unit,B: product_unit] :
% 5.45/5.75 ( ( inf_inf_Product_unit @ ( inf_inf_Product_unit @ X @ A ) @ ( inf_inf_Product_unit @ ( uminus2952777764628376836t_unit @ X ) @ B ) )
% 5.45/5.75 = bot_bot_Product_unit ) ).
% 5.45/5.75
% 5.45/5.75 % inf_cancel_left1
% 5.45/5.75 thf(fact_5183_subset__Compl__self__eq,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ord_le3146513528884898305at_nat @ A3 @ ( uminus6524753893492686040at_nat @ A3 ) )
% 5.45/5.75 = ( A3 = bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.75
% 5.45/5.75 % subset_Compl_self_eq
% 5.45/5.75 thf(fact_5184_subset__Compl__self__eq,axiom,
% 5.45/5.75 ! [A3: set_o] :
% 5.45/5.75 ( ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ A3 ) )
% 5.45/5.75 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.75
% 5.45/5.75 % subset_Compl_self_eq
% 5.45/5.75 thf(fact_5185_subset__Compl__self__eq,axiom,
% 5.45/5.75 ! [A3: set_nat] :
% 5.45/5.75 ( ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.45/5.75 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.75
% 5.45/5.75 % subset_Compl_self_eq
% 5.45/5.75 thf(fact_5186_subset__Compl__self__eq,axiom,
% 5.45/5.75 ! [A3: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.45/5.75 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % subset_Compl_self_eq
% 5.45/5.75 thf(fact_5187_Compl__Int,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( uminus6524753893492686040at_nat @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Int
% 5.45/5.75 thf(fact_5188_Compl__Int,axiom,
% 5.45/5.75 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( uminus4384627049435823934at_nat @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ ( uminus4384627049435823934at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Int
% 5.45/5.75 thf(fact_5189_Compl__Int,axiom,
% 5.45/5.75 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( uminus2330091110623919550at_nat @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ A3 ) @ ( uminus2330091110623919550at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Int
% 5.45/5.75 thf(fact_5190_Compl__Int,axiom,
% 5.45/5.75 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( uminus935396558254630718at_nat @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ ( uminus935396558254630718at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Int
% 5.45/5.75 thf(fact_5191_Compl__Int,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( uminus5710092332889474511et_nat @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Int
% 5.45/5.75 thf(fact_5192_Compl__Un,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( uminus6524753893492686040at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( inf_in2572325071724192079at_nat @ ( uminus6524753893492686040at_nat @ A3 ) @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Un
% 5.45/5.75 thf(fact_5193_Compl__Un,axiom,
% 5.45/5.75 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( uminus4384627049435823934at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( inf_in4302113700860409141at_nat @ ( uminus4384627049435823934at_nat @ A3 ) @ ( uminus4384627049435823934at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Un
% 5.45/5.75 thf(fact_5194_Compl__Un,axiom,
% 5.45/5.75 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( uminus2330091110623919550at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( inf_in1697001100524423349at_nat @ ( uminus2330091110623919550at_nat @ A3 ) @ ( uminus2330091110623919550at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Un
% 5.45/5.75 thf(fact_5195_Compl__Un,axiom,
% 5.45/5.75 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( uminus935396558254630718at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( inf_in7913087082777306421at_nat @ ( uminus935396558254630718at_nat @ A3 ) @ ( uminus935396558254630718at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Un
% 5.45/5.75 thf(fact_5196_Compl__Un,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( uminus5710092332889474511et_nat @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.75 = ( inf_inf_set_nat @ ( uminus5710092332889474511et_nat @ A3 ) @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_Un
% 5.45/5.75 thf(fact_5197_not__int__zless__negative,axiom,
% 5.45/5.75 ! [N2: nat,M: nat] :
% 5.45/5.75 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_int_zless_negative
% 5.45/5.75 thf(fact_5198_dense__eq0__I,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ! [E2: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.45/5.75 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.45/5.75 => ( X = zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % dense_eq0_I
% 5.45/5.75 thf(fact_5199_abs__eq__mult,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer] :
% 5.45/5.75 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.75 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.45/5.75 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.75 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.45/5.75 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_mult
% 5.45/5.75 thf(fact_5200_abs__eq__mult,axiom,
% 5.45/5.75 ! [A: rat,B: rat] :
% 5.45/5.75 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.75 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.45/5.75 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.75 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.45/5.75 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.75 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_mult
% 5.45/5.75 thf(fact_5201_abs__eq__mult,axiom,
% 5.45/5.75 ! [A: int,B: int] :
% 5.45/5.75 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.75 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.45/5.75 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.75 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.45/5.75 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.45/5.75 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_eq_mult
% 5.45/5.75 thf(fact_5202_abs__mult__pos,axiom,
% 5.45/5.75 ! [X: code_integer,Y: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.75 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.45/5.75 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_pos
% 5.45/5.75 thf(fact_5203_abs__mult__pos,axiom,
% 5.45/5.75 ! [X: rat,Y: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.75 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.45/5.75 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_pos
% 5.45/5.75 thf(fact_5204_abs__mult__pos,axiom,
% 5.45/5.75 ! [X: int,Y: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.75 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.45/5.75 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mult_pos
% 5.45/5.75 thf(fact_5205_abs__diff__triangle__ineq,axiom,
% 5.45/5.75 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D2 ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_triangle_ineq
% 5.45/5.75 thf(fact_5206_abs__diff__triangle__ineq,axiom,
% 5.45/5.75 ! [A: rat,B: rat,C: rat,D2: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D2 ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_triangle_ineq
% 5.45/5.75 thf(fact_5207_abs__diff__triangle__ineq,axiom,
% 5.45/5.75 ! [A: int,B: int,C: int,D2: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D2 ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_triangle_ineq
% 5.45/5.75 thf(fact_5208_abs__triangle__ineq4,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq4
% 5.45/5.75 thf(fact_5209_abs__triangle__ineq4,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq4
% 5.45/5.75 thf(fact_5210_abs__triangle__ineq4,axiom,
% 5.45/5.75 ! [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 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_triangle_ineq4
% 5.45/5.75 thf(fact_5211_abs__diff__le__iff,axiom,
% 5.45/5.75 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 5.45/5.75 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_le_iff
% 5.45/5.75 thf(fact_5212_abs__diff__le__iff,axiom,
% 5.45/5.75 ! [X: rat,A: rat,R3: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_le_iff
% 5.45/5.75 thf(fact_5213_abs__diff__le__iff,axiom,
% 5.45/5.75 ! [X: int,A: int,R3: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_le_iff
% 5.45/5.75 thf(fact_5214_abs__diff__less__iff,axiom,
% 5.45/5.75 ! [X: code_integer,A: code_integer,R3: code_integer] :
% 5.45/5.75 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_less_iff
% 5.45/5.75 thf(fact_5215_abs__diff__less__iff,axiom,
% 5.45/5.75 ! [X: rat,A: rat,R3: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_less_iff
% 5.45/5.75 thf(fact_5216_abs__diff__less__iff,axiom,
% 5.45/5.75 ! [X: int,A: int,R3: int] :
% 5.45/5.75 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R3 )
% 5.45/5.75 = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X )
% 5.45/5.75 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_diff_less_iff
% 5.45/5.75 thf(fact_5217_abs__div__pos,axiom,
% 5.45/5.75 ! [Y: rat,X: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.45/5.75 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.45/5.75 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_div_pos
% 5.45/5.75 thf(fact_5218_zero__le__power__abs,axiom,
% 5.45/5.75 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_le_power_abs
% 5.45/5.75 thf(fact_5219_zero__le__power__abs,axiom,
% 5.45/5.75 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_le_power_abs
% 5.45/5.75 thf(fact_5220_zero__le__power__abs,axiom,
% 5.45/5.75 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_le_power_abs
% 5.45/5.75 thf(fact_5221_not__zero__le__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_le_neg_numeral
% 5.45/5.75 thf(fact_5222_not__zero__le__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_le_neg_numeral
% 5.45/5.75 thf(fact_5223_not__zero__le__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_le_neg_numeral
% 5.45/5.75 thf(fact_5224_neg__numeral__le__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_zero
% 5.45/5.75 thf(fact_5225_neg__numeral__le__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_zero
% 5.45/5.75 thf(fact_5226_neg__numeral__le__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_zero
% 5.45/5.75 thf(fact_5227_le__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(1)
% 5.45/5.75 thf(fact_5228_le__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(1)
% 5.45/5.75 thf(fact_5229_le__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(1)
% 5.45/5.75 thf(fact_5230_le__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(3)
% 5.45/5.75 thf(fact_5231_le__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(3)
% 5.45/5.75 thf(fact_5232_le__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_one_simps(3)
% 5.45/5.75 thf(fact_5233_not__zero__less__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_less_neg_numeral
% 5.45/5.75 thf(fact_5234_not__zero__less__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_less_neg_numeral
% 5.45/5.75 thf(fact_5235_not__zero__less__neg__numeral,axiom,
% 5.45/5.75 ! [N2: num] :
% 5.45/5.75 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zero_less_neg_numeral
% 5.45/5.75 thf(fact_5236_neg__numeral__less__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_zero
% 5.45/5.75 thf(fact_5237_neg__numeral__less__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_zero
% 5.45/5.75 thf(fact_5238_neg__numeral__less__zero,axiom,
% 5.45/5.75 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_zero
% 5.45/5.75 thf(fact_5239_less__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(1)
% 5.45/5.75 thf(fact_5240_less__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(1)
% 5.45/5.75 thf(fact_5241_less__minus__one__simps_I1_J,axiom,
% 5.45/5.75 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(1)
% 5.45/5.75 thf(fact_5242_less__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(3)
% 5.45/5.75 thf(fact_5243_less__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(3)
% 5.45/5.75 thf(fact_5244_less__minus__one__simps_I3_J,axiom,
% 5.45/5.75 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_one_simps(3)
% 5.45/5.75 thf(fact_5245_not__one__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_le_neg_numeral
% 5.45/5.75 thf(fact_5246_not__one__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_le_neg_numeral
% 5.45/5.75 thf(fact_5247_not__one__le__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_le_neg_numeral
% 5.45/5.75 thf(fact_5248_not__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_one
% 5.45/5.75 thf(fact_5249_not__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_one
% 5.45/5.75 thf(fact_5250_not__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_le_neg_one
% 5.45/5.75 thf(fact_5251_neg__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_neg_one
% 5.45/5.75 thf(fact_5252_neg__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_neg_one
% 5.45/5.75 thf(fact_5253_neg__numeral__le__neg__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_neg_one
% 5.45/5.75 thf(fact_5254_neg__one__le__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_le_numeral
% 5.45/5.75 thf(fact_5255_neg__one__le__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_le_numeral
% 5.45/5.75 thf(fact_5256_neg__one__le__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_le_numeral
% 5.45/5.75 thf(fact_5257_neg__numeral__le__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_one
% 5.45/5.75 thf(fact_5258_neg__numeral__le__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_one
% 5.45/5.75 thf(fact_5259_neg__numeral__le__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_one
% 5.45/5.75 thf(fact_5260_not__neg__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_neg_one_less_neg_numeral
% 5.45/5.75 thf(fact_5261_not__neg__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_neg_one_less_neg_numeral
% 5.45/5.75 thf(fact_5262_not__neg__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_neg_one_less_neg_numeral
% 5.45/5.75 thf(fact_5263_not__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_less_neg_numeral
% 5.45/5.75 thf(fact_5264_not__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_less_neg_numeral
% 5.45/5.75 thf(fact_5265_not__one__less__neg__numeral,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_one_less_neg_numeral
% 5.45/5.75 thf(fact_5266_not__numeral__less__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_one
% 5.45/5.75 thf(fact_5267_not__numeral__less__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_one
% 5.45/5.75 thf(fact_5268_not__numeral__less__neg__one,axiom,
% 5.45/5.75 ! [M: num] :
% 5.45/5.75 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_numeral_less_neg_one
% 5.45/5.75 thf(fact_5269_neg__one__less__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_less_numeral
% 5.45/5.75 thf(fact_5270_neg__one__less__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_less_numeral
% 5.45/5.75 thf(fact_5271_neg__one__less__numeral,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_less_numeral
% 5.45/5.75 thf(fact_5272_neg__numeral__less__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_one
% 5.45/5.75 thf(fact_5273_neg__numeral__less__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_one
% 5.45/5.75 thf(fact_5274_neg__numeral__less__one,axiom,
% 5.45/5.75 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_one
% 5.45/5.75 thf(fact_5275_nonzero__neg__divide__eq__eq2,axiom,
% 5.45/5.75 ! [B: rat,C: rat,A: rat] :
% 5.45/5.75 ( ( B != zero_zero_rat )
% 5.45/5.75 => ( ( C
% 5.45/5.75 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.45/5.75 = ( ( times_times_rat @ C @ B )
% 5.45/5.75 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % nonzero_neg_divide_eq_eq2
% 5.45/5.75 thf(fact_5276_nonzero__neg__divide__eq__eq,axiom,
% 5.45/5.75 ! [B: rat,A: rat,C: rat] :
% 5.45/5.75 ( ( B != zero_zero_rat )
% 5.45/5.75 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.45/5.75 = C )
% 5.45/5.75 = ( ( uminus_uminus_rat @ A )
% 5.45/5.75 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % nonzero_neg_divide_eq_eq
% 5.45/5.75 thf(fact_5277_minus__divide__eq__eq,axiom,
% 5.45/5.75 ! [B: rat,C: rat,A: rat] :
% 5.45/5.75 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.75 = A )
% 5.45/5.75 = ( ( ( C != zero_zero_rat )
% 5.45/5.75 => ( ( uminus_uminus_rat @ B )
% 5.45/5.75 = ( times_times_rat @ A @ C ) ) )
% 5.45/5.75 & ( ( C = zero_zero_rat )
% 5.45/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_divide_eq_eq
% 5.45/5.75 thf(fact_5278_eq__minus__divide__eq,axiom,
% 5.45/5.75 ! [A: rat,B: rat,C: rat] :
% 5.45/5.75 ( ( A
% 5.45/5.75 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ( ( C != zero_zero_rat )
% 5.45/5.75 => ( ( times_times_rat @ A @ C )
% 5.45/5.75 = ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ( C = zero_zero_rat )
% 5.45/5.75 => ( A = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_minus_divide_eq
% 5.45/5.75 thf(fact_5279_inf__shunt,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ( inf_in2572325071724192079at_nat @ X @ Y )
% 5.45/5.75 = bot_bo2099793752762293965at_nat )
% 5.45/5.75 = ( ord_le3146513528884898305at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5280_inf__shunt,axiom,
% 5.45/5.75 ! [X: set_o,Y: set_o] :
% 5.45/5.75 ( ( ( inf_inf_set_o @ X @ Y )
% 5.45/5.75 = bot_bot_set_o )
% 5.45/5.75 = ( ord_less_eq_set_o @ X @ ( uminus_uminus_set_o @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5281_inf__shunt,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat] :
% 5.45/5.75 ( ( ( inf_inf_set_nat @ X @ Y )
% 5.45/5.75 = bot_bot_set_nat )
% 5.45/5.75 = ( ord_less_eq_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5282_inf__shunt,axiom,
% 5.45/5.75 ! [X: assn,Y: assn] :
% 5.45/5.75 ( ( ( inf_inf_assn @ X @ Y )
% 5.45/5.75 = bot_bot_assn )
% 5.45/5.75 = ( ord_less_eq_assn @ X @ ( uminus_uminus_assn @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5283_inf__shunt,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit] :
% 5.45/5.75 ( ( ( inf_inf_Product_unit @ X @ Y )
% 5.45/5.75 = bot_bot_Product_unit )
% 5.45/5.75 = ( ord_le3221252021190050221t_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5284_inf__shunt,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int] :
% 5.45/5.75 ( ( ( inf_inf_set_int @ X @ Y )
% 5.45/5.75 = bot_bot_set_int )
% 5.45/5.75 = ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % inf_shunt
% 5.45/5.75 thf(fact_5285_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_Pr1261947904930325089at_nat,Q6: set_Pr1261947904930325089at_nat,R3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ord_le3146513528884898305at_nat @ P3 @ ( sup_su6327502436637775413at_nat @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ P3 @ ( uminus6524753893492686040at_nat @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5286_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_Pr8693737435421807431at_nat,Q6: set_Pr8693737435421807431at_nat,R3: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( ord_le3000389064537975527at_nat @ P3 @ ( sup_su718114333110466843at_nat @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ P3 @ ( uminus4384627049435823934at_nat @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5287_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_Pr8551490117392284871at_nat,Q6: set_Pr8551490117392284871at_nat,R3: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( ord_le8081472938463900775at_nat @ P3 @ ( sup_su3035147773818789531at_nat @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ P3 @ ( uminus2330091110623919550at_nat @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5288_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_Pr4329608150637261639at_nat,Q6: set_Pr4329608150637261639at_nat,R3: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( ord_le1268244103169919719at_nat @ P3 @ ( sup_su5525570899277871387at_nat @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ P3 @ ( uminus935396558254630718at_nat @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5289_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_nat,Q6: set_nat,R3: set_nat] :
% 5.45/5.75 ( ( ord_less_eq_set_nat @ P3 @ ( sup_sup_set_nat @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ P3 @ ( uminus5710092332889474511et_nat @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5290_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: assn,Q6: assn,R3: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ P3 @ ( sup_sup_assn @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_less_eq_assn @ ( inf_inf_assn @ P3 @ ( uminus_uminus_assn @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5291_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: product_unit,Q6: product_unit,R3: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ P3 @ ( sup_sup_Product_unit @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ P3 @ ( uminus2952777764628376836t_unit @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5292_sup__neg__inf,axiom,
% 5.45/5.75 ! [P3: set_int,Q6: set_int,R3: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ P3 @ ( sup_sup_set_int @ Q6 @ R3 ) )
% 5.45/5.75 = ( ord_less_eq_set_int @ ( inf_inf_set_int @ P3 @ ( uminus1532241313380277803et_int @ Q6 ) ) @ R3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % sup_neg_inf
% 5.45/5.75 thf(fact_5293_shunt2,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ ( uminus6524753893492686040at_nat @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5294_shunt2,axiom,
% 5.45/5.75 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ X @ ( uminus4384627049435823934at_nat @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5295_shunt2,axiom,
% 5.45/5.75 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ ( uminus2330091110623919550at_nat @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5296_shunt2,axiom,
% 5.45/5.75 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ ( uminus935396558254630718at_nat @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5297_shunt2,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.75 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ ( uminus5710092332889474511et_nat @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5298_shunt2,axiom,
% 5.45/5.75 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ ( uminus_uminus_assn @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5299_shunt2,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ ( uminus2952777764628376836t_unit @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5300_shunt2,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) @ Z )
% 5.45/5.75 = ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ Y @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt2
% 5.45/5.75 thf(fact_5301_shunt1,axiom,
% 5.45/5.75 ! [X: set_Pr1261947904930325089at_nat,Y: set_Pr1261947904930325089at_nat,Z: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ord_le3146513528884898305at_nat @ ( inf_in2572325071724192079at_nat @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_le3146513528884898305at_nat @ X @ ( sup_su6327502436637775413at_nat @ ( uminus6524753893492686040at_nat @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5302_shunt1,axiom,
% 5.45/5.75 ! [X: set_Pr8693737435421807431at_nat,Y: set_Pr8693737435421807431at_nat,Z: set_Pr8693737435421807431at_nat] :
% 5.45/5.75 ( ( ord_le3000389064537975527at_nat @ ( inf_in4302113700860409141at_nat @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_le3000389064537975527at_nat @ X @ ( sup_su718114333110466843at_nat @ ( uminus4384627049435823934at_nat @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5303_shunt1,axiom,
% 5.45/5.75 ! [X: set_Pr8551490117392284871at_nat,Y: set_Pr8551490117392284871at_nat,Z: set_Pr8551490117392284871at_nat] :
% 5.45/5.75 ( ( ord_le8081472938463900775at_nat @ ( inf_in1697001100524423349at_nat @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_le8081472938463900775at_nat @ X @ ( sup_su3035147773818789531at_nat @ ( uminus2330091110623919550at_nat @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5304_shunt1,axiom,
% 5.45/5.75 ! [X: set_Pr4329608150637261639at_nat,Y: set_Pr4329608150637261639at_nat,Z: set_Pr4329608150637261639at_nat] :
% 5.45/5.75 ( ( ord_le1268244103169919719at_nat @ ( inf_in7913087082777306421at_nat @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_le1268244103169919719at_nat @ X @ ( sup_su5525570899277871387at_nat @ ( uminus935396558254630718at_nat @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5305_shunt1,axiom,
% 5.45/5.75 ! [X: set_nat,Y: set_nat,Z: set_nat] :
% 5.45/5.75 ( ( ord_less_eq_set_nat @ ( inf_inf_set_nat @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_less_eq_set_nat @ X @ ( sup_sup_set_nat @ ( uminus5710092332889474511et_nat @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5306_shunt1,axiom,
% 5.45/5.75 ! [X: assn,Y: assn,Z: assn] :
% 5.45/5.75 ( ( ord_less_eq_assn @ ( inf_inf_assn @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_less_eq_assn @ X @ ( sup_sup_assn @ ( uminus_uminus_assn @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5307_shunt1,axiom,
% 5.45/5.75 ! [X: product_unit,Y: product_unit,Z: product_unit] :
% 5.45/5.75 ( ( ord_le3221252021190050221t_unit @ ( inf_inf_Product_unit @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_le3221252021190050221t_unit @ X @ ( sup_sup_Product_unit @ ( uminus2952777764628376836t_unit @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5308_shunt1,axiom,
% 5.45/5.75 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.45/5.75 ( ( ord_less_eq_set_int @ ( inf_inf_set_int @ X @ Y ) @ Z )
% 5.45/5.75 = ( ord_less_eq_set_int @ X @ ( sup_sup_set_int @ ( uminus1532241313380277803et_int @ Y ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % shunt1
% 5.45/5.75 thf(fact_5309_power__minus,axiom,
% 5.45/5.75 ! [A: int,N2: nat] :
% 5.45/5.75 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.45/5.75 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus
% 5.45/5.75 thf(fact_5310_power__minus,axiom,
% 5.45/5.75 ! [A: code_integer,N2: nat] :
% 5.45/5.75 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus
% 5.45/5.75 thf(fact_5311_power__minus,axiom,
% 5.45/5.75 ! [A: rat,N2: nat] :
% 5.45/5.75 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.45/5.75 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus
% 5.45/5.75 thf(fact_5312_eucl__rel__int__dividesI,axiom,
% 5.45/5.75 ! [L: int,K: int,Q6: int] :
% 5.45/5.75 ( ( L != zero_zero_int )
% 5.45/5.75 => ( ( K
% 5.45/5.75 = ( times_times_int @ Q6 @ L ) )
% 5.45/5.75 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q6 @ zero_zero_int ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eucl_rel_int_dividesI
% 5.45/5.75 thf(fact_5313_disjoint__eq__subset__Compl,axiom,
% 5.45/5.75 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( ( inf_in2572325071724192079at_nat @ A3 @ B3 )
% 5.45/5.75 = bot_bo2099793752762293965at_nat )
% 5.45/5.75 = ( ord_le3146513528884898305at_nat @ A3 @ ( uminus6524753893492686040at_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % disjoint_eq_subset_Compl
% 5.45/5.75 thf(fact_5314_disjoint__eq__subset__Compl,axiom,
% 5.45/5.75 ! [A3: set_o,B3: set_o] :
% 5.45/5.75 ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.75 = bot_bot_set_o )
% 5.45/5.75 = ( ord_less_eq_set_o @ A3 @ ( uminus_uminus_set_o @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % disjoint_eq_subset_Compl
% 5.45/5.75 thf(fact_5315_disjoint__eq__subset__Compl,axiom,
% 5.45/5.75 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.75 ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.75 = bot_bot_set_nat )
% 5.45/5.75 = ( ord_less_eq_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % disjoint_eq_subset_Compl
% 5.45/5.75 thf(fact_5316_disjoint__eq__subset__Compl,axiom,
% 5.45/5.75 ! [A3: set_int,B3: set_int] :
% 5.45/5.75 ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.75 = bot_bot_set_int )
% 5.45/5.75 = ( ord_less_eq_set_int @ A3 @ ( uminus1532241313380277803et_int @ B3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % disjoint_eq_subset_Compl
% 5.45/5.75 thf(fact_5317_abs__mod__less,axiom,
% 5.45/5.75 ! [L: int,K: int] :
% 5.45/5.75 ( ( L != zero_zero_int )
% 5.45/5.75 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_mod_less
% 5.45/5.75 thf(fact_5318_int__cases4,axiom,
% 5.45/5.75 ! [M: int] :
% 5.45/5.75 ( ! [N5: nat] :
% 5.45/5.75 ( M
% 5.45/5.75 != ( semiri1314217659103216013at_int @ N5 ) )
% 5.45/5.75 => ~ ! [N5: nat] :
% 5.45/5.75 ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.75 => ( M
% 5.45/5.75 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % int_cases4
% 5.45/5.75 thf(fact_5319_int__zle__neg,axiom,
% 5.45/5.75 ! [N2: nat,M: nat] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.45/5.75 = ( ( N2 = zero_zero_nat )
% 5.45/5.75 & ( M = zero_zero_nat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % int_zle_neg
% 5.45/5.75 thf(fact_5320_negative__zle__0,axiom,
% 5.45/5.75 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % negative_zle_0
% 5.45/5.75 thf(fact_5321_nonpos__int__cases,axiom,
% 5.45/5.75 ! [K: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.45/5.75 => ~ ! [N5: nat] :
% 5.45/5.75 ( K
% 5.45/5.75 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % nonpos_int_cases
% 5.45/5.75 thf(fact_5322_eucl__rel__int,axiom,
% 5.45/5.75 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eucl_rel_int
% 5.45/5.75 thf(fact_5323_abs__add__one__gt__zero,axiom,
% 5.45/5.75 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_add_one_gt_zero
% 5.45/5.75 thf(fact_5324_abs__add__one__gt__zero,axiom,
% 5.45/5.75 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_add_one_gt_zero
% 5.45/5.75 thf(fact_5325_abs__add__one__gt__zero,axiom,
% 5.45/5.75 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % abs_add_one_gt_zero
% 5.45/5.75 thf(fact_5326_pos__minus__divide__less__eq,axiom,
% 5.45/5.75 ! [C: rat,B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pos_minus_divide_less_eq
% 5.45/5.75 thf(fact_5327_pos__less__minus__divide__eq,axiom,
% 5.45/5.75 ! [C: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pos_less_minus_divide_eq
% 5.45/5.75 thf(fact_5328_neg__minus__divide__less__eq,axiom,
% 5.45/5.75 ! [C: rat,B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_minus_divide_less_eq
% 5.45/5.75 thf(fact_5329_neg__less__minus__divide__eq,axiom,
% 5.45/5.75 ! [C: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_less_minus_divide_eq
% 5.45/5.75 thf(fact_5330_minus__divide__less__eq,axiom,
% 5.45/5.75 ! [B: rat,C: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_divide_less_eq
% 5.45/5.75 thf(fact_5331_less__minus__divide__eq,axiom,
% 5.45/5.75 ! [A: rat,B: rat,C: rat] :
% 5.45/5.75 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_minus_divide_eq
% 5.45/5.75 thf(fact_5332_divide__eq__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [B: rat,C: rat,W2: num] :
% 5.45/5.75 ( ( ( divide_divide_rat @ B @ C )
% 5.45/5.75 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.75 = ( ( ( C != zero_zero_rat )
% 5.45/5.75 => ( B
% 5.45/5.75 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.45/5.75 & ( ( C = zero_zero_rat )
% 5.45/5.75 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_eq_eq_numeral(2)
% 5.45/5.75 thf(fact_5333_eq__divide__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [W2: num,B: rat,C: rat] :
% 5.45/5.75 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 = ( divide_divide_rat @ B @ C ) )
% 5.45/5.75 = ( ( ( C != zero_zero_rat )
% 5.45/5.75 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C )
% 5.45/5.75 = B ) )
% 5.45/5.75 & ( ( C = zero_zero_rat )
% 5.45/5.75 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) )
% 5.45/5.75 = zero_zero_rat ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % eq_divide_eq_numeral(2)
% 5.45/5.75 thf(fact_5334_add__divide__eq__if__simps_I3_J,axiom,
% 5.45/5.75 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ( Z = zero_zero_rat )
% 5.45/5.75 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.45/5.75 = B ) )
% 5.45/5.75 & ( ( Z != zero_zero_rat )
% 5.45/5.75 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.45/5.75 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % add_divide_eq_if_simps(3)
% 5.45/5.75 thf(fact_5335_minus__divide__add__eq__iff,axiom,
% 5.45/5.75 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.75 ( ( Z != zero_zero_rat )
% 5.45/5.75 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.45/5.75 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_divide_add_eq_iff
% 5.45/5.75 thf(fact_5336_minus__divide__diff__eq__iff,axiom,
% 5.45/5.75 ! [Z: rat,X: rat,Y: rat] :
% 5.45/5.75 ( ( Z != zero_zero_rat )
% 5.45/5.75 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.45/5.75 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_divide_diff_eq_iff
% 5.45/5.75 thf(fact_5337_add__divide__eq__if__simps_I5_J,axiom,
% 5.45/5.75 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ( Z = zero_zero_rat )
% 5.45/5.75 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.45/5.75 = ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ( Z != zero_zero_rat )
% 5.45/5.75 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.45/5.75 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % add_divide_eq_if_simps(5)
% 5.45/5.75 thf(fact_5338_add__divide__eq__if__simps_I6_J,axiom,
% 5.45/5.75 ! [Z: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ( Z = zero_zero_rat )
% 5.45/5.75 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.45/5.75 = ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ( Z != zero_zero_rat )
% 5.45/5.75 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.45/5.75 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % add_divide_eq_if_simps(6)
% 5.45/5.75 thf(fact_5339_uminus__assn__def,axiom,
% 5.45/5.75 ( uminus_uminus_assn
% 5.45/5.75 = ( ^ [P4: assn] :
% 5.45/5.75 ( abs_assn
% 5.45/5.75 @ ^ [H6: produc3658429121746597890et_nat] :
% 5.45/5.75 ( ( in_range @ H6 )
% 5.45/5.75 & ~ ( rep_assn @ P4 @ H6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_assn_def
% 5.45/5.75 thf(fact_5340_int__cases3,axiom,
% 5.45/5.75 ! [K: int] :
% 5.45/5.75 ( ( K != zero_zero_int )
% 5.45/5.75 => ( ! [N5: nat] :
% 5.45/5.75 ( ( K
% 5.45/5.75 = ( semiri1314217659103216013at_int @ N5 ) )
% 5.45/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) )
% 5.45/5.75 => ~ ! [N5: nat] :
% 5.45/5.75 ( ( K
% 5.45/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 5.45/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % int_cases3
% 5.45/5.75 thf(fact_5341_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ord_less_nat @ N2 @ K )
% 5.45/5.75 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.45/5.75 = zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.45/5.75 thf(fact_5342_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ord_less_nat @ N2 @ K )
% 5.45/5.75 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.45/5.75 = zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.45/5.75 thf(fact_5343_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ord_less_nat @ N2 @ K )
% 5.45/5.75 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.45/5.75 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma
% 5.45/5.75 thf(fact_5344_pochhammer__of__nat__eq__0__iff,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.45/5.75 = zero_zero_rat )
% 5.45/5.75 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_iff
% 5.45/5.75 thf(fact_5345_pochhammer__of__nat__eq__0__iff,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.45/5.75 = zero_zero_int )
% 5.45/5.75 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_iff
% 5.45/5.75 thf(fact_5346_pochhammer__of__nat__eq__0__iff,axiom,
% 5.45/5.75 ! [N2: nat,K: nat] :
% 5.45/5.75 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.45/5.75 = zero_z3403309356797280102nteger )
% 5.45/5.75 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_iff
% 5.45/5.75 thf(fact_5347_pochhammer__eq__0__iff,axiom,
% 5.45/5.75 ! [A: rat,N2: nat] :
% 5.45/5.75 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.45/5.75 = zero_zero_rat )
% 5.45/5.75 = ( ? [K3: nat] :
% 5.45/5.75 ( ( ord_less_nat @ K3 @ N2 )
% 5.45/5.75 & ( A
% 5.45/5.75 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_eq_0_iff
% 5.45/5.75 thf(fact_5348_not__zle__0__negative,axiom,
% 5.45/5.75 ! [N2: nat] :
% 5.45/5.75 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % not_zle_0_negative
% 5.45/5.75 thf(fact_5349_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.45/5.75 != zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.45/5.75 thf(fact_5350_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.45/5.75 != zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.45/5.75 thf(fact_5351_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.45/5.75 != zero_z3403309356797280102nteger ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_of_nat_eq_0_lemma'
% 5.45/5.75 thf(fact_5352_negD,axiom,
% 5.45/5.75 ! [X: int] :
% 5.45/5.75 ( ( ord_less_int @ X @ zero_zero_int )
% 5.45/5.75 => ? [N5: nat] :
% 5.45/5.75 ( X
% 5.45/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N5 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % negD
% 5.45/5.75 thf(fact_5353_negative__zless__0,axiom,
% 5.45/5.75 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.45/5.75
% 5.45/5.75 % negative_zless_0
% 5.45/5.75 thf(fact_5354_verit__less__mono__div__int2,axiom,
% 5.45/5.75 ! [A3: int,B3: int,N2: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ A3 @ B3 )
% 5.45/5.75 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 5.45/5.75 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A3 @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % verit_less_mono_div_int2
% 5.45/5.75 thf(fact_5355_div__eq__minus1,axiom,
% 5.45/5.75 ! [B: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.75 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.45/5.75 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % div_eq_minus1
% 5.45/5.75 thf(fact_5356_power__minus_H,axiom,
% 5.45/5.75 ! [X: int,N2: nat] :
% 5.45/5.75 ( ( nO_MATCH_int_int @ one_one_int @ X )
% 5.45/5.75 => ( ( power_power_int @ ( uminus_uminus_int @ X ) @ N2 )
% 5.45/5.75 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ X @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus'
% 5.45/5.75 thf(fact_5357_power__minus_H,axiom,
% 5.45/5.75 ! [X: code_integer,N2: nat] :
% 5.45/5.75 ( ( nO_MAT8252062027627875367nteger @ one_one_Code_integer @ X )
% 5.45/5.75 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ N2 )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus'
% 5.45/5.75 thf(fact_5358_power__minus_H,axiom,
% 5.45/5.75 ! [X: rat,N2: nat] :
% 5.45/5.75 ( ( nO_MATCH_rat_rat @ one_one_rat @ X )
% 5.45/5.75 => ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ N2 )
% 5.45/5.75 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ X @ N2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % power_minus'
% 5.45/5.75 thf(fact_5359_pos__minus__divide__le__eq,axiom,
% 5.45/5.75 ! [C: rat,B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pos_minus_divide_le_eq
% 5.45/5.75 thf(fact_5360_pos__le__minus__divide__eq,axiom,
% 5.45/5.75 ! [C: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pos_le_minus_divide_eq
% 5.45/5.75 thf(fact_5361_neg__minus__divide__le__eq,axiom,
% 5.45/5.75 ! [C: rat,B: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_minus_divide_le_eq
% 5.45/5.75 thf(fact_5362_neg__le__minus__divide__eq,axiom,
% 5.45/5.75 ! [C: rat,A: rat,B: rat] :
% 5.45/5.75 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_le_minus_divide_eq
% 5.45/5.75 thf(fact_5363_minus__divide__le__eq,axiom,
% 5.45/5.75 ! [B: rat,C: rat,A: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_divide_le_eq
% 5.45/5.75 thf(fact_5364_le__minus__divide__eq,axiom,
% 5.45/5.75 ! [A: rat,B: rat,C: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_minus_divide_eq
% 5.45/5.75 thf(fact_5365_less__divide__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [W2: num,B: rat,C: rat] :
% 5.45/5.75 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % less_divide_eq_numeral(2)
% 5.45/5.75 thf(fact_5366_divide__less__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [B: rat,C: rat,W2: num] :
% 5.45/5.75 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_less_eq_numeral(2)
% 5.45/5.75 thf(fact_5367_neg__int__cases,axiom,
% 5.45/5.75 ! [K: int] :
% 5.45/5.75 ( ( ord_less_int @ K @ zero_zero_int )
% 5.45/5.75 => ~ ! [N5: nat] :
% 5.45/5.75 ( ( K
% 5.45/5.75 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N5 ) ) )
% 5.45/5.75 => ~ ( ord_less_nat @ zero_zero_nat @ N5 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_int_cases
% 5.45/5.75 thf(fact_5368_minus__mod__int__eq,axiom,
% 5.45/5.75 ! [L: int,K: int] :
% 5.45/5.75 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.45/5.75 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.45/5.75 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % minus_mod_int_eq
% 5.45/5.75 thf(fact_5369_zmod__minus1,axiom,
% 5.45/5.75 ! [B: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.75 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.45/5.75 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % zmod_minus1
% 5.45/5.75 thf(fact_5370_divide__le__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [B: rat,C: rat,W2: num] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % divide_le_eq_numeral(2)
% 5.45/5.75 thf(fact_5371_le__divide__eq__numeral_I2_J,axiom,
% 5.45/5.75 ! [W2: num,B: rat,C: rat] :
% 5.45/5.75 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.45/5.75 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) @ B ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.75 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ C ) ) )
% 5.45/5.75 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.45/5.75 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W2 ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % le_divide_eq_numeral(2)
% 5.45/5.75 thf(fact_5372_nat__intermed__int__val,axiom,
% 5.45/5.75 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.45/5.75 ( ! [I3: nat] :
% 5.45/5.75 ( ( ( ord_less_eq_nat @ M @ I3 )
% 5.45/5.75 & ( ord_less_nat @ I3 @ N2 ) )
% 5.45/5.75 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.45/5.75 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.75 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.45/5.75 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.45/5.75 => ? [I3: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ M @ I3 )
% 5.45/5.75 & ( ord_less_eq_nat @ I3 @ N2 )
% 5.45/5.75 & ( ( F @ I3 )
% 5.45/5.75 = K ) ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % nat_intermed_int_val
% 5.45/5.75 thf(fact_5373_incr__lemma,axiom,
% 5.45/5.75 ! [D2: int,Z: int,X: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.75 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % incr_lemma
% 5.45/5.75 thf(fact_5374_decr__lemma,axiom,
% 5.45/5.75 ! [D2: int,X: int,Z: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.75 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D2 ) ) @ Z ) ) ).
% 5.45/5.75
% 5.45/5.75 % decr_lemma
% 5.45/5.75 thf(fact_5375_pochhammer__absorb__comp,axiom,
% 5.45/5.75 ! [R3: rat,K: nat] :
% 5.45/5.75 ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 5.45/5.75 = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_absorb_comp
% 5.45/5.75 thf(fact_5376_pochhammer__absorb__comp,axiom,
% 5.45/5.75 ! [R3: int,K: nat] :
% 5.45/5.75 ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 5.45/5.75 = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_absorb_comp
% 5.45/5.75 thf(fact_5377_pochhammer__absorb__comp,axiom,
% 5.45/5.75 ! [R3: code_integer,K: nat] :
% 5.45/5.75 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 5.45/5.75 = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_absorb_comp
% 5.45/5.75 thf(fact_5378_div__pos__neg__trivial,axiom,
% 5.45/5.75 ! [K: int,L: int] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ K )
% 5.45/5.75 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.45/5.75 => ( ( divide_divide_int @ K @ L )
% 5.45/5.75 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % div_pos_neg_trivial
% 5.45/5.75 thf(fact_5379_nat__ivt__aux,axiom,
% 5.45/5.75 ! [N2: nat,F: nat > int,K: int] :
% 5.45/5.75 ( ! [I3: nat] :
% 5.45/5.75 ( ( ord_less_nat @ I3 @ N2 )
% 5.45/5.75 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) ) ) @ one_one_int ) )
% 5.45/5.75 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.45/5.75 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.45/5.75 => ? [I3: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.45/5.75 & ( ( F @ I3 )
% 5.45/5.75 = K ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % nat_ivt_aux
% 5.45/5.75 thf(fact_5380_pochhammer__minus,axiom,
% 5.45/5.75 ! [B: rat,K: nat] :
% 5.45/5.75 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.45/5.75 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_minus
% 5.45/5.75 thf(fact_5381_pochhammer__minus,axiom,
% 5.45/5.75 ! [B: int,K: nat] :
% 5.45/5.75 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.45/5.75 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_minus
% 5.45/5.75 thf(fact_5382_pochhammer__minus,axiom,
% 5.45/5.75 ! [B: code_integer,K: nat] :
% 5.45/5.75 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.45/5.75 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % pochhammer_minus
% 5.45/5.75 thf(fact_5383_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.45/5.75 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_power_add_eq_neg_one_power_diff
% 5.45/5.75 thf(fact_5384_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.45/5.75 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_power_add_eq_neg_one_power_diff
% 5.45/5.75 thf(fact_5385_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.45/5.75 ! [K: nat,N2: nat] :
% 5.45/5.75 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.75 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.45/5.75 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_one_power_add_eq_neg_one_power_diff
% 5.45/5.75 thf(fact_5386_upto_Opinduct,axiom,
% 5.45/5.75 ! [A0: int,A1: int,P: int > int > $o] :
% 5.45/5.75 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.45/5.75 => ( ! [I3: int,J2: int] :
% 5.45/5.75 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I3 @ J2 ) )
% 5.45/5.75 => ( ( ( ord_less_eq_int @ I3 @ J2 )
% 5.45/5.75 => ( P @ ( plus_plus_int @ I3 @ one_one_int ) @ J2 ) )
% 5.45/5.75 => ( P @ I3 @ J2 ) ) )
% 5.45/5.75 => ( P @ A0 @ A1 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % upto.pinduct
% 5.45/5.75 thf(fact_5387_bezw__0,axiom,
% 5.45/5.75 ! [X: nat] :
% 5.45/5.75 ( ( bezw @ X @ zero_zero_nat )
% 5.45/5.75 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.45/5.75
% 5.45/5.75 % bezw_0
% 5.45/5.75 thf(fact_5388_neg__numeral__le__ceiling,axiom,
% 5.45/5.75 ! [V: num,X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_le_ceiling
% 5.45/5.75 thf(fact_5389_ceiling__less__neg__numeral,axiom,
% 5.45/5.75 ! [X: rat,V: num] :
% 5.45/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_less_neg_numeral
% 5.45/5.75 thf(fact_5390_option_Osize_I3_J,axiom,
% 5.45/5.75 ( ( size_size_option_num @ none_num )
% 5.45/5.75 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.75
% 5.45/5.75 % option.size(3)
% 5.45/5.75 thf(fact_5391_ComplI,axiom,
% 5.45/5.75 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ~ ( member8440522571783428010at_nat @ C @ A3 )
% 5.45/5.75 => ( member8440522571783428010at_nat @ C @ ( uminus6524753893492686040at_nat @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplI
% 5.45/5.75 thf(fact_5392_ComplI,axiom,
% 5.45/5.75 ! [C: $o,A3: set_o] :
% 5.45/5.75 ( ~ ( member_o @ C @ A3 )
% 5.45/5.75 => ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplI
% 5.45/5.75 thf(fact_5393_ComplI,axiom,
% 5.45/5.75 ! [C: set_nat,A3: set_set_nat] :
% 5.45/5.75 ( ~ ( member_set_nat @ C @ A3 )
% 5.45/5.75 => ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplI
% 5.45/5.75 thf(fact_5394_ComplI,axiom,
% 5.45/5.75 ! [C: nat,A3: set_nat] :
% 5.45/5.75 ( ~ ( member_nat @ C @ A3 )
% 5.45/5.75 => ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplI
% 5.45/5.75 thf(fact_5395_ComplI,axiom,
% 5.45/5.75 ! [C: int,A3: set_int] :
% 5.45/5.75 ( ~ ( member_int @ C @ A3 )
% 5.45/5.75 => ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplI
% 5.45/5.75 thf(fact_5396_Compl__iff,axiom,
% 5.45/5.75 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( member8440522571783428010at_nat @ C @ ( uminus6524753893492686040at_nat @ A3 ) )
% 5.45/5.75 = ( ~ ( member8440522571783428010at_nat @ C @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_iff
% 5.45/5.75 thf(fact_5397_Compl__iff,axiom,
% 5.45/5.75 ! [C: $o,A3: set_o] :
% 5.45/5.75 ( ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) )
% 5.45/5.75 = ( ~ ( member_o @ C @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_iff
% 5.45/5.75 thf(fact_5398_Compl__iff,axiom,
% 5.45/5.75 ! [C: set_nat,A3: set_set_nat] :
% 5.45/5.75 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) )
% 5.45/5.75 = ( ~ ( member_set_nat @ C @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_iff
% 5.45/5.75 thf(fact_5399_Compl__iff,axiom,
% 5.45/5.75 ! [C: nat,A3: set_nat] :
% 5.45/5.75 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.45/5.75 = ( ~ ( member_nat @ C @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_iff
% 5.45/5.75 thf(fact_5400_Compl__iff,axiom,
% 5.45/5.75 ! [C: int,A3: set_int] :
% 5.45/5.75 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.45/5.75 = ( ~ ( member_int @ C @ A3 ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_iff
% 5.45/5.75 thf(fact_5401_ceiling__le__zero,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_le_zero
% 5.45/5.75 thf(fact_5402_zero__less__ceiling,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_less_ceiling
% 5.45/5.75 thf(fact_5403_ceiling__le__numeral,axiom,
% 5.45/5.75 ! [X: rat,V: num] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_le_numeral
% 5.45/5.75 thf(fact_5404_ceiling__less__one,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ zero_zero_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_less_one
% 5.45/5.75 thf(fact_5405_one__le__ceiling,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ zero_zero_rat @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % one_le_ceiling
% 5.45/5.75 thf(fact_5406_numeral__less__ceiling,axiom,
% 5.45/5.75 ! [V: num,X: rat] :
% 5.45/5.75 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % numeral_less_ceiling
% 5.45/5.75 thf(fact_5407_ceiling__le__one,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ one_one_int )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ one_one_rat ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_le_one
% 5.45/5.75 thf(fact_5408_one__less__ceiling,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ one_one_rat @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % one_less_ceiling
% 5.45/5.75 thf(fact_5409_ceiling__less__zero,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ zero_zero_int )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_less_zero
% 5.45/5.75 thf(fact_5410_zero__le__ceiling,axiom,
% 5.45/5.75 ! [X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % zero_le_ceiling
% 5.45/5.75 thf(fact_5411_ceiling__less__numeral,axiom,
% 5.45/5.75 ! [X: rat,V: num] :
% 5.45/5.75 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_less_numeral
% 5.45/5.75 thf(fact_5412_numeral__le__ceiling,axiom,
% 5.45/5.75 ! [V: num,X: rat] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % numeral_le_ceiling
% 5.45/5.75 thf(fact_5413_ceiling__le__neg__numeral,axiom,
% 5.45/5.75 ! [X: rat,V: num] :
% 5.45/5.75 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.45/5.75 = ( ord_less_eq_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % ceiling_le_neg_numeral
% 5.45/5.75 thf(fact_5414_neg__numeral__less__ceiling,axiom,
% 5.45/5.75 ! [V: num,X: rat] :
% 5.45/5.75 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.75 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.45/5.75
% 5.45/5.75 % neg_numeral_less_ceiling
% 5.45/5.75 thf(fact_5415_Collect__neg__eq,axiom,
% 5.45/5.75 ! [P: product_prod_int_int > $o] :
% 5.45/5.75 ( ( collec213857154873943460nt_int
% 5.45/5.75 @ ^ [X4: product_prod_int_int] :
% 5.45/5.75 ~ ( P @ X4 ) )
% 5.45/5.75 = ( uminus6221592323253981072nt_int @ ( collec213857154873943460nt_int @ P ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_neg_eq
% 5.45/5.75 thf(fact_5416_Collect__neg__eq,axiom,
% 5.45/5.75 ! [P: list_nat > $o] :
% 5.45/5.75 ( ( collect_list_nat
% 5.45/5.75 @ ^ [X4: list_nat] :
% 5.45/5.75 ~ ( P @ X4 ) )
% 5.45/5.75 = ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_neg_eq
% 5.45/5.75 thf(fact_5417_Collect__neg__eq,axiom,
% 5.45/5.75 ! [P: set_nat > $o] :
% 5.45/5.75 ( ( collect_set_nat
% 5.45/5.75 @ ^ [X4: set_nat] :
% 5.45/5.75 ~ ( P @ X4 ) )
% 5.45/5.75 = ( uminus613421341184616069et_nat @ ( collect_set_nat @ P ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_neg_eq
% 5.45/5.75 thf(fact_5418_Collect__neg__eq,axiom,
% 5.45/5.75 ! [P: nat > $o] :
% 5.45/5.75 ( ( collect_nat
% 5.45/5.75 @ ^ [X4: nat] :
% 5.45/5.75 ~ ( P @ X4 ) )
% 5.45/5.75 = ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_neg_eq
% 5.45/5.75 thf(fact_5419_Collect__neg__eq,axiom,
% 5.45/5.75 ! [P: int > $o] :
% 5.45/5.75 ( ( collect_int
% 5.45/5.75 @ ^ [X4: int] :
% 5.45/5.75 ~ ( P @ X4 ) )
% 5.45/5.75 = ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Collect_neg_eq
% 5.45/5.75 thf(fact_5420_Compl__eq,axiom,
% 5.45/5.75 ( uminus6524753893492686040at_nat
% 5.45/5.75 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( collec3392354462482085612at_nat
% 5.45/5.75 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.75 ~ ( member8440522571783428010at_nat @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5421_Compl__eq,axiom,
% 5.45/5.75 ( uminus_uminus_set_o
% 5.45/5.75 = ( ^ [A6: set_o] :
% 5.45/5.75 ( collect_o
% 5.45/5.75 @ ^ [X4: $o] :
% 5.45/5.75 ~ ( member_o @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5422_Compl__eq,axiom,
% 5.45/5.75 ( uminus6221592323253981072nt_int
% 5.45/5.75 = ( ^ [A6: set_Pr958786334691620121nt_int] :
% 5.45/5.75 ( collec213857154873943460nt_int
% 5.45/5.75 @ ^ [X4: product_prod_int_int] :
% 5.45/5.75 ~ ( member5262025264175285858nt_int @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5423_Compl__eq,axiom,
% 5.45/5.75 ( uminus3195874150345416415st_nat
% 5.45/5.75 = ( ^ [A6: set_list_nat] :
% 5.45/5.75 ( collect_list_nat
% 5.45/5.75 @ ^ [X4: list_nat] :
% 5.45/5.75 ~ ( member_list_nat @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5424_Compl__eq,axiom,
% 5.45/5.75 ( uminus613421341184616069et_nat
% 5.45/5.75 = ( ^ [A6: set_set_nat] :
% 5.45/5.75 ( collect_set_nat
% 5.45/5.75 @ ^ [X4: set_nat] :
% 5.45/5.75 ~ ( member_set_nat @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5425_Compl__eq,axiom,
% 5.45/5.75 ( uminus5710092332889474511et_nat
% 5.45/5.75 = ( ^ [A6: set_nat] :
% 5.45/5.75 ( collect_nat
% 5.45/5.75 @ ^ [X4: nat] :
% 5.45/5.75 ~ ( member_nat @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5426_Compl__eq,axiom,
% 5.45/5.75 ( uminus1532241313380277803et_int
% 5.45/5.75 = ( ^ [A6: set_int] :
% 5.45/5.75 ( collect_int
% 5.45/5.75 @ ^ [X4: int] :
% 5.45/5.75 ~ ( member_int @ X4 @ A6 ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % Compl_eq
% 5.45/5.75 thf(fact_5427_ComplD,axiom,
% 5.45/5.75 ! [C: product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( ( member8440522571783428010at_nat @ C @ ( uminus6524753893492686040at_nat @ A3 ) )
% 5.45/5.75 => ~ ( member8440522571783428010at_nat @ C @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplD
% 5.45/5.75 thf(fact_5428_ComplD,axiom,
% 5.45/5.75 ! [C: $o,A3: set_o] :
% 5.45/5.75 ( ( member_o @ C @ ( uminus_uminus_set_o @ A3 ) )
% 5.45/5.75 => ~ ( member_o @ C @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplD
% 5.45/5.75 thf(fact_5429_ComplD,axiom,
% 5.45/5.75 ! [C: set_nat,A3: set_set_nat] :
% 5.45/5.75 ( ( member_set_nat @ C @ ( uminus613421341184616069et_nat @ A3 ) )
% 5.45/5.75 => ~ ( member_set_nat @ C @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplD
% 5.45/5.75 thf(fact_5430_ComplD,axiom,
% 5.45/5.75 ! [C: nat,A3: set_nat] :
% 5.45/5.75 ( ( member_nat @ C @ ( uminus5710092332889474511et_nat @ A3 ) )
% 5.45/5.75 => ~ ( member_nat @ C @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplD
% 5.45/5.75 thf(fact_5431_ComplD,axiom,
% 5.45/5.75 ! [C: int,A3: set_int] :
% 5.45/5.75 ( ( member_int @ C @ ( uminus1532241313380277803et_int @ A3 ) )
% 5.45/5.75 => ~ ( member_int @ C @ A3 ) ) ).
% 5.45/5.75
% 5.45/5.75 % ComplD
% 5.45/5.75 thf(fact_5432_uminus__set__def,axiom,
% 5.45/5.75 ( uminus6524753893492686040at_nat
% 5.45/5.75 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 5.45/5.75 ( collec3392354462482085612at_nat
% 5.45/5.75 @ ( uminus8676089048583255045_nat_o
% 5.45/5.75 @ ^ [X4: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5433_uminus__set__def,axiom,
% 5.45/5.75 ( uminus_uminus_set_o
% 5.45/5.75 = ( ^ [A6: set_o] :
% 5.45/5.75 ( collect_o
% 5.45/5.75 @ ( uminus_uminus_o_o
% 5.45/5.75 @ ^ [X4: $o] : ( member_o @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5434_uminus__set__def,axiom,
% 5.45/5.75 ( uminus6221592323253981072nt_int
% 5.45/5.75 = ( ^ [A6: set_Pr958786334691620121nt_int] :
% 5.45/5.75 ( collec213857154873943460nt_int
% 5.45/5.75 @ ( uminus7117520113953359693_int_o
% 5.45/5.75 @ ^ [X4: product_prod_int_int] : ( member5262025264175285858nt_int @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5435_uminus__set__def,axiom,
% 5.45/5.75 ( uminus3195874150345416415st_nat
% 5.45/5.75 = ( ^ [A6: set_list_nat] :
% 5.45/5.75 ( collect_list_nat
% 5.45/5.75 @ ( uminus5770388063884162150_nat_o
% 5.45/5.75 @ ^ [X4: list_nat] : ( member_list_nat @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5436_uminus__set__def,axiom,
% 5.45/5.75 ( uminus613421341184616069et_nat
% 5.45/5.75 = ( ^ [A6: set_set_nat] :
% 5.45/5.75 ( collect_set_nat
% 5.45/5.75 @ ( uminus6401447641752708672_nat_o
% 5.45/5.75 @ ^ [X4: set_nat] : ( member_set_nat @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5437_uminus__set__def,axiom,
% 5.45/5.75 ( uminus5710092332889474511et_nat
% 5.45/5.75 = ( ^ [A6: set_nat] :
% 5.45/5.75 ( collect_nat
% 5.45/5.75 @ ( uminus_uminus_nat_o
% 5.45/5.75 @ ^ [X4: nat] : ( member_nat @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5438_uminus__set__def,axiom,
% 5.45/5.75 ( uminus1532241313380277803et_int
% 5.45/5.75 = ( ^ [A6: set_int] :
% 5.45/5.75 ( collect_int
% 5.45/5.75 @ ( uminus_uminus_int_o
% 5.45/5.75 @ ^ [X4: int] : ( member_int @ X4 @ A6 ) ) ) ) ) ).
% 5.45/5.75
% 5.45/5.75 % uminus_set_def
% 5.45/5.75 thf(fact_5439_size__neq__size__imp__neq,axiom,
% 5.45/5.75 ! [X: list_nat,Y: list_nat] :
% 5.45/5.75 ( ( ( size_size_list_nat @ X )
% 5.45/5.75 != ( size_size_list_nat @ Y ) )
% 5.45/5.75 => ( X != Y ) ) ).
% 5.45/5.75
% 5.45/5.75 % size_neq_size_imp_neq
% 5.45/5.75 thf(fact_5440_size__neq__size__imp__neq,axiom,
% 5.45/5.75 ! [X: list_o,Y: list_o] :
% 5.45/5.75 ( ( ( size_size_list_o @ X )
% 5.45/5.76 != ( size_size_list_o @ Y ) )
% 5.45/5.76 => ( X != Y ) ) ).
% 5.45/5.76
% 5.45/5.76 % size_neq_size_imp_neq
% 5.45/5.76 thf(fact_5441_ceiling__mono,axiom,
% 5.45/5.76 ! [Y: rat,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ Y @ X )
% 5.45/5.76 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_mono
% 5.45/5.76 thf(fact_5442_ceiling__less__cancel,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 5.45/5.76 => ( ord_less_rat @ X @ Y ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_less_cancel
% 5.45/5.76 thf(fact_5443_ceiling__add__le,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_add_le
% 5.45/5.76 thf(fact_5444_mult__ceiling__le,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.76 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_ceiling_le
% 5.45/5.76 thf(fact_5445_option_Osize_I4_J,axiom,
% 5.45/5.76 ! [X2: produc3260487557148687353it_nat] :
% 5.45/5.76 ( ( size_s2363601347547812957it_nat @ ( some_P7913643980934408916it_nat @ X2 ) )
% 5.45/5.76 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % option.size(4)
% 5.45/5.76 thf(fact_5446_option_Osize_I4_J,axiom,
% 5.45/5.76 ! [X2: num] :
% 5.45/5.76 ( ( size_size_option_num @ ( some_num @ X2 ) )
% 5.45/5.76 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % option.size(4)
% 5.45/5.76 thf(fact_5447_option_Osize_I4_J,axiom,
% 5.45/5.76 ! [X2: produc8664842809031399944it_nat] :
% 5.45/5.76 ( ( size_s8766407808098229740it_nat @ ( some_P1914260805536162275it_nat @ X2 ) )
% 5.45/5.76 = ( suc @ zero_zero_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % option.size(4)
% 5.45/5.76 thf(fact_5448_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5449_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5450_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5451_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5452_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5453_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5454_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5455_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5456_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5457_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5458_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5459_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_neg_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5460_floor__le__neg__numeral,axiom,
% 5.45/5.76 ! [X: rat,V: num] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.45/5.76 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_le_neg_numeral
% 5.45/5.76 thf(fact_5461_neg__numeral__less__floor,axiom,
% 5.45/5.76 ! [V: num,X: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_less_floor
% 5.45/5.76 thf(fact_5462_nat__le__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_le_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5463_of__int__le__iff,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_iff
% 5.45/5.76 thf(fact_5464_of__int__le__iff,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ W2 @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_iff
% 5.45/5.76 thf(fact_5465_of__int__less__iff,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_iff
% 5.45/5.76 thf(fact_5466_of__int__less__iff,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_int @ W2 @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_iff
% 5.45/5.76 thf(fact_5467_of__int__mult,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ring_18347121197199848620nteger @ ( times_times_int @ W2 @ Z ) )
% 5.45/5.76 = ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ W2 ) @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_mult
% 5.45/5.76 thf(fact_5468_of__int__mult,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ring_1_of_int_rat @ ( times_times_int @ W2 @ Z ) )
% 5.45/5.76 = ( times_times_rat @ ( ring_1_of_int_rat @ W2 ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_mult
% 5.45/5.76 thf(fact_5469_of__int__mult,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ring_1_of_int_int @ ( times_times_int @ W2 @ Z ) )
% 5.45/5.76 = ( times_times_int @ ( ring_1_of_int_int @ W2 ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_mult
% 5.45/5.76 thf(fact_5470_nat__le__0,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.45/5.76 => ( ( nat2 @ Z )
% 5.45/5.76 = zero_zero_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_le_0
% 5.45/5.76 thf(fact_5471_nat__0__iff,axiom,
% 5.45/5.76 ! [I2: int] :
% 5.45/5.76 ( ( ( nat2 @ I2 )
% 5.45/5.76 = zero_zero_nat )
% 5.45/5.76 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_0_iff
% 5.45/5.76 thf(fact_5472_zless__nat__conj,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.76 & ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % zless_nat_conj
% 5.45/5.76 thf(fact_5473_int__nat__eq,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.45/5.76 = Z ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.45/5.76 = zero_zero_int ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % int_nat_eq
% 5.45/5.76 thf(fact_5474_of__int__le__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ zero_z3403309356797280102nteger )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_0_iff
% 5.45/5.76 thf(fact_5475_of__int__le__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_0_iff
% 5.45/5.76 thf(fact_5476_of__int__le__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_0_iff
% 5.45/5.76 thf(fact_5477_of__int__0__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_le_iff
% 5.45/5.76 thf(fact_5478_of__int__0__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_le_iff
% 5.45/5.76 thf(fact_5479_of__int__0__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_le_iff
% 5.45/5.76 thf(fact_5480_of__int__less__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ zero_z3403309356797280102nteger )
% 5.45/5.76 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_0_iff
% 5.45/5.76 thf(fact_5481_of__int__less__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.45/5.76 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_0_iff
% 5.45/5.76 thf(fact_5482_of__int__less__0__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_0_iff
% 5.45/5.76 thf(fact_5483_of__int__0__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_less_iff
% 5.45/5.76 thf(fact_5484_of__int__0__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_less_iff
% 5.45/5.76 thf(fact_5485_of__int__0__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_0_less_iff
% 5.45/5.76 thf(fact_5486_of__int__numeral__le__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_le_iff
% 5.45/5.76 thf(fact_5487_of__int__numeral__le__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_le_iff
% 5.45/5.76 thf(fact_5488_of__int__numeral__le__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_le_iff
% 5.45/5.76 thf(fact_5489_of__int__le__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_iff
% 5.45/5.76 thf(fact_5490_of__int__le__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_iff
% 5.45/5.76 thf(fact_5491_of__int__le__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_iff
% 5.45/5.76 thf(fact_5492_of__int__numeral__less__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_less_iff
% 5.45/5.76 thf(fact_5493_of__int__numeral__less__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_less_iff
% 5.45/5.76 thf(fact_5494_of__int__numeral__less__iff,axiom,
% 5.45/5.76 ! [N2: num,Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_numeral_less_iff
% 5.45/5.76 thf(fact_5495_of__int__less__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_iff
% 5.45/5.76 thf(fact_5496_of__int__less__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_iff
% 5.45/5.76 thf(fact_5497_of__int__less__numeral__iff,axiom,
% 5.45/5.76 ! [Z: int,N2: num] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_iff
% 5.45/5.76 thf(fact_5498_of__int__le__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_1_iff
% 5.45/5.76 thf(fact_5499_of__int__le__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_1_iff
% 5.45/5.76 thf(fact_5500_of__int__le__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.45/5.76 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_1_iff
% 5.45/5.76 thf(fact_5501_of__int__1__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_le_iff
% 5.45/5.76 thf(fact_5502_of__int__1__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_le_iff
% 5.45/5.76 thf(fact_5503_of__int__1__le__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_le_iff
% 5.45/5.76 thf(fact_5504_of__int__less__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ Z ) @ one_one_Code_integer )
% 5.45/5.76 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_1_iff
% 5.45/5.76 thf(fact_5505_of__int__less__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.45/5.76 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_1_iff
% 5.45/5.76 thf(fact_5506_of__int__less__1__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.45/5.76 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_1_iff
% 5.45/5.76 thf(fact_5507_of__int__1__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( ring_18347121197199848620nteger @ Z ) )
% 5.45/5.76 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_less_iff
% 5.45/5.76 thf(fact_5508_of__int__1__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_less_iff
% 5.45/5.76 thf(fact_5509_of__int__1__less__iff,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.45/5.76 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_1_less_iff
% 5.45/5.76 thf(fact_5510_zero__le__floor,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ zero_zero_rat @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % zero_le_floor
% 5.45/5.76 thf(fact_5511_floor__less__zero,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_rat @ X @ zero_zero_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_zero
% 5.45/5.76 thf(fact_5512_numeral__le__floor,axiom,
% 5.45/5.76 ! [V: num,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_le_floor
% 5.45/5.76 thf(fact_5513_zero__less__floor,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % zero_less_floor
% 5.45/5.76 thf(fact_5514_zero__less__nat__eq,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % zero_less_nat_eq
% 5.45/5.76 thf(fact_5515_floor__le__zero,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_le_zero
% 5.45/5.76 thf(fact_5516_floor__less__numeral,axiom,
% 5.45/5.76 ! [X: rat,V: num] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.76 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_numeral
% 5.45/5.76 thf(fact_5517_one__le__floor,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ one_one_rat @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % one_le_floor
% 5.45/5.76 thf(fact_5518_floor__less__one,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.45/5.76 = ( ord_less_rat @ X @ one_one_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_one
% 5.45/5.76 thf(fact_5519_of__nat__nat,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_nat
% 5.45/5.76 thf(fact_5520_of__nat__nat,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ring_1_of_int_int @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_nat
% 5.45/5.76 thf(fact_5521_of__nat__nat,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri4939895301339042750nteger @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_nat
% 5.45/5.76 thf(fact_5522_of__int__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: int,B: int,W2: nat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5523_of__int__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: int,B: int,W2: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5524_of__int__le__of__int__power__cancel__iff,axiom,
% 5.45/5.76 ! [B: int,W2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_of_int_power_cancel_iff
% 5.45/5.76 thf(fact_5525_of__int__le__of__int__power__cancel__iff,axiom,
% 5.45/5.76 ! [B: int,W2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_of_int_power_cancel_iff
% 5.45/5.76 thf(fact_5526_of__int__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: int,B: int,W2: nat] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) )
% 5.45/5.76 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5527_of__int__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: int,B: int,W2: nat] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) )
% 5.45/5.76 = ( ord_less_int @ X @ ( power_power_int @ B @ W2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5528_of__int__less__of__int__power__cancel__iff,axiom,
% 5.45/5.76 ! [B: int,W2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_of_int_power_cancel_iff
% 5.45/5.76 thf(fact_5529_of__int__less__of__int__power__cancel__iff,axiom,
% 5.45/5.76 ! [B: int,W2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W2 ) @ ( ring_1_of_int_int @ X ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ B @ W2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_of_int_power_cancel_iff
% 5.45/5.76 thf(fact_5530_one__less__nat__eq,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % one_less_nat_eq
% 5.45/5.76 thf(fact_5531_numeral__less__floor,axiom,
% 5.45/5.76 ! [V: num,X: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_less_floor
% 5.45/5.76 thf(fact_5532_floor__le__numeral,axiom,
% 5.45/5.76 ! [X: rat,V: num] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( numeral_numeral_int @ V ) )
% 5.45/5.76 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_le_numeral
% 5.45/5.76 thf(fact_5533_neg__numeral__le__floor,axiom,
% 5.45/5.76 ! [V: num,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % neg_numeral_le_floor
% 5.45/5.76 thf(fact_5534_floor__less__neg__numeral,axiom,
% 5.45/5.76 ! [X: rat,V: num] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.45/5.76 = ( ord_less_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_neg_numeral
% 5.45/5.76 thf(fact_5535_of__int__le__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5536_of__int__le__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5537_of__int__le__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_le_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5538_numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5539_numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5540_numeral__power__le__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_le_of_int_cancel_iff
% 5.45/5.76 thf(fact_5541_of__int__less__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5542_of__int__less__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5543_of__int__less__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_less_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5544_numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5545_numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ X ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5546_numeral__power__less__of__int__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_less_of_int_cancel_iff
% 5.45/5.76 thf(fact_5547_numeral__power__less__nat__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.45/5.76 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_less_nat_cancel_iff
% 5.45/5.76 thf(fact_5548_nat__less__numeral__power__cancel__iff,axiom,
% 5.45/5.76 ! [A: int,X: num,N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) )
% 5.45/5.76 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_less_numeral_power_cancel_iff
% 5.45/5.76 thf(fact_5549_numeral__power__le__nat__cancel__iff,axiom,
% 5.45/5.76 ! [X: num,N2: nat,A: int] :
% 5.45/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N2 ) @ ( nat2 @ A ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N2 ) @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % numeral_power_le_nat_cancel_iff
% 5.45/5.76 thf(fact_5550_of__int__floor__le,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_floor_le
% 5.45/5.76 thf(fact_5551_le__floor__iff,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_floor_iff
% 5.45/5.76 thf(fact_5552_floor__less__iff,axiom,
% 5.45/5.76 ! [X: rat,Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.45/5.76 = ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_iff
% 5.45/5.76 thf(fact_5553_ex__le__of__int,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ? [Z2: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % ex_le_of_int
% 5.45/5.76 thf(fact_5554_ex__less__of__int,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ? [Z2: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % ex_less_of_int
% 5.45/5.76 thf(fact_5555_ex__of__int__less,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X ) ).
% 5.45/5.76
% 5.45/5.76 % ex_of_int_less
% 5.45/5.76 thf(fact_5556_mult__of__int__commute,axiom,
% 5.45/5.76 ! [X: int,Y: code_integer] :
% 5.45/5.76 ( ( times_3573771949741848930nteger @ ( ring_18347121197199848620nteger @ X ) @ Y )
% 5.45/5.76 = ( times_3573771949741848930nteger @ Y @ ( ring_18347121197199848620nteger @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_of_int_commute
% 5.45/5.76 thf(fact_5557_mult__of__int__commute,axiom,
% 5.45/5.76 ! [X: int,Y: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 5.45/5.76 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_of_int_commute
% 5.45/5.76 thf(fact_5558_mult__of__int__commute,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 5.45/5.76 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_of_int_commute
% 5.45/5.76 thf(fact_5559_length__induct,axiom,
% 5.45/5.76 ! [P: list_nat > $o,Xs: list_nat] :
% 5.45/5.76 ( ! [Xs2: list_nat] :
% 5.45/5.76 ( ! [Ys: list_nat] :
% 5.45/5.76 ( ( ord_less_nat @ ( size_size_list_nat @ Ys ) @ ( size_size_list_nat @ Xs2 ) )
% 5.45/5.76 => ( P @ Ys ) )
% 5.45/5.76 => ( P @ Xs2 ) )
% 5.45/5.76 => ( P @ Xs ) ) ).
% 5.45/5.76
% 5.45/5.76 % length_induct
% 5.45/5.76 thf(fact_5560_length__induct,axiom,
% 5.45/5.76 ! [P: list_o > $o,Xs: list_o] :
% 5.45/5.76 ( ! [Xs2: list_o] :
% 5.45/5.76 ( ! [Ys: list_o] :
% 5.45/5.76 ( ( ord_less_nat @ ( size_size_list_o @ Ys ) @ ( size_size_list_o @ Xs2 ) )
% 5.45/5.76 => ( P @ Ys ) )
% 5.45/5.76 => ( P @ Xs2 ) )
% 5.45/5.76 => ( P @ Xs ) ) ).
% 5.45/5.76
% 5.45/5.76 % length_induct
% 5.45/5.76 thf(fact_5561_of__nat__floor,axiom,
% 5.45/5.76 ! [R3: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 5.45/5.76 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R3 ) ) ) @ R3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_floor
% 5.45/5.76 thf(fact_5562_floor__unique,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X )
% 5.45/5.76 => ( ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.45/5.76 => ( ( archim3151403230148437115or_rat @ X )
% 5.45/5.76 = Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_unique
% 5.45/5.76 thf(fact_5563_floor__eq__iff,axiom,
% 5.45/5.76 ! [X: rat,A: int] :
% 5.45/5.76 ( ( ( archim3151403230148437115or_rat @ X )
% 5.45/5.76 = A )
% 5.45/5.76 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_eq_iff
% 5.45/5.76 thf(fact_5564_floor__split,axiom,
% 5.45/5.76 ! [P: int > $o,T5: rat] :
% 5.45/5.76 ( ( P @ ( archim3151403230148437115or_rat @ T5 ) )
% 5.45/5.76 = ( ! [I4: int] :
% 5.45/5.76 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I4 ) @ T5 )
% 5.45/5.76 & ( ord_less_rat @ T5 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) ) )
% 5.45/5.76 => ( P @ I4 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_split
% 5.45/5.76 thf(fact_5565_less__floor__iff,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.76 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % less_floor_iff
% 5.45/5.76 thf(fact_5566_floor__le__iff,axiom,
% 5.45/5.76 ! [X: rat,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ Z )
% 5.45/5.76 = ( ord_less_rat @ X @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_le_iff
% 5.45/5.76 thf(fact_5567_floor__correct,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X ) ) @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_correct
% 5.45/5.76 thf(fact_5568_floor__mono,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.76 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_mono
% 5.45/5.76 thf(fact_5569_floor__less__cancel,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) )
% 5.45/5.76 => ( ord_less_rat @ X @ Y ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_less_cancel
% 5.45/5.76 thf(fact_5570_nat__mono,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ X @ Y )
% 5.45/5.76 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mono
% 5.45/5.76 thf(fact_5571_eq__nat__nat__iff,axiom,
% 5.45/5.76 ! [Z: int,Z7: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.45/5.76 => ( ( ( nat2 @ Z )
% 5.45/5.76 = ( nat2 @ Z7 ) )
% 5.45/5.76 = ( Z = Z7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % eq_nat_nat_iff
% 5.45/5.76 thf(fact_5572_all__nat,axiom,
% 5.45/5.76 ( ( ^ [P5: nat > $o] :
% 5.45/5.76 ! [X5: nat] : ( P5 @ X5 ) )
% 5.45/5.76 = ( ^ [P4: nat > $o] :
% 5.45/5.76 ! [X4: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.45/5.76 => ( P4 @ ( nat2 @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % all_nat
% 5.45/5.76 thf(fact_5573_ex__nat,axiom,
% 5.45/5.76 ( ( ^ [P5: nat > $o] :
% 5.45/5.76 ? [X5: nat] : ( P5 @ X5 ) )
% 5.45/5.76 = ( ^ [P4: nat > $o] :
% 5.45/5.76 ? [X4: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.45/5.76 & ( P4 @ ( nat2 @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ex_nat
% 5.45/5.76 thf(fact_5574_le__of__int__ceiling,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_of_int_ceiling
% 5.45/5.76 thf(fact_5575_floor__le__ceiling,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim2889992004027027881ng_rat @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_le_ceiling
% 5.45/5.76 thf(fact_5576_floor__divide__lower,axiom,
% 5.45/5.76 ! [Q6: rat,P3: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 5.45/5.76 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ Q6 ) @ P3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_divide_lower
% 5.45/5.76 thf(fact_5577_of__int__of__nat,axiom,
% 5.45/5.76 ( ring_1_of_int_rat
% 5.45/5.76 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_of_nat
% 5.45/5.76 thf(fact_5578_of__int__of__nat,axiom,
% 5.45/5.76 ( ring_1_of_int_int
% 5.45/5.76 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_of_nat
% 5.45/5.76 thf(fact_5579_of__int__of__nat,axiom,
% 5.45/5.76 ( ring_18347121197199848620nteger
% 5.45/5.76 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_of_nat
% 5.45/5.76 thf(fact_5580_floor__divide__upper,axiom,
% 5.45/5.76 ! [Q6: rat,P3: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 5.45/5.76 => ( ord_less_rat @ P3 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ one_one_rat ) @ Q6 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_divide_upper
% 5.45/5.76 thf(fact_5581_nat__mono__iff,axiom,
% 5.45/5.76 ! [Z: int,W2: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mono_iff
% 5.45/5.76 thf(fact_5582_le__floor__add,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_floor_add
% 5.45/5.76 thf(fact_5583_zless__nat__eq__int__zless,axiom,
% 5.45/5.76 ! [M: nat,Z: int] :
% 5.45/5.76 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % zless_nat_eq_int_zless
% 5.45/5.76 thf(fact_5584_nat__le__iff,axiom,
% 5.45/5.76 ! [X: int,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N2 )
% 5.45/5.76 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_le_iff
% 5.45/5.76 thf(fact_5585_nat__0__le,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.45/5.76 = Z ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_0_le
% 5.45/5.76 thf(fact_5586_int__eq__iff,axiom,
% 5.45/5.76 ! [M: nat,Z: int] :
% 5.45/5.76 ( ( ( semiri1314217659103216013at_int @ M )
% 5.45/5.76 = Z )
% 5.45/5.76 = ( ( M
% 5.45/5.76 = ( nat2 @ Z ) )
% 5.45/5.76 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % int_eq_iff
% 5.45/5.76 thf(fact_5587_of__nat__ceiling,axiom,
% 5.45/5.76 ! [R3: rat] : ( ord_less_eq_rat @ R3 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_ceiling
% 5.45/5.76 thf(fact_5588_ceiling__le__iff,axiom,
% 5.45/5.76 ! [X: rat,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.45/5.76 = ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_le_iff
% 5.45/5.76 thf(fact_5589_less__ceiling__iff,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.76 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % less_ceiling_iff
% 5.45/5.76 thf(fact_5590_nat__plus__as__int,axiom,
% 5.45/5.76 ( plus_plus_nat
% 5.45/5.76 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_plus_as_int
% 5.45/5.76 thf(fact_5591_nat__times__as__int,axiom,
% 5.45/5.76 ( times_times_nat
% 5.45/5.76 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_times_as_int
% 5.45/5.76 thf(fact_5592_nat__minus__as__int,axiom,
% 5.45/5.76 ( minus_minus_nat
% 5.45/5.76 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_minus_as_int
% 5.45/5.76 thf(fact_5593_nat__div__as__int,axiom,
% 5.45/5.76 ( divide_divide_nat
% 5.45/5.76 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_div_as_int
% 5.45/5.76 thf(fact_5594_nat__mod__as__int,axiom,
% 5.45/5.76 ( modulo_modulo_nat
% 5.45/5.76 = ( ^ [A5: nat,B5: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A5 ) @ ( semiri1314217659103216013at_int @ B5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mod_as_int
% 5.45/5.76 thf(fact_5595_of__int__nonneg,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_nonneg
% 5.45/5.76 thf(fact_5596_of__int__nonneg,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_nonneg
% 5.45/5.76 thf(fact_5597_of__int__nonneg,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_nonneg
% 5.45/5.76 thf(fact_5598_of__int__pos,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( ring_18347121197199848620nteger @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_pos
% 5.45/5.76 thf(fact_5599_of__int__pos,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_pos
% 5.45/5.76 thf(fact_5600_of__int__pos,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_pos
% 5.45/5.76 thf(fact_5601_of__int__leD,axiom,
% 5.45/5.76 ! [N2: int,X: code_integer] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_leD
% 5.45/5.76 thf(fact_5602_of__int__leD,axiom,
% 5.45/5.76 ! [N2: int,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_leD
% 5.45/5.76 thf(fact_5603_of__int__leD,axiom,
% 5.45/5.76 ! [N2: int,X: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_leD
% 5.45/5.76 thf(fact_5604_of__int__lessD,axiom,
% 5.45/5.76 ! [N2: int,X: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_lessD
% 5.45/5.76 thf(fact_5605_of__int__lessD,axiom,
% 5.45/5.76 ! [N2: int,X: rat] :
% 5.45/5.76 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_lessD
% 5.45/5.76 thf(fact_5606_of__int__lessD,axiom,
% 5.45/5.76 ! [N2: int,X: int] :
% 5.45/5.76 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X )
% 5.45/5.76 => ( ( N2 = zero_zero_int )
% 5.45/5.76 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_int_lessD
% 5.45/5.76 thf(fact_5607_floor__exists,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ? [Z2: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_exists
% 5.45/5.76 thf(fact_5608_floor__exists1,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ? [X3: int] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X3 ) @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X3 @ one_one_int ) ) )
% 5.45/5.76 & ! [Y6: int] :
% 5.45/5.76 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y6 ) @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y6 @ one_one_int ) ) ) )
% 5.45/5.76 => ( Y6 = X3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_exists1
% 5.45/5.76 thf(fact_5609_nat__less__eq__zless,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_int @ W2 @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_less_eq_zless
% 5.45/5.76 thf(fact_5610_nat__le__eq__zle,axiom,
% 5.45/5.76 ! [W2: int,Z: int] :
% 5.45/5.76 ( ( ( ord_less_int @ zero_zero_int @ W2 )
% 5.45/5.76 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.45/5.76 => ( ( ord_less_eq_nat @ ( nat2 @ W2 ) @ ( nat2 @ Z ) )
% 5.45/5.76 = ( ord_less_eq_int @ W2 @ Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_le_eq_zle
% 5.45/5.76 thf(fact_5611_nat__eq__iff,axiom,
% 5.45/5.76 ! [W2: int,M: nat] :
% 5.45/5.76 ( ( ( nat2 @ W2 )
% 5.45/5.76 = M )
% 5.45/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( W2
% 5.45/5.76 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( M = zero_zero_nat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_eq_iff
% 5.45/5.76 thf(fact_5612_nat__eq__iff2,axiom,
% 5.45/5.76 ! [M: nat,W2: int] :
% 5.45/5.76 ( ( M
% 5.45/5.76 = ( nat2 @ W2 ) )
% 5.45/5.76 = ( ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( W2
% 5.45/5.76 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( M = zero_zero_nat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_eq_iff2
% 5.45/5.76 thf(fact_5613_of__nat__less__of__int__iff,axiom,
% 5.45/5.76 ! [N2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X ) )
% 5.45/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_less_of_int_iff
% 5.45/5.76 thf(fact_5614_of__nat__less__of__int__iff,axiom,
% 5.45/5.76 ! [N2: nat,X: int] :
% 5.45/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X ) )
% 5.45/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_less_of_int_iff
% 5.45/5.76 thf(fact_5615_of__nat__less__of__int__iff,axiom,
% 5.45/5.76 ! [N2: nat,X: int] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( ring_18347121197199848620nteger @ X ) )
% 5.45/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % of_nat_less_of_int_iff
% 5.45/5.76 thf(fact_5616_split__nat,axiom,
% 5.45/5.76 ! [P: nat > $o,I2: int] :
% 5.45/5.76 ( ( P @ ( nat2 @ I2 ) )
% 5.45/5.76 = ( ! [N: nat] :
% 5.45/5.76 ( ( I2
% 5.45/5.76 = ( semiri1314217659103216013at_int @ N ) )
% 5.45/5.76 => ( P @ N ) )
% 5.45/5.76 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 5.45/5.76 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % split_nat
% 5.45/5.76 thf(fact_5617_le__nat__iff,axiom,
% 5.45/5.76 ! [K: int,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.45/5.76 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.45/5.76 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_nat_iff
% 5.45/5.76 thf(fact_5618_nat__add__distrib,axiom,
% 5.45/5.76 ! [Z: int,Z7: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.45/5.76 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.45/5.76 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_add_distrib
% 5.45/5.76 thf(fact_5619_nat__mult__distrib,axiom,
% 5.45/5.76 ! [Z: int,Z7: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.45/5.76 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mult_distrib
% 5.45/5.76 thf(fact_5620_nat__diff__distrib,axiom,
% 5.45/5.76 ! [Z7: int,Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.45/5.76 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.45/5.76 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.45/5.76 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_diff_distrib
% 5.45/5.76 thf(fact_5621_nat__diff__distrib_H,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.76 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 5.45/5.76 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_diff_distrib'
% 5.45/5.76 thf(fact_5622_nat__abs__triangle__ineq,axiom,
% 5.45/5.76 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_abs_triangle_ineq
% 5.45/5.76 thf(fact_5623_nat__div__distrib,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.76 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.45/5.76 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_div_distrib
% 5.45/5.76 thf(fact_5624_nat__div__distrib_H,axiom,
% 5.45/5.76 ! [Y: int,X: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.76 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.45/5.76 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_div_distrib'
% 5.45/5.76 thf(fact_5625_nat__mod__distrib,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.76 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.76 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.45/5.76 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mod_distrib
% 5.45/5.76 thf(fact_5626_ceiling__diff__floor__le__1,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) @ one_one_int ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_diff_floor_le_1
% 5.45/5.76 thf(fact_5627_nat__power__eq,axiom,
% 5.45/5.76 ! [Z: int,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.45/5.76 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_power_eq
% 5.45/5.76 thf(fact_5628_le__mult__floor,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.45/5.76 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_mult_floor
% 5.45/5.76 thf(fact_5629_ceiling__correct,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) @ one_one_rat ) @ X )
% 5.45/5.76 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_correct
% 5.45/5.76 thf(fact_5630_ceiling__unique,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X )
% 5.45/5.76 => ( ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z ) )
% 5.45/5.76 => ( ( archim2889992004027027881ng_rat @ X )
% 5.45/5.76 = Z ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_unique
% 5.45/5.76 thf(fact_5631_ceiling__eq__iff,axiom,
% 5.45/5.76 ! [X: rat,A: int] :
% 5.45/5.76 ( ( ( archim2889992004027027881ng_rat @ X )
% 5.45/5.76 = A )
% 5.45/5.76 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X )
% 5.45/5.76 & ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_eq_iff
% 5.45/5.76 thf(fact_5632_ceiling__split,axiom,
% 5.45/5.76 ! [P: int > $o,T5: rat] :
% 5.45/5.76 ( ( P @ ( archim2889992004027027881ng_rat @ T5 ) )
% 5.45/5.76 = ( ! [I4: int] :
% 5.45/5.76 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I4 ) @ one_one_rat ) @ T5 )
% 5.45/5.76 & ( ord_less_eq_rat @ T5 @ ( ring_1_of_int_rat @ I4 ) ) )
% 5.45/5.76 => ( P @ I4 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_split
% 5.45/5.76 thf(fact_5633_ceiling__less__iff,axiom,
% 5.45/5.76 ! [X: rat,Z: int] :
% 5.45/5.76 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X ) @ Z )
% 5.45/5.76 = ( ord_less_eq_rat @ X @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_less_iff
% 5.45/5.76 thf(fact_5634_le__ceiling__iff,axiom,
% 5.45/5.76 ! [Z: int,X: rat] :
% 5.45/5.76 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X ) )
% 5.45/5.76 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_ceiling_iff
% 5.45/5.76 thf(fact_5635_Suc__nat__eq__nat__zadd1,axiom,
% 5.45/5.76 ! [Z: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.45/5.76 => ( ( suc @ ( nat2 @ Z ) )
% 5.45/5.76 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Suc_nat_eq_nat_zadd1
% 5.45/5.76 thf(fact_5636_nat__less__iff,axiom,
% 5.45/5.76 ! [W2: int,M: nat] :
% 5.45/5.76 ( ( ord_less_eq_int @ zero_zero_int @ W2 )
% 5.45/5.76 => ( ( ord_less_nat @ ( nat2 @ W2 ) @ M )
% 5.45/5.76 = ( ord_less_int @ W2 @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_less_iff
% 5.45/5.76 thf(fact_5637_nat__mult__distrib__neg,axiom,
% 5.45/5.76 ! [Z: int,Z7: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.45/5.76 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.45/5.76 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_mult_distrib_neg
% 5.45/5.76 thf(fact_5638_nat__abs__int__diff,axiom,
% 5.45/5.76 ! [A: nat,B: nat] :
% 5.45/5.76 ( ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.76 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.45/5.76 = ( minus_minus_nat @ B @ A ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.45/5.76 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.45/5.76 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nat_abs_int_diff
% 5.45/5.76 thf(fact_5639_diff__nat__eq__if,axiom,
% 5.45/5.76 ! [Z7: int,Z: int] :
% 5.45/5.76 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.45/5.76 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.45/5.76 = ( nat2 @ Z ) ) )
% 5.45/5.76 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.45/5.76 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.45/5.76 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % diff_nat_eq_if
% 5.45/5.76 thf(fact_5640_ceiling__divide__upper,axiom,
% 5.45/5.76 ! [Q6: rat,P3: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 5.45/5.76 => ( ord_less_eq_rat @ P3 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ Q6 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_divide_upper
% 5.45/5.76 thf(fact_5641_ceiling__divide__lower,axiom,
% 5.45/5.76 ! [Q6: rat,P3: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ Q6 )
% 5.45/5.76 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P3 @ Q6 ) ) ) @ one_one_rat ) @ Q6 ) @ P3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % ceiling_divide_lower
% 5.45/5.76 thf(fact_5642_floor__add,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.45/5.76 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.45/5.76 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.45/5.76 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.45/5.76 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % floor_add
% 5.45/5.76 thf(fact_5643_eucl__rel__int_Osimps,axiom,
% 5.45/5.76 ( eucl_rel_int
% 5.45/5.76 = ( ^ [A12: int,A22: int,A32: product_prod_int_int] :
% 5.45/5.76 ( ? [K3: int] :
% 5.45/5.76 ( ( A12 = K3 )
% 5.45/5.76 & ( A22 = zero_zero_int )
% 5.45/5.76 & ( A32
% 5.45/5.76 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.45/5.76 | ? [L2: int,K3: int,Q7: int] :
% 5.45/5.76 ( ( A12 = K3 )
% 5.45/5.76 & ( A22 = L2 )
% 5.45/5.76 & ( A32
% 5.45/5.76 = ( product_Pair_int_int @ Q7 @ zero_zero_int ) )
% 5.45/5.76 & ( L2 != zero_zero_int )
% 5.45/5.76 & ( K3
% 5.45/5.76 = ( times_times_int @ Q7 @ L2 ) ) )
% 5.45/5.76 | ? [R4: int,L2: int,K3: int,Q7: int] :
% 5.45/5.76 ( ( A12 = K3 )
% 5.45/5.76 & ( A22 = L2 )
% 5.45/5.76 & ( A32
% 5.45/5.76 = ( product_Pair_int_int @ Q7 @ R4 ) )
% 5.45/5.76 & ( ( sgn_sgn_int @ R4 )
% 5.45/5.76 = ( sgn_sgn_int @ L2 ) )
% 5.45/5.76 & ( ord_less_int @ ( abs_abs_int @ R4 ) @ ( abs_abs_int @ L2 ) )
% 5.45/5.76 & ( K3
% 5.45/5.76 = ( plus_plus_int @ ( times_times_int @ Q7 @ L2 ) @ R4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % eucl_rel_int.simps
% 5.45/5.76 thf(fact_5644_eucl__rel__int_Ocases,axiom,
% 5.45/5.76 ! [A1: int,A23: int,A33: product_prod_int_int] :
% 5.45/5.76 ( ( eucl_rel_int @ A1 @ A23 @ A33 )
% 5.45/5.76 => ( ( ( A23 = zero_zero_int )
% 5.45/5.76 => ( A33
% 5.45/5.76 != ( product_Pair_int_int @ zero_zero_int @ A1 ) ) )
% 5.45/5.76 => ( ! [Q5: int] :
% 5.45/5.76 ( ( A33
% 5.45/5.76 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 5.45/5.76 => ( ( A23 != zero_zero_int )
% 5.45/5.76 => ( A1
% 5.45/5.76 != ( times_times_int @ Q5 @ A23 ) ) ) )
% 5.45/5.76 => ~ ! [R2: int,Q5: int] :
% 5.45/5.76 ( ( A33
% 5.45/5.76 = ( product_Pair_int_int @ Q5 @ R2 ) )
% 5.45/5.76 => ( ( ( sgn_sgn_int @ R2 )
% 5.45/5.76 = ( sgn_sgn_int @ A23 ) )
% 5.45/5.76 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 5.45/5.76 => ( A1
% 5.45/5.76 != ( plus_plus_int @ ( times_times_int @ Q5 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % eucl_rel_int.cases
% 5.45/5.76 thf(fact_5645_nonempty__has__size,axiom,
% 5.45/5.76 ! [S: multis2468970476368604999at_nat] :
% 5.45/5.76 ( ( S != zero_z1048942125864253310at_nat )
% 5.45/5.76 = ( ord_less_nat @ zero_zero_nat @ ( size_s8510653225128441779at_nat @ S ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nonempty_has_size
% 5.45/5.76 thf(fact_5646_mult__ceiling__le__Ints,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_ceiling_le_Ints
% 5.45/5.76 thf(fact_5647_mult__ceiling__le__Ints,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mult_ceiling_le_Ints
% 5.45/5.76 thf(fact_5648_sgn__less,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_less
% 5.45/5.76 thf(fact_5649_sgn__less,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.45/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_less
% 5.45/5.76 thf(fact_5650_sgn__less,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_less
% 5.45/5.76 thf(fact_5651_sgn__greater,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_greater
% 5.45/5.76 thf(fact_5652_sgn__greater,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.45/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_greater
% 5.45/5.76 thf(fact_5653_sgn__greater,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_greater
% 5.45/5.76 thf(fact_5654_divide__sgn,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 5.45/5.76 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % divide_sgn
% 5.45/5.76 thf(fact_5655_sgn__pos,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.76 => ( ( sgn_sgn_Code_integer @ A )
% 5.45/5.76 = one_one_Code_integer ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_pos
% 5.45/5.76 thf(fact_5656_sgn__pos,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( sgn_sgn_rat @ A )
% 5.45/5.76 = one_one_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_pos
% 5.45/5.76 thf(fact_5657_sgn__pos,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ A )
% 5.45/5.76 => ( ( sgn_sgn_int @ A )
% 5.45/5.76 = one_one_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_pos
% 5.45/5.76 thf(fact_5658_frac__gt__0__iff,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) )
% 5.45/5.76 = ( ~ ( member_rat @ X @ ring_1_Ints_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % frac_gt_0_iff
% 5.45/5.76 thf(fact_5659_sgn__neg,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.76 => ( ( sgn_sgn_int @ A )
% 5.45/5.76 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_neg
% 5.45/5.76 thf(fact_5660_sgn__neg,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.76 => ( ( sgn_sgn_Code_integer @ A )
% 5.45/5.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_neg
% 5.45/5.76 thf(fact_5661_sgn__neg,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.76 => ( ( sgn_sgn_rat @ A )
% 5.45/5.76 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_neg
% 5.45/5.76 thf(fact_5662_union__diff__assoc,axiom,
% 5.45/5.76 ! [C3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat,A3: multis2468970476368604999at_nat] :
% 5.45/5.76 ( ( ( minus_4286766774447292334at_nat @ C3 @ B3 )
% 5.45/5.76 = zero_z1048942125864253310at_nat )
% 5.45/5.76 => ( ( minus_4286766774447292334at_nat @ ( plus_p7104986032573967614at_nat @ A3 @ B3 ) @ C3 )
% 5.45/5.76 = ( plus_p7104986032573967614at_nat @ A3 @ ( minus_4286766774447292334at_nat @ B3 @ C3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % union_diff_assoc
% 5.45/5.76 thf(fact_5663_sgn__mult,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer] :
% 5.45/5.76 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.76 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult
% 5.45/5.76 thf(fact_5664_sgn__mult,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 5.45/5.76 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult
% 5.45/5.76 thf(fact_5665_sgn__mult,axiom,
% 5.45/5.76 ! [A: int,B: int] :
% 5.45/5.76 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 5.45/5.76 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult
% 5.45/5.76 thf(fact_5666_Ints__mult,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( member_Code_integer @ B @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( member_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ring_11222124179247155820nteger ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_mult
% 5.45/5.76 thf(fact_5667_Ints__mult,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.45/5.76 => ( member_rat @ ( times_times_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_mult
% 5.45/5.76 thf(fact_5668_Ints__mult,axiom,
% 5.45/5.76 ! [A: int,B: int] :
% 5.45/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.45/5.76 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.45/5.76 => ( member_int @ ( times_times_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_mult
% 5.45/5.76 thf(fact_5669_linordered__idom__class_Oabs__sgn,axiom,
% 5.45/5.76 ( abs_abs_Code_integer
% 5.45/5.76 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % linordered_idom_class.abs_sgn
% 5.45/5.76 thf(fact_5670_linordered__idom__class_Oabs__sgn,axiom,
% 5.45/5.76 ( abs_abs_rat
% 5.45/5.76 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % linordered_idom_class.abs_sgn
% 5.45/5.76 thf(fact_5671_linordered__idom__class_Oabs__sgn,axiom,
% 5.45/5.76 ( abs_abs_int
% 5.45/5.76 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % linordered_idom_class.abs_sgn
% 5.45/5.76 thf(fact_5672_abs__mult__sgn,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % abs_mult_sgn
% 5.45/5.76 thf(fact_5673_abs__mult__sgn,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % abs_mult_sgn
% 5.45/5.76 thf(fact_5674_abs__mult__sgn,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % abs_mult_sgn
% 5.45/5.76 thf(fact_5675_sgn__mult__abs,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult_abs
% 5.45/5.76 thf(fact_5676_sgn__mult__abs,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult_abs
% 5.45/5.76 thf(fact_5677_sgn__mult__abs,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.45/5.76 = A ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_mult_abs
% 5.45/5.76 thf(fact_5678_mult__sgn__abs,axiom,
% 5.45/5.76 ! [X: code_integer] :
% 5.45/5.76 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X ) @ ( abs_abs_Code_integer @ X ) )
% 5.45/5.76 = X ) ).
% 5.45/5.76
% 5.45/5.76 % mult_sgn_abs
% 5.45/5.76 thf(fact_5679_mult__sgn__abs,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( sgn_sgn_rat @ X ) @ ( abs_abs_rat @ X ) )
% 5.45/5.76 = X ) ).
% 5.45/5.76
% 5.45/5.76 % mult_sgn_abs
% 5.45/5.76 thf(fact_5680_mult__sgn__abs,axiom,
% 5.45/5.76 ! [X: int] :
% 5.45/5.76 ( ( times_times_int @ ( sgn_sgn_int @ X ) @ ( abs_abs_int @ X ) )
% 5.45/5.76 = X ) ).
% 5.45/5.76
% 5.45/5.76 % mult_sgn_abs
% 5.45/5.76 thf(fact_5681_frac__ge__0,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X ) ) ).
% 5.45/5.76
% 5.45/5.76 % frac_ge_0
% 5.45/5.76 thf(fact_5682_frac__lt__1,axiom,
% 5.45/5.76 ! [X: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X ) @ one_one_rat ) ).
% 5.45/5.76
% 5.45/5.76 % frac_lt_1
% 5.45/5.76 thf(fact_5683_frac__unique__iff,axiom,
% 5.45/5.76 ! [X: rat,A: rat] :
% 5.45/5.76 ( ( ( archimedean_frac_rat @ X )
% 5.45/5.76 = A )
% 5.45/5.76 = ( ( member_rat @ ( minus_minus_rat @ X @ A ) @ ring_1_Ints_rat )
% 5.45/5.76 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % frac_unique_iff
% 5.45/5.76 thf(fact_5684_sgn__1__pos,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.45/5.76 = one_one_Code_integer )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_pos
% 5.45/5.76 thf(fact_5685_sgn__1__pos,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.45/5.76 = one_one_rat )
% 5.45/5.76 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_pos
% 5.45/5.76 thf(fact_5686_sgn__1__pos,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ( sgn_sgn_int @ A )
% 5.45/5.76 = one_one_int )
% 5.45/5.76 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_pos
% 5.45/5.76 thf(fact_5687_zsgn__def,axiom,
% 5.45/5.76 ( sgn_sgn_int
% 5.45/5.76 = ( ^ [I4: int] : ( if_int @ ( I4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % zsgn_def
% 5.45/5.76 thf(fact_5688_sgn__1__neg,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( ( sgn_sgn_int @ A )
% 5.45/5.76 = ( uminus_uminus_int @ one_one_int ) )
% 5.45/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_neg
% 5.45/5.76 thf(fact_5689_sgn__1__neg,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( ( sgn_sgn_Code_integer @ A )
% 5.45/5.76 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_neg
% 5.45/5.76 thf(fact_5690_sgn__1__neg,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( ( sgn_sgn_rat @ A )
% 5.45/5.76 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.45/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_1_neg
% 5.45/5.76 thf(fact_5691_sgn__if,axiom,
% 5.45/5.76 ( sgn_sgn_int
% 5.45/5.76 = ( ^ [X4: int] : ( if_int @ ( X4 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X4 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_if
% 5.45/5.76 thf(fact_5692_sgn__if,axiom,
% 5.45/5.76 ( sgn_sgn_Code_integer
% 5.45/5.76 = ( ^ [X4: code_integer] : ( if_Code_integer @ ( X4 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X4 ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_if
% 5.45/5.76 thf(fact_5693_sgn__if,axiom,
% 5.45/5.76 ( sgn_sgn_rat
% 5.45/5.76 = ( ^ [X4: rat] : ( if_rat @ ( X4 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X4 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % sgn_if
% 5.45/5.76 thf(fact_5694_Ints__odd__less__0,axiom,
% 5.45/5.76 ! [A: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ A @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ A ) @ zero_z3403309356797280102nteger )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_odd_less_0
% 5.45/5.76 thf(fact_5695_Ints__odd__less__0,axiom,
% 5.45/5.76 ! [A: rat] :
% 5.45/5.76 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.45/5.76 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_odd_less_0
% 5.45/5.76 thf(fact_5696_Ints__odd__less__0,axiom,
% 5.45/5.76 ! [A: int] :
% 5.45/5.76 ( ( member_int @ A @ ring_1_Ints_int )
% 5.45/5.76 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.45/5.76 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_odd_less_0
% 5.45/5.76 thf(fact_5697_Ints__nonzero__abs__ge1,axiom,
% 5.45/5.76 ! [X: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( X != zero_z3403309356797280102nteger )
% 5.45/5.76 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_ge1
% 5.45/5.76 thf(fact_5698_Ints__nonzero__abs__ge1,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( X != zero_zero_rat )
% 5.45/5.76 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_ge1
% 5.45/5.76 thf(fact_5699_Ints__nonzero__abs__ge1,axiom,
% 5.45/5.76 ! [X: int] :
% 5.45/5.76 ( ( member_int @ X @ ring_1_Ints_int )
% 5.45/5.76 => ( ( X != zero_zero_int )
% 5.45/5.76 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_ge1
% 5.45/5.76 thf(fact_5700_Ints__nonzero__abs__less1,axiom,
% 5.45/5.76 ! [X: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer )
% 5.45/5.76 => ( X = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_less1
% 5.45/5.76 thf(fact_5701_Ints__nonzero__abs__less1,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat )
% 5.45/5.76 => ( X = zero_zero_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_less1
% 5.45/5.76 thf(fact_5702_Ints__nonzero__abs__less1,axiom,
% 5.45/5.76 ! [X: int] :
% 5.45/5.76 ( ( member_int @ X @ ring_1_Ints_int )
% 5.45/5.76 => ( ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int )
% 5.45/5.76 => ( X = zero_zero_int ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_nonzero_abs_less1
% 5.45/5.76 thf(fact_5703_Ints__eq__abs__less1,axiom,
% 5.45/5.76 ! [X: code_integer,Y: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ X @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 5.45/5.76 => ( ( X = Y )
% 5.45/5.76 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_eq_abs_less1
% 5.45/5.76 thf(fact_5704_Ints__eq__abs__less1,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( member_rat @ X @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 5.45/5.76 => ( ( X = Y )
% 5.45/5.76 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_eq_abs_less1
% 5.45/5.76 thf(fact_5705_Ints__eq__abs__less1,axiom,
% 5.45/5.76 ! [X: int,Y: int] :
% 5.45/5.76 ( ( member_int @ X @ ring_1_Ints_int )
% 5.45/5.76 => ( ( member_int @ Y @ ring_1_Ints_int )
% 5.45/5.76 => ( ( X = Y )
% 5.45/5.76 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Ints_eq_abs_less1
% 5.45/5.76 thf(fact_5706_frac__eq,axiom,
% 5.45/5.76 ! [X: rat] :
% 5.45/5.76 ( ( ( archimedean_frac_rat @ X )
% 5.45/5.76 = X )
% 5.45/5.76 = ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.76 & ( ord_less_rat @ X @ one_one_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % frac_eq
% 5.45/5.76 thf(fact_5707_frac__add,axiom,
% 5.45/5.76 ! [X: rat,Y: rat] :
% 5.45/5.76 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.45/5.76 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.45/5.76 = ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.45/5.76 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X @ Y ) )
% 5.45/5.76 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % frac_add
% 5.45/5.76 thf(fact_5708_eucl__rel__int__remainderI,axiom,
% 5.45/5.76 ! [R3: int,L: int,K: int,Q6: int] :
% 5.45/5.76 ( ( ( sgn_sgn_int @ R3 )
% 5.45/5.76 = ( sgn_sgn_int @ L ) )
% 5.45/5.76 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 5.45/5.76 => ( ( K
% 5.45/5.76 = ( plus_plus_int @ ( times_times_int @ Q6 @ L ) @ R3 ) )
% 5.45/5.76 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q6 @ R3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % eucl_rel_int_remainderI
% 5.45/5.76 thf(fact_5709_le__mult__floor__Ints,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_mult_floor_Ints
% 5.45/5.76 thf(fact_5710_le__mult__floor__Ints,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.45/5.76 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.45/5.76 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % le_mult_floor_Ints
% 5.45/5.76 thf(fact_5711_slice__len,axiom,
% 5.45/5.76 ! [From: nat,To: nat,Xs: list_nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ From @ To )
% 5.45/5.76 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 5.45/5.76 => ( ( size_size_list_nat @ ( slice_nat @ From @ To @ Xs ) )
% 5.45/5.76 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % slice_len
% 5.45/5.76 thf(fact_5712_slice__len,axiom,
% 5.45/5.76 ! [From: nat,To: nat,Xs: list_o] :
% 5.45/5.76 ( ( ord_less_eq_nat @ From @ To )
% 5.45/5.76 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 5.45/5.76 => ( ( size_size_list_o @ ( slice_o @ From @ To @ Xs ) )
% 5.45/5.76 = ( minus_minus_nat @ To @ From ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % slice_len
% 5.45/5.76 thf(fact_5713_gbinomial__absorption_H,axiom,
% 5.45/5.76 ! [K: nat,A: rat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.76 => ( ( gbinomial_rat @ A @ K )
% 5.45/5.76 = ( times_times_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_absorption'
% 5.45/5.76 thf(fact_5714_pochhammer__same,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 5.45/5.76 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % pochhammer_same
% 5.45/5.76 thf(fact_5715_pochhammer__same,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.45/5.76 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % pochhammer_same
% 5.45/5.76 thf(fact_5716_pochhammer__same,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.45/5.76 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % pochhammer_same
% 5.45/5.76 thf(fact_5717_fact__reduce,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.76 => ( ( semiri773545260158071498ct_rat @ N2 )
% 5.45/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_reduce
% 5.45/5.76 thf(fact_5718_fact__reduce,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.76 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.45/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_reduce
% 5.45/5.76 thf(fact_5719_fact__reduce,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.76 => ( ( semiri3624122377584611663nteger @ N2 )
% 5.45/5.76 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_reduce
% 5.45/5.76 thf(fact_5720_fact__reduce,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.76 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.45/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_reduce
% 5.45/5.76 thf(fact_5721_fact__num__eq__if,axiom,
% 5.45/5.76 ( semiri773545260158071498ct_rat
% 5.45/5.76 = ( ^ [M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ M3 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_num_eq_if
% 5.45/5.76 thf(fact_5722_fact__num__eq__if,axiom,
% 5.45/5.76 ( semiri1406184849735516958ct_int
% 5.45/5.76 = ( ^ [M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_num_eq_if
% 5.45/5.76 thf(fact_5723_fact__num__eq__if,axiom,
% 5.45/5.76 ( semiri3624122377584611663nteger
% 5.45/5.76 = ( ^ [M3: nat] : ( if_Code_integer @ ( M3 = zero_zero_nat ) @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M3 ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_num_eq_if
% 5.45/5.76 thf(fact_5724_fact__num__eq__if,axiom,
% 5.45/5.76 ( semiri1408675320244567234ct_nat
% 5.45/5.76 = ( ^ [M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M3 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_num_eq_if
% 5.45/5.76 thf(fact_5725_rotate1__length01,axiom,
% 5.45/5.76 ! [Xs: list_nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 5.45/5.76 => ( ( rotate1_nat @ Xs )
% 5.45/5.76 = Xs ) ) ).
% 5.45/5.76
% 5.45/5.76 % rotate1_length01
% 5.45/5.76 thf(fact_5726_rotate1__length01,axiom,
% 5.45/5.76 ! [Xs: list_o] :
% 5.45/5.76 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 5.45/5.76 => ( ( rotate1_o @ Xs )
% 5.45/5.76 = Xs ) ) ).
% 5.45/5.76
% 5.45/5.76 % rotate1_length01
% 5.45/5.76 thf(fact_5727_cpmi,axiom,
% 5.45/5.76 ! [D3: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ? [Z5: int] :
% 5.45/5.76 ! [X3: int] :
% 5.45/5.76 ( ( ord_less_int @ X3 @ Z5 )
% 5.45/5.76 => ( ( P @ X3 )
% 5.45/5.76 = ( P6 @ X3 ) ) )
% 5.45/5.76 => ( ! [X3: int] :
% 5.45/5.76 ( ! [Xa2: int] :
% 5.45/5.76 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb2: int] :
% 5.45/5.76 ( ( member_int @ Xb2 @ B3 )
% 5.45/5.76 => ( X3
% 5.45/5.76 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.45/5.76 => ( ( P @ X3 )
% 5.45/5.76 => ( P @ ( minus_minus_int @ X3 @ D3 ) ) ) )
% 5.45/5.76 => ( ! [X3: int,K2: int] :
% 5.45/5.76 ( ( P6 @ X3 )
% 5.45/5.76 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.76 => ( ( ? [X11: int] : ( P @ X11 ) )
% 5.45/5.76 = ( ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 & ( P6 @ X4 ) )
% 5.45/5.76 | ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 & ? [Y4: int] :
% 5.45/5.76 ( ( member_int @ Y4 @ B3 )
% 5.45/5.76 & ( P @ ( plus_plus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % cpmi
% 5.45/5.76 thf(fact_5728_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: set_int,H: set_int,L3: set_int,H3: set_int] :
% 5.45/5.76 ( ( ( set_or370866239135849197et_int @ L @ H )
% 5.45/5.76 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_less_eq_set_int @ L @ H )
% 5.45/5.76 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5729_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: rat,H: rat,L3: rat,H3: rat] :
% 5.45/5.76 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_less_eq_rat @ L @ H )
% 5.45/5.76 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5730_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: num,H: num,L3: num,H3: num] :
% 5.45/5.76 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 5.45/5.76 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_less_eq_num @ L @ H )
% 5.45/5.76 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5731_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: int,H: int,L3: int,H3: int] :
% 5.45/5.76 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 5.45/5.76 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_less_eq_int @ L @ H )
% 5.45/5.76 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5732_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: nat,H: nat,L3: nat,H3: nat] :
% 5.45/5.76 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 5.45/5.76 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_less_eq_nat @ L @ H )
% 5.45/5.76 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5733_Icc__eq__Icc,axiom,
% 5.45/5.76 ! [L: code_integer,H: code_integer,L3: code_integer,H3: code_integer] :
% 5.45/5.76 ( ( ( set_or189985376899183464nteger @ L @ H )
% 5.45/5.76 = ( set_or189985376899183464nteger @ L3 @ H3 ) )
% 5.45/5.76 = ( ( ( L = L3 )
% 5.45/5.76 & ( H = H3 ) )
% 5.45/5.76 | ( ~ ( ord_le3102999989581377725nteger @ L @ H )
% 5.45/5.76 & ~ ( ord_le3102999989581377725nteger @ L3 @ H3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Icc_eq_Icc
% 5.45/5.76 thf(fact_5734_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: $o,L: $o,U: $o] :
% 5.45/5.76 ( ( member_o @ I2 @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_o @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_o @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5735_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 5.45/5.76 ( ( member_set_nat @ I2 @ ( set_or4548717258645045905et_nat @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_set_nat @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5736_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: set_int,L: set_int,U: set_int] :
% 5.45/5.76 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_set_int @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5737_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: rat,L: rat,U: rat] :
% 5.45/5.76 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_rat @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5738_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: num,L: num,U: num] :
% 5.45/5.76 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_num @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5739_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: int,L: int,U: int] :
% 5.45/5.76 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_int @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5740_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: nat,L: nat,U: nat] :
% 5.45/5.76 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.45/5.76 = ( ( ord_less_eq_nat @ L @ I2 )
% 5.45/5.76 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5741_atLeastAtMost__iff,axiom,
% 5.45/5.76 ! [I2: code_integer,L: code_integer,U: code_integer] :
% 5.45/5.76 ( ( member_Code_integer @ I2 @ ( set_or189985376899183464nteger @ L @ U ) )
% 5.45/5.76 = ( ( ord_le3102999989581377725nteger @ L @ I2 )
% 5.45/5.76 & ( ord_le3102999989581377725nteger @ I2 @ U ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastAtMost_iff
% 5.45/5.76 thf(fact_5742_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: $o,B: $o] :
% 5.45/5.76 ( ( bot_bot_set_o
% 5.45/5.76 = ( set_or8904488021354931149Most_o @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5743_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: set_int,B: set_int] :
% 5.45/5.76 ( ( bot_bot_set_set_int
% 5.45/5.76 = ( set_or370866239135849197et_int @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5744_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( bot_bot_set_rat
% 5.45/5.76 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5745_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: num,B: num] :
% 5.45/5.76 ( ( bot_bot_set_num
% 5.45/5.76 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5746_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: int,B: int] :
% 5.45/5.76 ( ( bot_bot_set_int
% 5.45/5.76 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5747_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: nat,B: nat] :
% 5.45/5.76 ( ( bot_bot_set_nat
% 5.45/5.76 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5748_atLeastatMost__empty__iff2,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer] :
% 5.45/5.76 ( ( bot_bo3990330152332043303nteger
% 5.45/5.76 = ( set_or189985376899183464nteger @ A @ B ) )
% 5.45/5.76 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff2
% 5.45/5.76 thf(fact_5749_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: $o,B: $o] :
% 5.45/5.76 ( ( ( set_or8904488021354931149Most_o @ A @ B )
% 5.45/5.76 = bot_bot_set_o )
% 5.45/5.76 = ( ~ ( ord_less_eq_o @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5750_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: set_int,B: set_int] :
% 5.45/5.76 ( ( ( set_or370866239135849197et_int @ A @ B )
% 5.45/5.76 = bot_bot_set_set_int )
% 5.45/5.76 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5751_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: rat,B: rat] :
% 5.45/5.76 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat )
% 5.45/5.76 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5752_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: num,B: num] :
% 5.45/5.76 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.45/5.76 = bot_bot_set_num )
% 5.45/5.76 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5753_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: int,B: int] :
% 5.45/5.76 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.45/5.76 = bot_bot_set_int )
% 5.45/5.76 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5754_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: nat,B: nat] :
% 5.45/5.76 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.45/5.76 = bot_bot_set_nat )
% 5.45/5.76 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5755_atLeastatMost__empty__iff,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer] :
% 5.45/5.76 ( ( ( set_or189985376899183464nteger @ A @ B )
% 5.45/5.76 = bot_bo3990330152332043303nteger )
% 5.45/5.76 = ( ~ ( ord_le3102999989581377725nteger @ A @ B ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty_iff
% 5.45/5.76 thf(fact_5756_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: $o,A: $o] :
% 5.45/5.76 ( ( ord_less_o @ B @ A )
% 5.45/5.76 => ( ( set_or8904488021354931149Most_o @ A @ B )
% 5.45/5.76 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5757_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: assn,A: assn] :
% 5.45/5.76 ( ( ord_less_assn @ B @ A )
% 5.45/5.76 => ( ( set_or7959216805967363635t_assn @ A @ B )
% 5.45/5.76 = bot_bot_set_assn ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5758_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: rat,A: rat] :
% 5.45/5.76 ( ( ord_less_rat @ B @ A )
% 5.45/5.76 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5759_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: num,A: num] :
% 5.45/5.76 ( ( ord_less_num @ B @ A )
% 5.45/5.76 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.45/5.76 = bot_bot_set_num ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5760_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: int,A: int] :
% 5.45/5.76 ( ( ord_less_int @ B @ A )
% 5.45/5.76 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.45/5.76 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5761_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: nat,A: nat] :
% 5.45/5.76 ( ( ord_less_nat @ B @ A )
% 5.45/5.76 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.45/5.76 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5762_atLeastatMost__empty,axiom,
% 5.45/5.76 ! [B: code_integer,A: code_integer] :
% 5.45/5.76 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.45/5.76 => ( ( set_or189985376899183464nteger @ A @ B )
% 5.45/5.76 = bot_bo3990330152332043303nteger ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_empty
% 5.45/5.76 thf(fact_5763_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: set_int,B: set_int,C: set_int,D2: set_int] :
% 5.45/5.76 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.76 & ( ord_less_eq_set_int @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5764_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.76 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.76 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5765_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.76 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_num @ C @ A )
% 5.45/5.76 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5766_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_int @ C @ A )
% 5.45/5.76 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5767_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.76 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5768_atLeastatMost__subset__iff,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.76 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 5.45/5.76 = ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.76 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.45/5.76 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_subset_iff
% 5.45/5.76 thf(fact_5769_slice__complete,axiom,
% 5.45/5.76 ! [Xs: list_nat] :
% 5.45/5.76 ( ( slice_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) @ Xs )
% 5.45/5.76 = Xs ) ).
% 5.45/5.76
% 5.45/5.76 % slice_complete
% 5.45/5.76 thf(fact_5770_slice__complete,axiom,
% 5.45/5.76 ! [Xs: list_o] :
% 5.45/5.76 ( ( slice_o @ zero_zero_nat @ ( size_size_list_o @ Xs ) @ Xs )
% 5.45/5.76 = Xs ) ).
% 5.45/5.76
% 5.45/5.76 % slice_complete
% 5.45/5.76 thf(fact_5771_fact__Suc,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( semiri773545260158071498ct_rat @ ( suc @ N2 ) )
% 5.45/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_Suc
% 5.45/5.76 thf(fact_5772_fact__Suc,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.45/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_Suc
% 5.45/5.76 thf(fact_5773_fact__Suc,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( semiri3624122377584611663nteger @ ( suc @ N2 ) )
% 5.45/5.76 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( suc @ N2 ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_Suc
% 5.45/5.76 thf(fact_5774_fact__Suc,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.45/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_Suc
% 5.45/5.76 thf(fact_5775_mset__distrib,axiom,
% 5.45/5.76 ! [A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat,M6: multis2468970476368604999at_nat,N7: multis2468970476368604999at_nat] :
% 5.45/5.76 ( ( ( plus_p7104986032573967614at_nat @ A3 @ B3 )
% 5.45/5.76 = ( plus_p7104986032573967614at_nat @ M6 @ N7 ) )
% 5.45/5.76 => ~ ! [Am: multis2468970476368604999at_nat,An: multis2468970476368604999at_nat] :
% 5.45/5.76 ( ( A3
% 5.45/5.76 = ( plus_p7104986032573967614at_nat @ Am @ An ) )
% 5.45/5.76 => ! [Bm: multis2468970476368604999at_nat,Bn: multis2468970476368604999at_nat] :
% 5.45/5.76 ( ( B3
% 5.45/5.76 = ( plus_p7104986032573967614at_nat @ Bm @ Bn ) )
% 5.45/5.76 => ( ( M6
% 5.45/5.76 = ( plus_p7104986032573967614at_nat @ Am @ Bm ) )
% 5.45/5.76 => ( N7
% 5.45/5.76 != ( plus_p7104986032573967614at_nat @ An @ Bn ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % mset_distrib
% 5.45/5.76 thf(fact_5776_fact__mono__nat,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mono_nat
% 5.45/5.76 thf(fact_5777_fact__ge__self,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_self
% 5.45/5.76 thf(fact_5778_ivl__disj__un__two__touch_I4_J,axiom,
% 5.45/5.76 ! [L: rat,M: rat,U: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ L @ M )
% 5.45/5.76 => ( ( ord_less_eq_rat @ M @ U )
% 5.45/5.76 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ivl_disj_un_two_touch(4)
% 5.45/5.76 thf(fact_5779_ivl__disj__un__two__touch_I4_J,axiom,
% 5.45/5.76 ! [L: num,M: num,U: num] :
% 5.45/5.76 ( ( ord_less_eq_num @ L @ M )
% 5.45/5.76 => ( ( ord_less_eq_num @ M @ U )
% 5.45/5.76 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M ) @ ( set_or7049704709247886629st_num @ M @ U ) )
% 5.45/5.76 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ivl_disj_un_two_touch(4)
% 5.45/5.76 thf(fact_5780_ivl__disj__un__two__touch_I4_J,axiom,
% 5.45/5.76 ! [L: int,M: int,U: int] :
% 5.45/5.76 ( ( ord_less_eq_int @ L @ M )
% 5.45/5.76 => ( ( ord_less_eq_int @ M @ U )
% 5.45/5.76 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 5.45/5.76 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ivl_disj_un_two_touch(4)
% 5.45/5.76 thf(fact_5781_ivl__disj__un__two__touch_I4_J,axiom,
% 5.45/5.76 ! [L: nat,M: nat,U: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ L @ M )
% 5.45/5.76 => ( ( ord_less_eq_nat @ M @ U )
% 5.45/5.76 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 5.45/5.76 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ivl_disj_un_two_touch(4)
% 5.45/5.76 thf(fact_5782_ivl__disj__un__two__touch_I4_J,axiom,
% 5.45/5.76 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.76 ( ( ord_le3102999989581377725nteger @ L @ M )
% 5.45/5.76 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 5.45/5.76 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 5.45/5.76 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ivl_disj_un_two_touch(4)
% 5.45/5.76 thf(fact_5783_fact__less__mono__nat,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.76 => ( ( ord_less_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_less_mono_nat
% 5.45/5.76 thf(fact_5784_fact__ge__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_zero
% 5.45/5.76 thf(fact_5785_fact__ge__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_zero
% 5.45/5.76 thf(fact_5786_fact__ge__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_zero
% 5.45/5.76 thf(fact_5787_fact__ge__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_zero
% 5.45/5.76 thf(fact_5788_fact__not__neg,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ~ ( ord_le6747313008572928689nteger @ ( semiri3624122377584611663nteger @ N2 ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.76
% 5.45/5.76 % fact_not_neg
% 5.45/5.76 thf(fact_5789_fact__not__neg,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 5.45/5.76
% 5.45/5.76 % fact_not_neg
% 5.45/5.76 thf(fact_5790_fact__not__neg,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.45/5.76
% 5.45/5.76 % fact_not_neg
% 5.45/5.76 thf(fact_5791_fact__not__neg,axiom,
% 5.45/5.76 ! [N2: nat] :
% 5.45/5.76 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.45/5.76
% 5.45/5.76 % fact_not_neg
% 5.45/5.76 thf(fact_5792_fact__gt__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_gt_zero
% 5.45/5.76 thf(fact_5793_fact__gt__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_gt_zero
% 5.45/5.76 thf(fact_5794_fact__gt__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_gt_zero
% 5.45/5.76 thf(fact_5795_fact__gt__zero,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_gt_zero
% 5.45/5.76 thf(fact_5796_fact__ge__1,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_1
% 5.45/5.76 thf(fact_5797_fact__ge__1,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_1
% 5.45/5.76 thf(fact_5798_fact__ge__1,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_1
% 5.45/5.76 thf(fact_5799_fact__ge__1,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_1
% 5.45/5.76 thf(fact_5800_fact__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mono
% 5.45/5.76 thf(fact_5801_fact__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mono
% 5.45/5.76 thf(fact_5802_fact__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mono
% 5.45/5.76 thf(fact_5803_gbinomial__pochhammer,axiom,
% 5.45/5.76 ( gbinomial_rat
% 5.45/5.76 = ( ^ [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 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_pochhammer
% 5.45/5.76 thf(fact_5804_gbinomial__absorb__comp,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.45/5.76 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_absorb_comp
% 5.45/5.76 thf(fact_5805_gbinomial__mult__1,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.45/5.76 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_mult_1
% 5.45/5.76 thf(fact_5806_gbinomial__mult__1_H,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.45/5.76 = ( plus_plus_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ K ) @ ( gbinomial_rat @ A @ K ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_mult_1'
% 5.45/5.76 thf(fact_5807_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.45/5.76 ! [K: nat,A: rat] :
% 5.45/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.45/5.76 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_ge_n_over_k_pow_k
% 5.45/5.76 thf(fact_5808_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: assn,B: assn,C: assn,D2: assn] :
% 5.45/5.76 ( ( ord_less_set_assn @ ( set_or7959216805967363635t_assn @ A @ B ) @ ( set_or7959216805967363635t_assn @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_assn @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_assn @ C @ A )
% 5.45/5.76 & ( ord_less_eq_assn @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_assn @ C @ A )
% 5.45/5.76 | ( ord_less_assn @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_assn @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5809_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: set_int,B: set_int,C: set_int,D2: set_int] :
% 5.45/5.76 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.76 & ( ord_less_eq_set_int @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_set_int @ C @ A )
% 5.45/5.76 | ( ord_less_set_int @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_set_int @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5810_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.76 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.76 & ( ord_less_eq_rat @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_rat @ C @ A )
% 5.45/5.76 | ( ord_less_rat @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_rat @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5811_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.76 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_num @ C @ A )
% 5.45/5.76 & ( ord_less_eq_num @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_num @ C @ A )
% 5.45/5.76 | ( ord_less_num @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_num @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5812_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.76 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_int @ C @ A )
% 5.45/5.76 & ( ord_less_eq_int @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_int @ C @ A )
% 5.45/5.76 | ( ord_less_int @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_int @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5813_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.76 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.45/5.76 | ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.76 & ( ord_less_eq_nat @ B @ D2 )
% 5.45/5.76 & ( ( ord_less_nat @ C @ A )
% 5.45/5.76 | ( ord_less_nat @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_less_eq_nat @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5814_atLeastatMost__psubset__iff,axiom,
% 5.45/5.76 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.76 ( ( ord_le1307284697595431911nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or189985376899183464nteger @ C @ D2 ) )
% 5.45/5.76 = ( ( ~ ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.76 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.45/5.76 & ( ord_le3102999989581377725nteger @ B @ D2 )
% 5.45/5.76 & ( ( ord_le6747313008572928689nteger @ C @ A )
% 5.45/5.76 | ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) )
% 5.45/5.76 & ( ord_le3102999989581377725nteger @ C @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % atLeastatMost_psubset_iff
% 5.45/5.76 thf(fact_5815_fact__ge__Suc__0__nat,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_ge_Suc_0_nat
% 5.45/5.76 thf(fact_5816_fact__less__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.76 => ( ( ord_less_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_less_mono
% 5.45/5.76 thf(fact_5817_fact__less__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.76 => ( ( ord_less_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_less_mono
% 5.45/5.76 thf(fact_5818_fact__less__mono,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.76 => ( ( ord_less_nat @ M @ N2 )
% 5.45/5.76 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_less_mono
% 5.45/5.76 thf(fact_5819_fact__mod,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.45/5.76 = zero_zero_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mod
% 5.45/5.76 thf(fact_5820_fact__mod,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.45/5.76 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mod
% 5.45/5.76 thf(fact_5821_fact__mod,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ( modulo8411746178871703098atural @ ( semiri2447717529341329178atural @ N2 ) @ ( semiri2447717529341329178atural @ M ) )
% 5.45/5.76 = zero_z2226904508553997617atural ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mod
% 5.45/5.76 thf(fact_5822_fact__mod,axiom,
% 5.45/5.76 ! [M: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.76 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.45/5.76 = zero_zero_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_mod
% 5.45/5.76 thf(fact_5823_fact__le__power,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_le3102999989581377725nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri4939895301339042750nteger @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_le_power
% 5.45/5.76 thf(fact_5824_fact__le__power,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_le_power
% 5.45/5.76 thf(fact_5825_fact__le__power,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_le_power
% 5.45/5.76 thf(fact_5826_fact__le__power,axiom,
% 5.45/5.76 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_le_power
% 5.45/5.76 thf(fact_5827_Suc__times__gbinomial,axiom,
% 5.45/5.76 ! [K: nat,A: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.45/5.76 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Suc_times_gbinomial
% 5.45/5.76 thf(fact_5828_gbinomial__absorption,axiom,
% 5.45/5.76 ! [K: nat,A: rat] :
% 5.45/5.76 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.45/5.76 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_absorption
% 5.45/5.76 thf(fact_5829_gbinomial__trinomial__revision,axiom,
% 5.45/5.76 ! [K: nat,M: nat,A: rat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.76 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.45/5.76 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_trinomial_revision
% 5.45/5.76 thf(fact_5830_gbinomial__code,axiom,
% 5.45/5.76 ( gbinomial_rat
% 5.45/5.76 = ( ^ [A5: rat,K3: nat] :
% 5.45/5.76 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.45/5.76 @ ( divide_divide_rat
% 5.45/5.76 @ ( set_fo1949268297981939178at_rat
% 5.45/5.76 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.45/5.76 @ zero_zero_nat
% 5.45/5.76 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.45/5.76 @ one_one_rat )
% 5.45/5.76 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_code
% 5.45/5.76 thf(fact_5831_fact__div__fact__le__pow,axiom,
% 5.45/5.76 ! [R3: nat,N2: nat] :
% 5.45/5.76 ( ( ord_less_eq_nat @ R3 @ N2 )
% 5.45/5.76 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R3 ) ) ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % fact_div_fact_le_pow
% 5.45/5.76 thf(fact_5832_gbinomial__rec,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.45/5.76 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_rec
% 5.45/5.76 thf(fact_5833_gbinomial__factors,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.45/5.76 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_factors
% 5.45/5.76 thf(fact_5834_gbinomial__negated__upper,axiom,
% 5.45/5.76 ( gbinomial_rat
% 5.45/5.76 = ( ^ [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 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_negated_upper
% 5.45/5.76 thf(fact_5835_gbinomial__index__swap,axiom,
% 5.45/5.76 ! [K: nat,N2: nat] :
% 5.45/5.76 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 5.45/5.76 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_index_swap
% 5.45/5.76 thf(fact_5836_periodic__finite__ex,axiom,
% 5.45/5.76 ! [D2: int,P: int > $o] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D2 )
% 5.45/5.76 => ( ! [X3: int,K2: int] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 = ( P @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D2 ) ) ) )
% 5.45/5.76 => ( ( ? [X11: int] : ( P @ X11 ) )
% 5.45/5.76 = ( ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D2 ) )
% 5.45/5.76 & ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % periodic_finite_ex
% 5.45/5.76 thf(fact_5837_aset_I7_J,axiom,
% 5.45/5.76 ! [D3: int,A3: set_int,T5: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_int @ T5 @ X7 )
% 5.45/5.76 => ( ord_less_int @ T5 @ ( plus_plus_int @ X7 @ D3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(7)
% 5.45/5.76 thf(fact_5838_aset_I5_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ T5 @ A3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_int @ X7 @ T5 )
% 5.45/5.76 => ( ord_less_int @ ( plus_plus_int @ X7 @ D3 ) @ T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(5)
% 5.45/5.76 thf(fact_5839_aset_I4_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ T5 @ A3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( X7 != T5 )
% 5.45/5.76 => ( ( plus_plus_int @ X7 @ D3 )
% 5.45/5.76 != T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(4)
% 5.45/5.76 thf(fact_5840_aset_I3_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ ( plus_plus_int @ T5 @ one_one_int ) @ A3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( X7 = T5 )
% 5.45/5.76 => ( ( plus_plus_int @ X7 @ D3 )
% 5.45/5.76 = T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(3)
% 5.45/5.76 thf(fact_5841_bset_I7_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,B3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ T5 @ B3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_int @ T5 @ X7 )
% 5.45/5.76 => ( ord_less_int @ T5 @ ( minus_minus_int @ X7 @ D3 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(7)
% 5.45/5.76 thf(fact_5842_bset_I5_J,axiom,
% 5.45/5.76 ! [D3: int,B3: set_int,T5: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_int @ X7 @ T5 )
% 5.45/5.76 => ( ord_less_int @ ( minus_minus_int @ X7 @ D3 ) @ T5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(5)
% 5.45/5.76 thf(fact_5843_bset_I4_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,B3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ T5 @ B3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( X7 != T5 )
% 5.45/5.76 => ( ( minus_minus_int @ X7 @ D3 )
% 5.45/5.76 != T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(4)
% 5.45/5.76 thf(fact_5844_bset_I3_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,B3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ ( minus_minus_int @ T5 @ one_one_int ) @ B3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( X7 = T5 )
% 5.45/5.76 => ( ( minus_minus_int @ X7 @ D3 )
% 5.45/5.76 = T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(3)
% 5.45/5.76 thf(fact_5845_gbinomial__minus,axiom,
% 5.45/5.76 ! [A: rat,K: nat] :
% 5.45/5.76 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.45/5.76 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_minus
% 5.45/5.76 thf(fact_5846_gbinomial__reduce__nat,axiom,
% 5.45/5.76 ! [K: nat,A: rat] :
% 5.45/5.76 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.76 => ( ( gbinomial_rat @ A @ K )
% 5.45/5.76 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % gbinomial_reduce_nat
% 5.45/5.76 thf(fact_5847_aset_I8_J,axiom,
% 5.45/5.76 ! [D3: int,A3: set_int,T5: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_eq_int @ T5 @ X7 )
% 5.45/5.76 => ( ord_less_eq_int @ T5 @ ( plus_plus_int @ X7 @ D3 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(8)
% 5.45/5.76 thf(fact_5848_aset_I6_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ ( plus_plus_int @ T5 @ one_one_int ) @ A3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ A3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_eq_int @ X7 @ T5 )
% 5.45/5.76 => ( ord_less_eq_int @ ( plus_plus_int @ X7 @ D3 ) @ T5 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % aset(6)
% 5.45/5.76 thf(fact_5849_bset_I8_J,axiom,
% 5.45/5.76 ! [D3: int,T5: int,B3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ( member_int @ ( minus_minus_int @ T5 @ one_one_int ) @ B3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_eq_int @ T5 @ X7 )
% 5.45/5.76 => ( ord_less_eq_int @ T5 @ ( minus_minus_int @ X7 @ D3 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(8)
% 5.45/5.76 thf(fact_5850_bset_I6_J,axiom,
% 5.45/5.76 ! [D3: int,B3: set_int,T5: int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ! [Xa3: int] :
% 5.45/5.76 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb3: int] :
% 5.45/5.76 ( ( member_int @ Xb3 @ B3 )
% 5.45/5.76 => ( X7
% 5.45/5.76 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.45/5.76 => ( ( ord_less_eq_int @ X7 @ T5 )
% 5.45/5.76 => ( ord_less_eq_int @ ( minus_minus_int @ X7 @ D3 ) @ T5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bset(6)
% 5.45/5.76 thf(fact_5851_cppi,axiom,
% 5.45/5.76 ! [D3: int,P: int > $o,P6: int > $o,A3: set_int] :
% 5.45/5.76 ( ( ord_less_int @ zero_zero_int @ D3 )
% 5.45/5.76 => ( ? [Z5: int] :
% 5.45/5.76 ! [X3: int] :
% 5.45/5.76 ( ( ord_less_int @ Z5 @ X3 )
% 5.45/5.76 => ( ( P @ X3 )
% 5.45/5.76 = ( P6 @ X3 ) ) )
% 5.45/5.76 => ( ! [X3: int] :
% 5.45/5.76 ( ! [Xa2: int] :
% 5.45/5.76 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 => ! [Xb2: int] :
% 5.45/5.76 ( ( member_int @ Xb2 @ A3 )
% 5.45/5.76 => ( X3
% 5.45/5.76 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.45/5.76 => ( ( P @ X3 )
% 5.45/5.76 => ( P @ ( plus_plus_int @ X3 @ D3 ) ) ) )
% 5.45/5.76 => ( ! [X3: int,K2: int] :
% 5.45/5.76 ( ( P6 @ X3 )
% 5.45/5.76 = ( P6 @ ( minus_minus_int @ X3 @ ( times_times_int @ K2 @ D3 ) ) ) )
% 5.45/5.76 => ( ( ? [X11: int] : ( P @ X11 ) )
% 5.45/5.76 = ( ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 & ( P6 @ X4 ) )
% 5.45/5.76 | ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( set_or1266510415728281911st_int @ one_one_int @ D3 ) )
% 5.45/5.76 & ? [Y4: int] :
% 5.45/5.76 ( ( member_int @ Y4 @ A3 )
% 5.45/5.76 & ( P @ ( minus_minus_int @ Y4 @ X4 ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % cppi
% 5.45/5.76 thf(fact_5852_slice__nth,axiom,
% 5.45/5.76 ! [From: nat,To: nat,Xs: list_int,I2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ From @ To )
% 5.45/5.76 => ( ( ord_less_eq_nat @ To @ ( size_size_list_int @ Xs ) )
% 5.45/5.76 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 5.45/5.76 => ( ( nth_int @ ( slice_int @ From @ To @ Xs ) @ I2 )
% 5.45/5.76 = ( nth_int @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % slice_nth
% 5.45/5.76 thf(fact_5853_slice__nth,axiom,
% 5.45/5.76 ! [From: nat,To: nat,Xs: list_nat,I2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ From @ To )
% 5.45/5.76 => ( ( ord_less_eq_nat @ To @ ( size_size_list_nat @ Xs ) )
% 5.45/5.76 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 5.45/5.76 => ( ( nth_nat @ ( slice_nat @ From @ To @ Xs ) @ I2 )
% 5.45/5.76 = ( nth_nat @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % slice_nth
% 5.45/5.76 thf(fact_5854_slice__nth,axiom,
% 5.45/5.76 ! [From: nat,To: nat,Xs: list_o,I2: nat] :
% 5.45/5.76 ( ( ord_less_nat @ From @ To )
% 5.45/5.76 => ( ( ord_less_eq_nat @ To @ ( size_size_list_o @ Xs ) )
% 5.45/5.76 => ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ To @ From ) )
% 5.45/5.76 => ( ( nth_o @ ( slice_o @ From @ To @ Xs ) @ I2 )
% 5.45/5.76 = ( nth_o @ Xs @ ( plus_plus_nat @ From @ I2 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % slice_nth
% 5.45/5.76 thf(fact_5855_image__affinity__atLeastAtMost__div__diff,axiom,
% 5.45/5.76 ! [A: rat,B: rat,M: rat,C: rat] :
% 5.45/5.76 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = bot_bot_set_rat ) )
% 5.45/5.76 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 != bot_bot_set_rat )
% 5.45/5.76 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M ) @ C ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( divide_divide_rat @ B @ M ) @ C ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ M ) @ C ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_affinity_atLeastAtMost_div_diff
% 5.45/5.76 thf(fact_5856_image__affinity__atLeastAtMost__div,axiom,
% 5.45/5.76 ! [A: rat,B: rat,M: rat,C: rat] :
% 5.45/5.76 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = bot_bot_set_rat ) )
% 5.45/5.76 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 != bot_bot_set_rat )
% 5.45/5.76 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M ) @ C ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( divide_divide_rat @ X4 @ M ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( divide_divide_rat @ B @ M ) @ C ) @ ( plus_plus_rat @ ( divide_divide_rat @ A @ M ) @ C ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_affinity_atLeastAtMost_div
% 5.45/5.76 thf(fact_5857_image__affinity__atLeastAtMost__diff,axiom,
% 5.45/5.76 ! [A: rat,B: rat,M: rat,C: rat] :
% 5.45/5.76 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = bot_bot_set_rat ) )
% 5.45/5.76 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 != bot_bot_set_rat )
% 5.45/5.76 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M @ A ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M @ B ) @ C ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( minus_minus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ ( times_times_rat @ M @ B ) @ C ) @ ( minus_minus_rat @ ( times_times_rat @ M @ A ) @ C ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_affinity_atLeastAtMost_diff
% 5.45/5.76 thf(fact_5858_image__affinity__atLeastAtMost,axiom,
% 5.45/5.76 ! [A: rat,B: rat,M: rat,C: rat] :
% 5.45/5.76 ( ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 = bot_bot_set_rat )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = bot_bot_set_rat ) )
% 5.45/5.76 & ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.45/5.76 != bot_bot_set_rat )
% 5.45/5.76 => ( ( ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M @ A ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M @ B ) @ C ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_rat @ zero_zero_rat @ M )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( plus_plus_rat @ ( times_times_rat @ M @ X4 ) @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ ( times_times_rat @ M @ B ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ M @ A ) @ C ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_affinity_atLeastAtMost
% 5.45/5.76 thf(fact_5859_image__mult__atLeastAtMost__if_H,axiom,
% 5.45/5.76 ! [X: rat,Y: rat,C: rat] :
% 5.45/5.76 ( ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.76 => ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( times_times_rat @ X4 @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( times_times_rat @ X @ C ) @ ( times_times_rat @ Y @ C ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( times_times_rat @ X4 @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( times_times_rat @ Y @ C ) @ ( times_times_rat @ X @ C ) ) ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [X4: rat] : ( times_times_rat @ X4 @ C )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.76 = bot_bot_set_rat ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mult_atLeastAtMost_if'
% 5.45/5.76 thf(fact_5860_prod__decode__aux_Oelims,axiom,
% 5.45/5.76 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.45/5.76 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.45/5.76 = Y )
% 5.45/5.76 => ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.45/5.76 => ( Y
% 5.45/5.76 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.45/5.76 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.45/5.76 => ( Y
% 5.45/5.76 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % prod_decode_aux.elims
% 5.45/5.76 thf(fact_5861_image__eqI,axiom,
% 5.45/5.76 ! [B: $o,F: $o > $o,X: $o,A3: set_o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_o @ B @ ( image_o_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5862_image__eqI,axiom,
% 5.45/5.76 ! [B: nat,F: $o > nat,X: $o,A3: set_o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_nat @ B @ ( image_o_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5863_image__eqI,axiom,
% 5.45/5.76 ! [B: int,F: $o > int,X: $o,A3: set_o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_int @ B @ ( image_o_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5864_image__eqI,axiom,
% 5.45/5.76 ! [B: $o,F: nat > $o,X: nat,A3: set_nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_o @ B @ ( image_nat_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5865_image__eqI,axiom,
% 5.45/5.76 ! [B: nat,F: nat > nat,X: nat,A3: set_nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_nat @ B @ ( image_nat_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5866_image__eqI,axiom,
% 5.45/5.76 ! [B: int,F: nat > int,X: nat,A3: set_nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_int @ B @ ( image_nat_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5867_image__eqI,axiom,
% 5.45/5.76 ! [B: $o,F: int > $o,X: int,A3: set_int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_o @ B @ ( image_int_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5868_image__eqI,axiom,
% 5.45/5.76 ! [B: nat,F: int > nat,X: int,A3: set_int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_nat @ B @ ( image_int_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5869_image__eqI,axiom,
% 5.45/5.76 ! [B: int,F: int > int,X: int,A3: set_int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_int @ B @ ( image_int_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5870_image__eqI,axiom,
% 5.45/5.76 ! [B: set_nat,F: $o > set_nat,X: $o,A3: set_o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_set_nat @ B @ ( image_o_set_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_eqI
% 5.45/5.76 thf(fact_5871_image__ident,axiom,
% 5.45/5.76 ! [Y7: set_nat] :
% 5.45/5.76 ( ( image_nat_nat
% 5.45/5.76 @ ^ [X4: nat] : X4
% 5.45/5.76 @ Y7 )
% 5.45/5.76 = Y7 ) ).
% 5.45/5.76
% 5.45/5.76 % image_ident
% 5.45/5.76 thf(fact_5872_image__ident,axiom,
% 5.45/5.76 ! [Y7: set_int] :
% 5.45/5.76 ( ( image_int_int
% 5.45/5.76 @ ^ [X4: int] : X4
% 5.45/5.76 @ Y7 )
% 5.45/5.76 = Y7 ) ).
% 5.45/5.76
% 5.45/5.76 % image_ident
% 5.45/5.76 thf(fact_5873_image__empty,axiom,
% 5.45/5.76 ! [F: $o > $o] :
% 5.45/5.76 ( ( image_o_o @ F @ bot_bot_set_o )
% 5.45/5.76 = bot_bot_set_o ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5874_image__empty,axiom,
% 5.45/5.76 ! [F: $o > nat] :
% 5.45/5.76 ( ( image_o_nat @ F @ bot_bot_set_o )
% 5.45/5.76 = bot_bot_set_nat ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5875_image__empty,axiom,
% 5.45/5.76 ! [F: $o > int] :
% 5.45/5.76 ( ( image_o_int @ F @ bot_bot_set_o )
% 5.45/5.76 = bot_bot_set_int ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5876_image__empty,axiom,
% 5.45/5.76 ! [F: nat > $o] :
% 5.45/5.76 ( ( image_nat_o @ F @ bot_bot_set_nat )
% 5.45/5.76 = bot_bot_set_o ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5877_image__empty,axiom,
% 5.45/5.76 ! [F: nat > nat] :
% 5.45/5.76 ( ( image_nat_nat @ F @ bot_bot_set_nat )
% 5.45/5.76 = bot_bot_set_nat ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5878_image__empty,axiom,
% 5.45/5.76 ! [F: nat > int] :
% 5.45/5.76 ( ( image_nat_int @ F @ bot_bot_set_nat )
% 5.45/5.76 = bot_bot_set_int ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5879_image__empty,axiom,
% 5.45/5.76 ! [F: int > $o] :
% 5.45/5.76 ( ( image_int_o @ F @ bot_bot_set_int )
% 5.45/5.76 = bot_bot_set_o ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5880_image__empty,axiom,
% 5.45/5.76 ! [F: int > nat] :
% 5.45/5.76 ( ( image_int_nat @ F @ bot_bot_set_int )
% 5.45/5.76 = bot_bot_set_nat ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5881_image__empty,axiom,
% 5.45/5.76 ! [F: int > int] :
% 5.45/5.76 ( ( image_int_int @ F @ bot_bot_set_int )
% 5.45/5.76 = bot_bot_set_int ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5882_image__empty,axiom,
% 5.45/5.76 ! [F: nat > set_nat] :
% 5.45/5.76 ( ( image_nat_set_nat @ F @ bot_bot_set_nat )
% 5.45/5.76 = bot_bot_set_set_nat ) ).
% 5.45/5.76
% 5.45/5.76 % image_empty
% 5.45/5.76 thf(fact_5883_empty__is__image,axiom,
% 5.45/5.76 ! [F: $o > $o,A3: set_o] :
% 5.45/5.76 ( ( bot_bot_set_o
% 5.45/5.76 = ( image_o_o @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5884_empty__is__image,axiom,
% 5.45/5.76 ! [F: nat > $o,A3: set_nat] :
% 5.45/5.76 ( ( bot_bot_set_o
% 5.45/5.76 = ( image_nat_o @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5885_empty__is__image,axiom,
% 5.45/5.76 ! [F: int > $o,A3: set_int] :
% 5.45/5.76 ( ( bot_bot_set_o
% 5.45/5.76 = ( image_int_o @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5886_empty__is__image,axiom,
% 5.45/5.76 ! [F: $o > nat,A3: set_o] :
% 5.45/5.76 ( ( bot_bot_set_nat
% 5.45/5.76 = ( image_o_nat @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5887_empty__is__image,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( bot_bot_set_nat
% 5.45/5.76 = ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5888_empty__is__image,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( bot_bot_set_nat
% 5.45/5.76 = ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5889_empty__is__image,axiom,
% 5.45/5.76 ! [F: $o > int,A3: set_o] :
% 5.45/5.76 ( ( bot_bot_set_int
% 5.45/5.76 = ( image_o_int @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5890_empty__is__image,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( bot_bot_set_int
% 5.45/5.76 = ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5891_empty__is__image,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int] :
% 5.45/5.76 ( ( bot_bot_set_int
% 5.45/5.76 = ( image_int_int @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5892_empty__is__image,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( bot_bot_set_set_nat
% 5.45/5.76 = ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % empty_is_image
% 5.45/5.76 thf(fact_5893_image__is__empty,axiom,
% 5.45/5.76 ! [F: $o > $o,A3: set_o] :
% 5.45/5.76 ( ( ( image_o_o @ F @ A3 )
% 5.45/5.76 = bot_bot_set_o )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5894_image__is__empty,axiom,
% 5.45/5.76 ! [F: nat > $o,A3: set_nat] :
% 5.45/5.76 ( ( ( image_nat_o @ F @ A3 )
% 5.45/5.76 = bot_bot_set_o )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5895_image__is__empty,axiom,
% 5.45/5.76 ! [F: int > $o,A3: set_int] :
% 5.45/5.76 ( ( ( image_int_o @ F @ A3 )
% 5.45/5.76 = bot_bot_set_o )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5896_image__is__empty,axiom,
% 5.45/5.76 ! [F: $o > nat,A3: set_o] :
% 5.45/5.76 ( ( ( image_o_nat @ F @ A3 )
% 5.45/5.76 = bot_bot_set_nat )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5897_image__is__empty,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( ( image_nat_nat @ F @ A3 )
% 5.45/5.76 = bot_bot_set_nat )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5898_image__is__empty,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( ( image_int_nat @ F @ A3 )
% 5.45/5.76 = bot_bot_set_nat )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5899_image__is__empty,axiom,
% 5.45/5.76 ! [F: $o > int,A3: set_o] :
% 5.45/5.76 ( ( ( image_o_int @ F @ A3 )
% 5.45/5.76 = bot_bot_set_int )
% 5.45/5.76 = ( A3 = bot_bot_set_o ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5900_image__is__empty,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( ( image_nat_int @ F @ A3 )
% 5.45/5.76 = bot_bot_set_int )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5901_image__is__empty,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int] :
% 5.45/5.76 ( ( ( image_int_int @ F @ A3 )
% 5.45/5.76 = bot_bot_set_int )
% 5.45/5.76 = ( A3 = bot_bot_set_int ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5902_image__is__empty,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( ( image_nat_set_nat @ F @ A3 )
% 5.45/5.76 = bot_bot_set_set_nat )
% 5.45/5.76 = ( A3 = bot_bot_set_nat ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_is_empty
% 5.45/5.76 thf(fact_5903_image__add__0,axiom,
% 5.45/5.76 ! [S: set_Code_integer] :
% 5.45/5.76 ( ( image_4470545334726330049nteger @ ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger ) @ S )
% 5.45/5.76 = S ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_0
% 5.45/5.76 thf(fact_5904_image__add__0,axiom,
% 5.45/5.76 ! [S: set_mu2057375006010111271at_nat] :
% 5.45/5.76 ( ( image_2516384619306764229at_nat @ ( plus_p7104986032573967614at_nat @ zero_z1048942125864253310at_nat ) @ S )
% 5.45/5.76 = S ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_0
% 5.45/5.76 thf(fact_5905_image__add__0,axiom,
% 5.45/5.76 ! [S: set_rat] :
% 5.45/5.76 ( ( image_rat_rat @ ( plus_plus_rat @ zero_zero_rat ) @ S )
% 5.45/5.76 = S ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_0
% 5.45/5.76 thf(fact_5906_image__add__0,axiom,
% 5.45/5.76 ! [S: set_nat] :
% 5.45/5.76 ( ( image_nat_nat @ ( plus_plus_nat @ zero_zero_nat ) @ S )
% 5.45/5.76 = S ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_0
% 5.45/5.76 thf(fact_5907_image__add__0,axiom,
% 5.45/5.76 ! [S: set_int] :
% 5.45/5.76 ( ( image_int_int @ ( plus_plus_int @ zero_zero_int ) @ S )
% 5.45/5.76 = S ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_0
% 5.45/5.76 thf(fact_5908_image__add__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [K: rat,I2: rat,J: rat] :
% 5.45/5.76 ( ( image_rat_rat
% 5.45/5.76 @ ^ [N: rat] : ( plus_plus_rat @ N @ K )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ I2 @ J ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_atLeastAtMost'
% 5.45/5.76 thf(fact_5909_image__add__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [K: int,I2: int,J: int] :
% 5.45/5.76 ( ( image_int_int
% 5.45/5.76 @ ^ [N: int] : ( plus_plus_int @ N @ K )
% 5.45/5.76 @ ( set_or1266510415728281911st_int @ I2 @ J ) )
% 5.45/5.76 = ( set_or1266510415728281911st_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_atLeastAtMost'
% 5.45/5.76 thf(fact_5910_image__add__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [K: nat,I2: nat,J: nat] :
% 5.45/5.76 ( ( image_nat_nat
% 5.45/5.76 @ ^ [N: nat] : ( plus_plus_nat @ N @ K )
% 5.45/5.76 @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.45/5.76 = ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_atLeastAtMost'
% 5.45/5.76 thf(fact_5911_image__add__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [K: code_integer,I2: code_integer,J: code_integer] :
% 5.45/5.76 ( ( image_4470545334726330049nteger
% 5.45/5.76 @ ^ [N: code_integer] : ( plus_p5714425477246183910nteger @ N @ K )
% 5.45/5.76 @ ( set_or189985376899183464nteger @ I2 @ J ) )
% 5.45/5.76 = ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_add_atLeastAtMost'
% 5.45/5.76 thf(fact_5912_image__minus__const__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [D2: rat,A: rat,B: rat] :
% 5.45/5.76 ( ( image_rat_rat
% 5.45/5.76 @ ^ [T3: rat] : ( minus_minus_rat @ T3 @ D2 )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( minus_minus_rat @ A @ D2 ) @ ( minus_minus_rat @ B @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_minus_const_atLeastAtMost'
% 5.45/5.76 thf(fact_5913_image__minus__const__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [D2: int,A: int,B: int] :
% 5.45/5.76 ( ( image_int_int
% 5.45/5.76 @ ^ [T3: int] : ( minus_minus_int @ T3 @ D2 )
% 5.45/5.76 @ ( set_or1266510415728281911st_int @ A @ B ) )
% 5.45/5.76 = ( set_or1266510415728281911st_int @ ( minus_minus_int @ A @ D2 ) @ ( minus_minus_int @ B @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_minus_const_atLeastAtMost'
% 5.45/5.76 thf(fact_5914_image__minus__const__atLeastAtMost_H,axiom,
% 5.45/5.76 ! [D2: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.76 ( ( image_4470545334726330049nteger
% 5.45/5.76 @ ^ [T3: code_integer] : ( minus_8373710615458151222nteger @ T3 @ D2 )
% 5.45/5.76 @ ( set_or189985376899183464nteger @ A @ B ) )
% 5.45/5.76 = ( set_or189985376899183464nteger @ ( minus_8373710615458151222nteger @ A @ D2 ) @ ( minus_8373710615458151222nteger @ B @ D2 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_minus_const_atLeastAtMost'
% 5.45/5.76 thf(fact_5915_if__image__distrib,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > int,G: int > int,S: set_int] :
% 5.45/5.76 ( ( image_int_int
% 5.45/5.76 @ ^ [X4: int] : ( if_int @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ S @ ( collect_int @ P ) ) )
% 5.45/5.76 @ ( image_int_int @ G
% 5.45/5.76 @ ( inf_inf_set_int @ S
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5916_if__image__distrib,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > int,G: nat > int,S: set_nat] :
% 5.45/5.76 ( ( image_nat_int
% 5.45/5.76 @ ^ [X4: nat] : ( if_int @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ S @ ( collect_nat @ P ) ) )
% 5.45/5.76 @ ( image_nat_int @ G
% 5.45/5.76 @ ( inf_inf_set_nat @ S
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5917_if__image__distrib,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > nat,G: int > nat,S: set_int] :
% 5.45/5.76 ( ( image_int_nat
% 5.45/5.76 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ S @ ( collect_int @ P ) ) )
% 5.45/5.76 @ ( image_int_nat @ G
% 5.45/5.76 @ ( inf_inf_set_int @ S
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5918_if__image__distrib,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > nat,G: nat > nat,S: set_nat] :
% 5.45/5.76 ( ( image_nat_nat
% 5.45/5.76 @ ^ [X4: nat] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ S @ ( collect_nat @ P ) ) )
% 5.45/5.76 @ ( image_nat_nat @ G
% 5.45/5.76 @ ( inf_inf_set_nat @ S
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5919_if__image__distrib,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > set_nat,G: nat > set_nat,S: set_nat] :
% 5.45/5.76 ( ( image_nat_set_nat
% 5.45/5.76 @ ^ [X4: nat] : ( if_set_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_set_nat @ ( image_nat_set_nat @ F @ ( inf_inf_set_nat @ S @ ( collect_nat @ P ) ) )
% 5.45/5.76 @ ( image_nat_set_nat @ G
% 5.45/5.76 @ ( inf_inf_set_nat @ S
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5920_if__image__distrib,axiom,
% 5.45/5.76 ! [P: list_nat > $o,F: list_nat > nat,G: list_nat > nat,S: set_list_nat] :
% 5.45/5.76 ( ( image_list_nat_nat
% 5.45/5.76 @ ^ [X4: list_nat] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_list_nat_nat @ F @ ( inf_inf_set_list_nat @ S @ ( collect_list_nat @ P ) ) )
% 5.45/5.76 @ ( image_list_nat_nat @ G
% 5.45/5.76 @ ( inf_inf_set_list_nat @ S
% 5.45/5.76 @ ( collect_list_nat
% 5.45/5.76 @ ^ [X4: list_nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5921_if__image__distrib,axiom,
% 5.45/5.76 ! [P: set_nat > $o,F: set_nat > nat,G: set_nat > nat,S: set_set_nat] :
% 5.45/5.76 ( ( image_set_nat_nat
% 5.45/5.76 @ ^ [X4: set_nat] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_set_nat_nat @ F @ ( inf_inf_set_set_nat @ S @ ( collect_set_nat @ P ) ) )
% 5.45/5.76 @ ( image_set_nat_nat @ G
% 5.45/5.76 @ ( inf_inf_set_set_nat @ S
% 5.45/5.76 @ ( collect_set_nat
% 5.45/5.76 @ ^ [X4: set_nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5922_if__image__distrib,axiom,
% 5.45/5.76 ! [P: product_prod_int_int > $o,F: product_prod_int_int > nat,G: product_prod_int_int > nat,S: set_Pr958786334691620121nt_int] :
% 5.45/5.76 ( ( image_5044651549707136836nt_nat
% 5.45/5.76 @ ^ [X4: product_prod_int_int] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_5044651549707136836nt_nat @ F @ ( inf_in2269163501485487111nt_int @ S @ ( collec213857154873943460nt_int @ P ) ) )
% 5.45/5.76 @ ( image_5044651549707136836nt_nat @ G
% 5.45/5.76 @ ( inf_in2269163501485487111nt_int @ S
% 5.45/5.76 @ ( collec213857154873943460nt_int
% 5.45/5.76 @ ^ [X4: product_prod_int_int] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5923_if__image__distrib,axiom,
% 5.45/5.76 ! [P: product_prod_nat_nat > $o,F: product_prod_nat_nat > nat,G: product_prod_nat_nat > nat,S: set_Pr1261947904930325089at_nat] :
% 5.45/5.76 ( ( image_2486076414777270412at_nat
% 5.45/5.76 @ ^ [X4: product_prod_nat_nat] : ( if_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_2486076414777270412at_nat @ F @ ( inf_in2572325071724192079at_nat @ S @ ( collec3392354462482085612at_nat @ P ) ) )
% 5.45/5.76 @ ( image_2486076414777270412at_nat @ G
% 5.45/5.76 @ ( inf_in2572325071724192079at_nat @ S
% 5.45/5.76 @ ( collec3392354462482085612at_nat
% 5.45/5.76 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5924_if__image__distrib,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > produc859450856879609959at_nat,G: int > produc859450856879609959at_nat,S: set_int] :
% 5.45/5.76 ( ( image_6031046145702598900at_nat
% 5.45/5.76 @ ^ [X4: int] : ( if_Pro4507677147265585453at_nat @ ( P @ X4 ) @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.76 @ S )
% 5.45/5.76 = ( sup_su718114333110466843at_nat @ ( image_6031046145702598900at_nat @ F @ ( inf_inf_set_int @ S @ ( collect_int @ P ) ) )
% 5.45/5.76 @ ( image_6031046145702598900at_nat @ G
% 5.45/5.76 @ ( inf_inf_set_int @ S
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ~ ( P @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % if_image_distrib
% 5.45/5.76 thf(fact_5925_image__mult__atLeastAtMost,axiom,
% 5.45/5.76 ! [D2: rat,A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 5.45/5.76 => ( ( image_rat_rat @ ( times_times_rat @ D2 ) @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( times_times_rat @ D2 @ A ) @ ( times_times_rat @ D2 @ B ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mult_atLeastAtMost
% 5.45/5.76 thf(fact_5926_image__divide__atLeastAtMost,axiom,
% 5.45/5.76 ! [D2: rat,A: rat,B: rat] :
% 5.45/5.76 ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 5.45/5.76 => ( ( image_rat_rat
% 5.45/5.76 @ ^ [C4: rat] : ( divide_divide_rat @ C4 @ D2 )
% 5.45/5.76 @ ( set_or633870826150836451st_rat @ A @ B ) )
% 5.45/5.76 = ( set_or633870826150836451st_rat @ ( divide_divide_rat @ A @ D2 ) @ ( divide_divide_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_divide_atLeastAtMost
% 5.45/5.76 thf(fact_5927_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,B: $o,F: $o > $o] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_o @ B @ ( image_o_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5928_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,B: nat,F: $o > nat] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_nat @ B @ ( image_o_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5929_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,B: int,F: $o > int] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_int @ B @ ( image_o_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5930_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,B: $o,F: nat > $o] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_o @ B @ ( image_nat_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5931_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,B: nat,F: nat > nat] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_nat @ B @ ( image_nat_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5932_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,B: int,F: nat > int] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_int @ B @ ( image_nat_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5933_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,B: $o,F: int > $o] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_o @ B @ ( image_int_o @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5934_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,B: nat,F: int > nat] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_nat @ B @ ( image_int_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5935_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,B: int,F: int > int] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_int @ B @ ( image_int_int @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5936_rev__image__eqI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,B: set_nat,F: $o > set_nat] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( ( B
% 5.45/5.76 = ( F @ X ) )
% 5.45/5.76 => ( member_set_nat @ B @ ( image_o_set_nat @ F @ A3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % rev_image_eqI
% 5.45/5.76 thf(fact_5937_ball__imageD,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat,P: set_nat > $o] :
% 5.45/5.76 ( ! [X3: set_nat] :
% 5.45/5.76 ( ( member_set_nat @ X3 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 => ( P @ X3 ) )
% 5.45/5.76 => ! [X7: nat] :
% 5.45/5.76 ( ( member_nat @ X7 @ A3 )
% 5.45/5.76 => ( P @ ( F @ X7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ball_imageD
% 5.45/5.76 thf(fact_5938_ball__imageD,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,P: nat > $o] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 => ( P @ X3 ) )
% 5.45/5.76 => ! [X7: nat] :
% 5.45/5.76 ( ( member_nat @ X7 @ A3 )
% 5.45/5.76 => ( P @ ( F @ X7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ball_imageD
% 5.45/5.76 thf(fact_5939_ball__imageD,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat,P: int > $o] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 => ( P @ X3 ) )
% 5.45/5.76 => ! [X7: nat] :
% 5.45/5.76 ( ( member_nat @ X7 @ A3 )
% 5.45/5.76 => ( P @ ( F @ X7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ball_imageD
% 5.45/5.76 thf(fact_5940_ball__imageD,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,P: nat > $o] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 => ( P @ X3 ) )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ( member_int @ X7 @ A3 )
% 5.45/5.76 => ( P @ ( F @ X7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ball_imageD
% 5.45/5.76 thf(fact_5941_ball__imageD,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int,P: int > $o] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 => ( P @ X3 ) )
% 5.45/5.76 => ! [X7: int] :
% 5.45/5.76 ( ( member_int @ X7 @ A3 )
% 5.45/5.76 => ( P @ ( F @ X7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % ball_imageD
% 5.45/5.76 thf(fact_5942_image__cong,axiom,
% 5.45/5.76 ! [M6: set_nat,N7: set_nat,F: nat > set_nat,G: nat > set_nat] :
% 5.45/5.76 ( ( M6 = N7 )
% 5.45/5.76 => ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ N7 )
% 5.45/5.76 => ( ( F @ X3 )
% 5.45/5.76 = ( G @ X3 ) ) )
% 5.45/5.76 => ( ( image_nat_set_nat @ F @ M6 )
% 5.45/5.76 = ( image_nat_set_nat @ G @ N7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_cong
% 5.45/5.76 thf(fact_5943_image__cong,axiom,
% 5.45/5.76 ! [M6: set_nat,N7: set_nat,F: nat > nat,G: nat > nat] :
% 5.45/5.76 ( ( M6 = N7 )
% 5.45/5.76 => ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ N7 )
% 5.45/5.76 => ( ( F @ X3 )
% 5.45/5.76 = ( G @ X3 ) ) )
% 5.45/5.76 => ( ( image_nat_nat @ F @ M6 )
% 5.45/5.76 = ( image_nat_nat @ G @ N7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_cong
% 5.45/5.76 thf(fact_5944_image__cong,axiom,
% 5.45/5.76 ! [M6: set_nat,N7: set_nat,F: nat > int,G: nat > int] :
% 5.45/5.76 ( ( M6 = N7 )
% 5.45/5.76 => ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ N7 )
% 5.45/5.76 => ( ( F @ X3 )
% 5.45/5.76 = ( G @ X3 ) ) )
% 5.45/5.76 => ( ( image_nat_int @ F @ M6 )
% 5.45/5.76 = ( image_nat_int @ G @ N7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_cong
% 5.45/5.76 thf(fact_5945_image__cong,axiom,
% 5.45/5.76 ! [M6: set_int,N7: set_int,F: int > nat,G: int > nat] :
% 5.45/5.76 ( ( M6 = N7 )
% 5.45/5.76 => ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ N7 )
% 5.45/5.76 => ( ( F @ X3 )
% 5.45/5.76 = ( G @ X3 ) ) )
% 5.45/5.76 => ( ( image_int_nat @ F @ M6 )
% 5.45/5.76 = ( image_int_nat @ G @ N7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_cong
% 5.45/5.76 thf(fact_5946_image__cong,axiom,
% 5.45/5.76 ! [M6: set_int,N7: set_int,F: int > int,G: int > int] :
% 5.45/5.76 ( ( M6 = N7 )
% 5.45/5.76 => ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ N7 )
% 5.45/5.76 => ( ( F @ X3 )
% 5.45/5.76 = ( G @ X3 ) ) )
% 5.45/5.76 => ( ( image_int_int @ F @ M6 )
% 5.45/5.76 = ( image_int_int @ G @ N7 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_cong
% 5.45/5.76 thf(fact_5947_bex__imageD,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat,P: set_nat > $o] :
% 5.45/5.76 ( ? [X7: set_nat] :
% 5.45/5.76 ( ( member_set_nat @ X7 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X7 ) )
% 5.45/5.76 => ? [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bex_imageD
% 5.45/5.76 thf(fact_5948_bex__imageD,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,P: nat > $o] :
% 5.45/5.76 ( ? [X7: nat] :
% 5.45/5.76 ( ( member_nat @ X7 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X7 ) )
% 5.45/5.76 => ? [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bex_imageD
% 5.45/5.76 thf(fact_5949_bex__imageD,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat,P: int > $o] :
% 5.45/5.76 ( ? [X7: int] :
% 5.45/5.76 ( ( member_int @ X7 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 & ( P @ X7 ) )
% 5.45/5.76 => ? [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bex_imageD
% 5.45/5.76 thf(fact_5950_bex__imageD,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,P: nat > $o] :
% 5.45/5.76 ( ? [X7: nat] :
% 5.45/5.76 ( ( member_nat @ X7 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X7 ) )
% 5.45/5.76 => ? [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bex_imageD
% 5.45/5.76 thf(fact_5951_bex__imageD,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int,P: int > $o] :
% 5.45/5.76 ( ? [X7: int] :
% 5.45/5.76 ( ( member_int @ X7 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 & ( P @ X7 ) )
% 5.45/5.76 => ? [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % bex_imageD
% 5.45/5.76 thf(fact_5952_image__iff,axiom,
% 5.45/5.76 ! [Z: set_nat,F: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( member_set_nat @ Z @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( Z
% 5.45/5.76 = ( F @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_iff
% 5.45/5.76 thf(fact_5953_image__iff,axiom,
% 5.45/5.76 ! [Z: nat,F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( member_nat @ Z @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( Z
% 5.45/5.76 = ( F @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_iff
% 5.45/5.76 thf(fact_5954_image__iff,axiom,
% 5.45/5.76 ! [Z: nat,F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( member_nat @ Z @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 & ( Z
% 5.45/5.76 = ( F @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_iff
% 5.45/5.76 thf(fact_5955_image__iff,axiom,
% 5.45/5.76 ! [Z: int,F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( member_int @ Z @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 = ( ? [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( Z
% 5.45/5.76 = ( F @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_iff
% 5.45/5.76 thf(fact_5956_image__iff,axiom,
% 5.45/5.76 ! [Z: int,F: int > int,A3: set_int] :
% 5.45/5.76 ( ( member_int @ Z @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 = ( ? [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 & ( Z
% 5.45/5.76 = ( F @ X4 ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_iff
% 5.45/5.76 thf(fact_5957_imageI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,F: $o > $o] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X ) @ ( image_o_o @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5958_imageI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,F: $o > nat] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X ) @ ( image_o_nat @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5959_imageI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,F: $o > int] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X ) @ ( image_o_int @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5960_imageI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,F: nat > $o] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X ) @ ( image_nat_o @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5961_imageI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,F: nat > nat] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X ) @ ( image_nat_nat @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5962_imageI,axiom,
% 5.45/5.76 ! [X: nat,A3: set_nat,F: nat > int] :
% 5.45/5.76 ( ( member_nat @ X @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X ) @ ( image_nat_int @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5963_imageI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,F: int > $o] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X ) @ ( image_int_o @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5964_imageI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,F: int > nat] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X ) @ ( image_int_nat @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5965_imageI,axiom,
% 5.45/5.76 ! [X: int,A3: set_int,F: int > int] :
% 5.45/5.76 ( ( member_int @ X @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X ) @ ( image_int_int @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5966_imageI,axiom,
% 5.45/5.76 ! [X: $o,A3: set_o,F: $o > set_nat] :
% 5.45/5.76 ( ( member_o @ X @ A3 )
% 5.45/5.76 => ( member_set_nat @ ( F @ X ) @ ( image_o_set_nat @ F @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageI
% 5.45/5.76 thf(fact_5967_imageE,axiom,
% 5.45/5.76 ! [B: $o,F: $o > $o,A3: set_o] :
% 5.45/5.76 ( ( member_o @ B @ ( image_o_o @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: $o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_o @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5968_imageE,axiom,
% 5.45/5.76 ! [B: $o,F: nat > $o,A3: set_nat] :
% 5.45/5.76 ( ( member_o @ B @ ( image_nat_o @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_nat @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5969_imageE,axiom,
% 5.45/5.76 ! [B: $o,F: int > $o,A3: set_int] :
% 5.45/5.76 ( ( member_o @ B @ ( image_int_o @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_int @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5970_imageE,axiom,
% 5.45/5.76 ! [B: nat,F: $o > nat,A3: set_o] :
% 5.45/5.76 ( ( member_nat @ B @ ( image_o_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: $o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_o @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5971_imageE,axiom,
% 5.45/5.76 ! [B: nat,F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( member_nat @ B @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_nat @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5972_imageE,axiom,
% 5.45/5.76 ! [B: nat,F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( member_nat @ B @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_int @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5973_imageE,axiom,
% 5.45/5.76 ! [B: int,F: $o > int,A3: set_o] :
% 5.45/5.76 ( ( member_int @ B @ ( image_o_int @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: $o] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_o @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5974_imageE,axiom,
% 5.45/5.76 ! [B: int,F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( member_int @ B @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_nat @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5975_imageE,axiom,
% 5.45/5.76 ! [B: int,F: int > int,A3: set_int] :
% 5.45/5.76 ( ( member_int @ B @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: int] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_int @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5976_imageE,axiom,
% 5.45/5.76 ! [B: $o,F: set_nat > $o,A3: set_set_nat] :
% 5.45/5.76 ( ( member_o @ B @ ( image_set_nat_o @ F @ A3 ) )
% 5.45/5.76 => ~ ! [X3: set_nat] :
% 5.45/5.76 ( ( B
% 5.45/5.76 = ( F @ X3 ) )
% 5.45/5.76 => ~ ( member_set_nat @ X3 @ A3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % imageE
% 5.45/5.76 thf(fact_5977_image__image,axiom,
% 5.45/5.76 ! [F: nat > nat,G: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( image_nat_nat @ F @ ( image_nat_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_nat
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5978_image__image,axiom,
% 5.45/5.76 ! [F: nat > nat,G: int > nat,A3: set_int] :
% 5.45/5.76 ( ( image_nat_nat @ F @ ( image_int_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_int_nat
% 5.45/5.76 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5979_image__image,axiom,
% 5.45/5.76 ! [F: nat > int,G: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( image_nat_int @ F @ ( image_nat_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_int
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5980_image__image,axiom,
% 5.45/5.76 ! [F: nat > int,G: int > nat,A3: set_int] :
% 5.45/5.76 ( ( image_nat_int @ F @ ( image_int_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_int_int
% 5.45/5.76 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5981_image__image,axiom,
% 5.45/5.76 ! [F: int > nat,G: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( image_int_nat @ F @ ( image_nat_int @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_nat
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5982_image__image,axiom,
% 5.45/5.76 ! [F: int > nat,G: int > int,A3: set_int] :
% 5.45/5.76 ( ( image_int_nat @ F @ ( image_int_int @ G @ A3 ) )
% 5.45/5.76 = ( image_int_nat
% 5.45/5.76 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5983_image__image,axiom,
% 5.45/5.76 ! [F: int > int,G: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( image_int_int @ F @ ( image_nat_int @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_int
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5984_image__image,axiom,
% 5.45/5.76 ! [F: int > int,G: int > int,A3: set_int] :
% 5.45/5.76 ( ( image_int_int @ F @ ( image_int_int @ G @ A3 ) )
% 5.45/5.76 = ( image_int_int
% 5.45/5.76 @ ^ [X4: int] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5985_image__image,axiom,
% 5.45/5.76 ! [F: set_nat > nat,G: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( image_set_nat_nat @ F @ ( image_nat_set_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_nat
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5986_image__image,axiom,
% 5.45/5.76 ! [F: set_nat > int,G: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( image_set_nat_int @ F @ ( image_nat_set_nat @ G @ A3 ) )
% 5.45/5.76 = ( image_nat_int
% 5.45/5.76 @ ^ [X4: nat] : ( F @ ( G @ X4 ) )
% 5.45/5.76 @ A3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_image
% 5.45/5.76 thf(fact_5987_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: $o > $o,A3: set_o,P: $o > $o] :
% 5.45/5.76 ( ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ ( image_o_o @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_o_o @ F
% 5.45/5.76 @ ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5988_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: nat > $o,A3: set_nat,P: $o > $o] :
% 5.45/5.76 ( ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ ( image_nat_o @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_nat_o @ F
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5989_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: int > $o,A3: set_int,P: $o > $o] :
% 5.45/5.76 ( ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ ( image_int_o @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_int_o @ F
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5990_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: $o > nat,A3: set_o,P: nat > $o] :
% 5.45/5.76 ( ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ ( image_o_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_o_nat @ F
% 5.45/5.76 @ ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5991_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,P: nat > $o] :
% 5.45/5.76 ( ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_nat_nat @ F
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5992_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,P: nat > $o] :
% 5.45/5.76 ( ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_int_nat @ F
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5993_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: $o > int,A3: set_o,P: int > $o] :
% 5.45/5.76 ( ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( image_o_int @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_o_int @ F
% 5.45/5.76 @ ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5994_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat,P: int > $o] :
% 5.45/5.76 ( ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_nat_int @ F
% 5.45/5.76 @ ( collect_nat
% 5.45/5.76 @ ^ [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5995_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int,P: int > $o] :
% 5.45/5.76 ( ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_int_int @ F
% 5.45/5.76 @ ( collect_int
% 5.45/5.76 @ ^ [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5996_Compr__image__eq,axiom,
% 5.45/5.76 ! [F: list_nat > $o,A3: set_list_nat,P: $o > $o] :
% 5.45/5.76 ( ( collect_o
% 5.45/5.76 @ ^ [X4: $o] :
% 5.45/5.76 ( ( member_o @ X4 @ ( image_list_nat_o @ F @ A3 ) )
% 5.45/5.76 & ( P @ X4 ) ) )
% 5.45/5.76 = ( image_list_nat_o @ F
% 5.45/5.76 @ ( collect_list_nat
% 5.45/5.76 @ ^ [X4: list_nat] :
% 5.45/5.76 ( ( member_list_nat @ X4 @ A3 )
% 5.45/5.76 & ( P @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Compr_image_eq
% 5.45/5.76 thf(fact_5997_prod__decode__aux_Ocases,axiom,
% 5.45/5.76 ! [X: product_prod_nat_nat] :
% 5.45/5.76 ~ ! [K2: nat,M5: nat] :
% 5.45/5.76 ( X
% 5.45/5.76 != ( product_Pair_nat_nat @ K2 @ M5 ) ) ).
% 5.45/5.76
% 5.45/5.76 % prod_decode_aux.cases
% 5.45/5.76 thf(fact_5998_subset__image__iff,axiom,
% 5.45/5.76 ! [B3: set_set_nat,F: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( ord_le6893508408891458716et_nat @ B3 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [AA: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ AA @ A3 )
% 5.45/5.76 & ( B3
% 5.45/5.76 = ( image_nat_set_nat @ F @ AA ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_image_iff
% 5.45/5.76 thf(fact_5999_subset__image__iff,axiom,
% 5.45/5.76 ! [B3: set_nat,F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ B3 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [AA: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ AA @ A3 )
% 5.45/5.76 & ( B3
% 5.45/5.76 = ( image_nat_nat @ F @ AA ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_image_iff
% 5.45/5.76 thf(fact_6000_subset__image__iff,axiom,
% 5.45/5.76 ! [B3: set_nat,F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ B3 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 = ( ? [AA: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ AA @ A3 )
% 5.45/5.76 & ( B3
% 5.45/5.76 = ( image_int_nat @ F @ AA ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_image_iff
% 5.45/5.76 thf(fact_6001_subset__image__iff,axiom,
% 5.45/5.76 ! [B3: set_int,F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ B3 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 = ( ? [AA: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ AA @ A3 )
% 5.45/5.76 & ( B3
% 5.45/5.76 = ( image_nat_int @ F @ AA ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_image_iff
% 5.45/5.76 thf(fact_6002_subset__image__iff,axiom,
% 5.45/5.76 ! [B3: set_int,F: int > int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ B3 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 = ( ? [AA: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ AA @ A3 )
% 5.45/5.76 & ( B3
% 5.45/5.76 = ( image_int_int @ F @ AA ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_image_iff
% 5.45/5.76 thf(fact_6003_image__subset__iff,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat,B3: set_set_nat] :
% 5.45/5.76 ( ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A3 ) @ B3 )
% 5.45/5.76 = ( ! [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 => ( member_set_nat @ ( F @ X4 ) @ B3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subset_iff
% 5.45/5.76 thf(fact_6004_image__subset__iff,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A3 ) @ B3 )
% 5.45/5.76 = ( ! [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X4 ) @ B3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subset_iff
% 5.45/5.76 thf(fact_6005_image__subset__iff,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,B3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A3 ) @ B3 )
% 5.45/5.76 = ( ! [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X4 ) @ B3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subset_iff
% 5.45/5.76 thf(fact_6006_image__subset__iff,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat,B3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ ( image_nat_int @ F @ A3 ) @ B3 )
% 5.45/5.76 = ( ! [X4: nat] :
% 5.45/5.76 ( ( member_nat @ X4 @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X4 ) @ B3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subset_iff
% 5.45/5.76 thf(fact_6007_image__subset__iff,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int,B3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ ( image_int_int @ F @ A3 ) @ B3 )
% 5.45/5.76 = ( ! [X4: int] :
% 5.45/5.76 ( ( member_int @ X4 @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X4 ) @ B3 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subset_iff
% 5.45/5.76 thf(fact_6008_subset__imageE,axiom,
% 5.45/5.76 ! [B3: set_set_nat,F: nat > set_nat,A3: set_nat] :
% 5.45/5.76 ( ( ord_le6893508408891458716et_nat @ B3 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [C5: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.76 => ( B3
% 5.45/5.76 != ( image_nat_set_nat @ F @ C5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_imageE
% 5.45/5.76 thf(fact_6009_subset__imageE,axiom,
% 5.45/5.76 ! [B3: set_nat,F: nat > nat,A3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ B3 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [C5: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.76 => ( B3
% 5.45/5.76 != ( image_nat_nat @ F @ C5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_imageE
% 5.45/5.76 thf(fact_6010_subset__imageE,axiom,
% 5.45/5.76 ! [B3: set_nat,F: int > nat,A3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ B3 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.76 => ~ ! [C5: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ C5 @ A3 )
% 5.45/5.76 => ( B3
% 5.45/5.76 != ( image_int_nat @ F @ C5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_imageE
% 5.45/5.76 thf(fact_6011_subset__imageE,axiom,
% 5.45/5.76 ! [B3: set_int,F: nat > int,A3: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ B3 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.76 => ~ ! [C5: set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.76 => ( B3
% 5.45/5.76 != ( image_nat_int @ F @ C5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_imageE
% 5.45/5.76 thf(fact_6012_subset__imageE,axiom,
% 5.45/5.76 ! [B3: set_int,F: int > int,A3: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ B3 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.76 => ~ ! [C5: set_int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ C5 @ A3 )
% 5.45/5.76 => ( B3
% 5.45/5.76 != ( image_int_int @ F @ C5 ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % subset_imageE
% 5.45/5.76 thf(fact_6013_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_o,F: $o > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: $o] :
% 5.45/5.76 ( ( member_o @ X3 @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_o_o @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6014_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_o,F: $o > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: $o] :
% 5.45/5.76 ( ( member_o @ X3 @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_o_nat @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6015_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_nat,F: nat > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6016_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_nat,F: nat > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6017_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_int,F: int > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ A3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_int_o @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6018_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_int,F: int > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ A3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6019_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_o,F: $o > int,B3: set_int] :
% 5.45/5.76 ( ! [X3: $o] :
% 5.45/5.76 ( ( member_o @ X3 @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_o_int @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6020_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_nat,F: nat > int,B3: set_int] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( member_nat @ X3 @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6021_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_int,F: int > int,B3: set_int] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( member_int @ X3 @ A3 )
% 5.45/5.76 => ( member_int @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6022_image__subsetI,axiom,
% 5.45/5.76 ! [A3: set_o,F: $o > set_nat,B3: set_set_nat] :
% 5.45/5.76 ( ! [X3: $o] :
% 5.45/5.76 ( ( member_o @ X3 @ A3 )
% 5.45/5.76 => ( member_set_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_le6893508408891458716et_nat @ ( image_o_set_nat @ F @ A3 ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_subsetI
% 5.45/5.76 thf(fact_6023_image__mono,axiom,
% 5.45/5.76 ! [A3: set_nat,B3: set_nat,F: nat > set_nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.76 => ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ A3 ) @ ( image_nat_set_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mono
% 5.45/5.76 thf(fact_6024_image__mono,axiom,
% 5.45/5.76 ! [A3: set_nat,B3: set_nat,F: nat > nat] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ A3 ) @ ( image_nat_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mono
% 5.45/5.76 thf(fact_6025_image__mono,axiom,
% 5.45/5.76 ! [A3: set_nat,B3: set_nat,F: nat > int] :
% 5.45/5.76 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ A3 ) @ ( image_nat_int @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mono
% 5.45/5.76 thf(fact_6026_image__mono,axiom,
% 5.45/5.76 ! [A3: set_int,B3: set_int,F: int > nat] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ A3 ) @ ( image_int_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mono
% 5.45/5.76 thf(fact_6027_image__mono,axiom,
% 5.45/5.76 ! [A3: set_int,B3: set_int,F: int > int] :
% 5.45/5.76 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_int_int @ F @ A3 ) @ ( image_int_int @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_mono
% 5.45/5.76 thf(fact_6028_image__Un,axiom,
% 5.45/5.76 ! [F: int > int,A3: set_int,B3: set_int] :
% 5.45/5.76 ( ( image_int_int @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_int @ ( image_int_int @ F @ A3 ) @ ( image_int_int @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6029_image__Un,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,B3: set_int] :
% 5.45/5.76 ( ( image_int_nat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_int_nat @ F @ A3 ) @ ( image_int_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6030_image__Un,axiom,
% 5.45/5.76 ! [F: nat > int,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( image_nat_int @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_int @ ( image_nat_int @ F @ A3 ) @ ( image_nat_int @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6031_image__Un,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( image_nat_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_nat_nat @ F @ A3 ) @ ( image_nat_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6032_image__Un,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( image_nat_set_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_set_nat @ ( image_nat_set_nat @ F @ A3 ) @ ( image_nat_set_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6033_image__Un,axiom,
% 5.45/5.76 ! [F: produc859450856879609959at_nat > nat,A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] :
% 5.45/5.76 ( ( image_6160980552072806642at_nat @ F @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_6160980552072806642at_nat @ F @ A3 ) @ ( image_6160980552072806642at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6034_image__Un,axiom,
% 5.45/5.76 ! [F: nat > produc859450856879609959at_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( image_3276603626957510736at_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_su718114333110466843at_nat @ ( image_3276603626957510736at_nat @ F @ A3 ) @ ( image_3276603626957510736at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6035_image__Un,axiom,
% 5.45/5.76 ! [F: produc4166570645942440679at_nat > nat,A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] :
% 5.45/5.76 ( ( image_6009382790362589554at_nat @ F @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_6009382790362589554at_nat @ F @ A3 ) @ ( image_6009382790362589554at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6036_image__Un,axiom,
% 5.45/5.76 ! [F: produc3843707927480180839at_nat > nat,A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] :
% 5.45/5.76 ( ( image_3198525501578754290at_nat @ F @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_sup_set_nat @ ( image_3198525501578754290at_nat @ F @ A3 ) @ ( image_3198525501578754290at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6037_image__Un,axiom,
% 5.45/5.76 ! [F: nat > produc4166570645942440679at_nat,A3: set_nat,B3: set_nat] :
% 5.45/5.76 ( ( image_5319605298250079696at_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.76 = ( sup_su3035147773818789531at_nat @ ( image_5319605298250079696at_nat @ F @ A3 ) @ ( image_5319605298250079696at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Un
% 5.45/5.76 thf(fact_6038_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_nat_o @ F @ ( collect_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6039_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( collect_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6040_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_int_o @ F @ ( collect_int @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6041_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( collect_int @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6042_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: nat > $o,F: nat > int,B3: set_int] :
% 5.45/5.76 ( ! [X3: nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_int @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( collect_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6043_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: int > $o,F: int > int,B3: set_int] :
% 5.45/5.76 ( ! [X3: int] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_int @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_int @ ( image_int_int @ F @ ( collect_int @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6044_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: list_nat > $o,F: list_nat > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: list_nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_list_nat_o @ F @ ( collect_list_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6045_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: list_nat > $o,F: list_nat > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: list_nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_list_nat_nat @ F @ ( collect_list_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6046_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: set_nat > $o,F: set_nat > $o,B3: set_o] :
% 5.45/5.76 ( ! [X3: set_nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_o @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_o @ ( image_set_nat_o @ F @ ( collect_set_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6047_image__Collect__subsetI,axiom,
% 5.45/5.76 ! [P: set_nat > $o,F: set_nat > nat,B3: set_nat] :
% 5.45/5.76 ( ! [X3: set_nat] :
% 5.45/5.76 ( ( P @ X3 )
% 5.45/5.76 => ( member_nat @ ( F @ X3 ) @ B3 ) )
% 5.45/5.76 => ( ord_less_eq_set_nat @ ( image_set_nat_nat @ F @ ( collect_set_nat @ P ) ) @ B3 ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Collect_subsetI
% 5.45/5.76 thf(fact_6048_obtain__list__from__elements,axiom,
% 5.45/5.76 ! [N2: nat,P: int > nat > $o] :
% 5.45/5.76 ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ N2 )
% 5.45/5.76 => ? [Li: int] : ( P @ Li @ I3 ) )
% 5.45/5.76 => ~ ! [L4: list_int] :
% 5.45/5.76 ( ( ( size_size_list_int @ L4 )
% 5.45/5.76 = N2 )
% 5.45/5.76 => ~ ! [I: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I @ N2 )
% 5.45/5.76 => ( P @ ( nth_int @ L4 @ I ) @ I ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % obtain_list_from_elements
% 5.45/5.76 thf(fact_6049_obtain__list__from__elements,axiom,
% 5.45/5.76 ! [N2: nat,P: nat > nat > $o] :
% 5.45/5.76 ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ N2 )
% 5.45/5.76 => ? [Li: nat] : ( P @ Li @ I3 ) )
% 5.45/5.76 => ~ ! [L4: list_nat] :
% 5.45/5.76 ( ( ( size_size_list_nat @ L4 )
% 5.45/5.76 = N2 )
% 5.45/5.76 => ~ ! [I: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I @ N2 )
% 5.45/5.76 => ( P @ ( nth_nat @ L4 @ I ) @ I ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % obtain_list_from_elements
% 5.45/5.76 thf(fact_6050_obtain__list__from__elements,axiom,
% 5.45/5.76 ! [N2: nat,P: $o > nat > $o] :
% 5.45/5.76 ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ N2 )
% 5.45/5.76 => ? [Li: $o] : ( P @ Li @ I3 ) )
% 5.45/5.76 => ~ ! [L4: list_o] :
% 5.45/5.76 ( ( ( size_size_list_o @ L4 )
% 5.45/5.76 = N2 )
% 5.45/5.76 => ~ ! [I: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I @ N2 )
% 5.45/5.76 => ( P @ ( nth_o @ L4 @ I ) @ I ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % obtain_list_from_elements
% 5.45/5.76 thf(fact_6051_list__eq__iff__nth__eq,axiom,
% 5.45/5.76 ( ( ^ [Y5: list_int,Z3: list_int] : ( Y5 = Z3 ) )
% 5.45/5.76 = ( ^ [Xs3: list_int,Ys2: list_int] :
% 5.45/5.76 ( ( ( size_size_list_int @ Xs3 )
% 5.45/5.76 = ( size_size_list_int @ Ys2 ) )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs3 ) )
% 5.45/5.76 => ( ( nth_int @ Xs3 @ I4 )
% 5.45/5.76 = ( nth_int @ Ys2 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % list_eq_iff_nth_eq
% 5.45/5.76 thf(fact_6052_list__eq__iff__nth__eq,axiom,
% 5.45/5.76 ( ( ^ [Y5: list_nat,Z3: list_nat] : ( Y5 = Z3 ) )
% 5.45/5.76 = ( ^ [Xs3: list_nat,Ys2: list_nat] :
% 5.45/5.76 ( ( ( size_size_list_nat @ Xs3 )
% 5.45/5.76 = ( size_size_list_nat @ Ys2 ) )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs3 ) )
% 5.45/5.76 => ( ( nth_nat @ Xs3 @ I4 )
% 5.45/5.76 = ( nth_nat @ Ys2 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % list_eq_iff_nth_eq
% 5.45/5.76 thf(fact_6053_list__eq__iff__nth__eq,axiom,
% 5.45/5.76 ( ( ^ [Y5: list_o,Z3: list_o] : ( Y5 = Z3 ) )
% 5.45/5.76 = ( ^ [Xs3: list_o,Ys2: list_o] :
% 5.45/5.76 ( ( ( size_size_list_o @ Xs3 )
% 5.45/5.76 = ( size_size_list_o @ Ys2 ) )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs3 ) )
% 5.45/5.76 => ( ( nth_o @ Xs3 @ I4 )
% 5.45/5.76 = ( nth_o @ Ys2 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % list_eq_iff_nth_eq
% 5.45/5.76 thf(fact_6054_Skolem__list__nth,axiom,
% 5.45/5.76 ! [K: nat,P: nat > int > $o] :
% 5.45/5.76 ( ( ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ? [X11: int] : ( P @ I4 @ X11 ) ) )
% 5.45/5.76 = ( ? [Xs3: list_int] :
% 5.45/5.76 ( ( ( size_size_list_int @ Xs3 )
% 5.45/5.76 = K )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ( P @ I4 @ ( nth_int @ Xs3 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Skolem_list_nth
% 5.45/5.76 thf(fact_6055_Skolem__list__nth,axiom,
% 5.45/5.76 ! [K: nat,P: nat > nat > $o] :
% 5.45/5.76 ( ( ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ? [X11: nat] : ( P @ I4 @ X11 ) ) )
% 5.45/5.76 = ( ? [Xs3: list_nat] :
% 5.45/5.76 ( ( ( size_size_list_nat @ Xs3 )
% 5.45/5.76 = K )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ( P @ I4 @ ( nth_nat @ Xs3 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Skolem_list_nth
% 5.45/5.76 thf(fact_6056_Skolem__list__nth,axiom,
% 5.45/5.76 ! [K: nat,P: nat > $o > $o] :
% 5.45/5.76 ( ( ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ? [X11: $o] : ( P @ I4 @ X11 ) ) )
% 5.45/5.76 = ( ? [Xs3: list_o] :
% 5.45/5.76 ( ( ( size_size_list_o @ Xs3 )
% 5.45/5.76 = K )
% 5.45/5.76 & ! [I4: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I4 @ K )
% 5.45/5.76 => ( P @ I4 @ ( nth_o @ Xs3 @ I4 ) ) ) ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % Skolem_list_nth
% 5.45/5.76 thf(fact_6057_nth__equalityI,axiom,
% 5.45/5.76 ! [Xs: list_int,Ys3: list_int] :
% 5.45/5.76 ( ( ( size_size_list_int @ Xs )
% 5.45/5.76 = ( size_size_list_int @ Ys3 ) )
% 5.45/5.76 => ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.45/5.76 => ( ( nth_int @ Xs @ I3 )
% 5.45/5.76 = ( nth_int @ Ys3 @ I3 ) ) )
% 5.45/5.76 => ( Xs = Ys3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nth_equalityI
% 5.45/5.76 thf(fact_6058_nth__equalityI,axiom,
% 5.45/5.76 ! [Xs: list_nat,Ys3: list_nat] :
% 5.45/5.76 ( ( ( size_size_list_nat @ Xs )
% 5.45/5.76 = ( size_size_list_nat @ Ys3 ) )
% 5.45/5.76 => ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.45/5.76 => ( ( nth_nat @ Xs @ I3 )
% 5.45/5.76 = ( nth_nat @ Ys3 @ I3 ) ) )
% 5.45/5.76 => ( Xs = Ys3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nth_equalityI
% 5.45/5.76 thf(fact_6059_nth__equalityI,axiom,
% 5.45/5.76 ! [Xs: list_o,Ys3: list_o] :
% 5.45/5.76 ( ( ( size_size_list_o @ Xs )
% 5.45/5.76 = ( size_size_list_o @ Ys3 ) )
% 5.45/5.76 => ( ! [I3: nat] :
% 5.45/5.76 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.45/5.76 => ( ( nth_o @ Xs @ I3 )
% 5.45/5.76 = ( nth_o @ Ys3 @ I3 ) ) )
% 5.45/5.76 => ( Xs = Ys3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % nth_equalityI
% 5.45/5.76 thf(fact_6060_image__Int__subset,axiom,
% 5.45/5.76 ! [F: int > nat,A3: set_int,B3: set_int] : ( ord_less_eq_set_nat @ ( image_int_nat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( inf_inf_set_nat @ ( image_int_nat @ F @ A3 ) @ ( image_int_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Int_subset
% 5.45/5.76 thf(fact_6061_image__Int__subset,axiom,
% 5.45/5.76 ! [F: nat > set_nat,A3: set_nat,B3: set_nat] : ( ord_le6893508408891458716et_nat @ ( image_nat_set_nat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( inf_inf_set_set_nat @ ( image_nat_set_nat @ F @ A3 ) @ ( image_nat_set_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Int_subset
% 5.45/5.76 thf(fact_6062_image__Int__subset,axiom,
% 5.45/5.76 ! [F: nat > nat,A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( image_nat_nat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( inf_inf_set_nat @ ( image_nat_nat @ F @ A3 ) @ ( image_nat_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Int_subset
% 5.45/5.76 thf(fact_6063_image__Int__subset,axiom,
% 5.45/5.76 ! [F: nat > product_prod_nat_nat,A3: set_nat,B3: set_nat] : ( ord_le3146513528884898305at_nat @ ( image_5846123807819985514at_nat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( inf_in2572325071724192079at_nat @ ( image_5846123807819985514at_nat @ F @ A3 ) @ ( image_5846123807819985514at_nat @ F @ B3 ) ) ) ).
% 5.45/5.76
% 5.45/5.76 % image_Int_subset
% 5.45/5.76 thf(fact_6064_image__Int__subset,axiom,
% 5.45/5.76 ! [F: product_prod_nat_nat > nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_nat @ ( image_2486076414777270412at_nat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) @ ( inf_inf_set_nat @ ( image_2486076414777270412at_nat @ F @ A3 ) @ ( image_2486076414777270412at_nat @ F @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_Int_subset
% 5.45/5.77 thf(fact_6065_image__Int__subset,axiom,
% 5.45/5.77 ! [F: product_prod_nat_nat > product_prod_nat_nat,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ ( image_5168914502847457605at_nat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) @ ( inf_in2572325071724192079at_nat @ ( image_5168914502847457605at_nat @ F @ A3 ) @ ( image_5168914502847457605at_nat @ F @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_Int_subset
% 5.45/5.77 thf(fact_6066_image__Int__subset,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( image_int_int @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( inf_inf_set_int @ ( image_int_int @ F @ A3 ) @ ( image_int_int @ F @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_Int_subset
% 5.45/5.77 thf(fact_6067_image__Int__subset,axiom,
% 5.45/5.77 ! [F: nat > int,A3: set_nat,B3: set_nat] : ( ord_less_eq_set_int @ ( image_nat_int @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( inf_inf_set_int @ ( image_nat_int @ F @ A3 ) @ ( image_nat_int @ F @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_Int_subset
% 5.45/5.77 thf(fact_6068_image__Int__subset,axiom,
% 5.45/5.77 ! [F: product_prod_nat_nat > int,A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] : ( ord_less_eq_set_int @ ( image_2483585944268220136at_int @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) @ ( inf_inf_set_int @ ( image_2483585944268220136at_int @ F @ A3 ) @ ( image_2483585944268220136at_int @ F @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_Int_subset
% 5.45/5.77 thf(fact_6069_image__diff__subset,axiom,
% 5.45/5.77 ! [F: nat > set_nat,A3: set_nat,B3: set_nat] : ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ ( image_nat_set_nat @ F @ A3 ) @ ( image_nat_set_nat @ F @ B3 ) ) @ ( image_nat_set_nat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_diff_subset
% 5.45/5.77 thf(fact_6070_image__diff__subset,axiom,
% 5.45/5.77 ! [F: int > nat,A3: set_int,B3: set_int] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_int_nat @ F @ A3 ) @ ( image_int_nat @ F @ B3 ) ) @ ( image_int_nat @ F @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_diff_subset
% 5.45/5.77 thf(fact_6071_image__diff__subset,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ ( image_nat_nat @ F @ A3 ) @ ( image_nat_nat @ F @ B3 ) ) @ ( image_nat_nat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_diff_subset
% 5.45/5.77 thf(fact_6072_image__diff__subset,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_int_int @ F @ A3 ) @ ( image_int_int @ F @ B3 ) ) @ ( image_int_int @ F @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_diff_subset
% 5.45/5.77 thf(fact_6073_image__diff__subset,axiom,
% 5.45/5.77 ! [F: nat > int,A3: set_nat,B3: set_nat] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ ( image_nat_int @ F @ A3 ) @ ( image_nat_int @ F @ B3 ) ) @ ( image_nat_int @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_diff_subset
% 5.45/5.77 thf(fact_6074_ex__nat__less,axiom,
% 5.45/5.77 ! [N2: nat,P: nat > $o] :
% 5.45/5.77 ( ( ? [M3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.45/5.77 & ( P @ M3 ) ) )
% 5.45/5.77 = ( ? [X4: nat] :
% 5.45/5.77 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.77 & ( P @ X4 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ex_nat_less
% 5.45/5.77 thf(fact_6075_all__nat__less,axiom,
% 5.45/5.77 ! [N2: nat,P: nat > $o] :
% 5.45/5.77 ( ( ! [M3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.45/5.77 => ( P @ M3 ) ) )
% 5.45/5.77 = ( ! [X4: nat] :
% 5.45/5.77 ( ( member_nat @ X4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.77 => ( P @ X4 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % all_nat_less
% 5.45/5.77 thf(fact_6076_None__notin__image__Some,axiom,
% 5.45/5.77 ! [A3: set_Pr7098220151150636591it_nat] :
% 5.45/5.77 ~ ( member1310632352865511136it_nat @ none_P2651198173097904984it_nat @ ( image_2003495143432273353it_nat @ some_P7913643980934408916it_nat @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % None_notin_image_Some
% 5.45/5.77 thf(fact_6077_None__notin__image__Some,axiom,
% 5.45/5.77 ! [A3: set_num] :
% 5.45/5.77 ~ ( member_option_num @ none_num @ ( image_num_option_num @ some_num @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % None_notin_image_Some
% 5.45/5.77 thf(fact_6078_None__notin__image__Some,axiom,
% 5.45/5.77 ! [A3: set_Pr1354866905816374718it_nat] :
% 5.45/5.77 ~ ( member5596548051065438575it_nat @ none_P9117596204409417319it_nat @ ( image_3455408117458022631it_nat @ some_P1914260805536162275it_nat @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % None_notin_image_Some
% 5.45/5.77 thf(fact_6079_nth__rotate1,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_int] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ( nth_int @ ( rotate1_int @ Xs ) @ N2 )
% 5.45/5.77 = ( nth_int @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_int @ Xs ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_rotate1
% 5.45/5.77 thf(fact_6080_nth__rotate1,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_nat] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ( nth_nat @ ( rotate1_nat @ Xs ) @ N2 )
% 5.45/5.77 = ( nth_nat @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_nat @ Xs ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_rotate1
% 5.45/5.77 thf(fact_6081_nth__rotate1,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_o] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ( nth_o @ ( rotate1_o @ Xs ) @ N2 )
% 5.45/5.77 = ( nth_o @ Xs @ ( modulo_modulo_nat @ ( suc @ N2 ) @ ( size_size_list_o @ Xs ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_rotate1
% 5.45/5.77 thf(fact_6082_image__mult__atLeastAtMost__if,axiom,
% 5.45/5.77 ! [C: rat,X: rat,Y: rat] :
% 5.45/5.77 ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.77 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.77 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ X ) @ ( times_times_rat @ C @ Y ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.45/5.77 => ( ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.77 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.77 = ( set_or633870826150836451st_rat @ ( times_times_rat @ C @ Y ) @ ( times_times_rat @ C @ X ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.45/5.77 => ( ( image_rat_rat @ ( times_times_rat @ C ) @ ( set_or633870826150836451st_rat @ X @ Y ) )
% 5.45/5.77 = bot_bot_set_rat ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_mult_atLeastAtMost_if
% 5.45/5.77 thf(fact_6083_prod__decode__aux_Osimps,axiom,
% 5.45/5.77 ( nat_prod_decode_aux
% 5.45/5.77 = ( ^ [K3: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K3 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K3 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K3 ) @ ( minus_minus_nat @ M3 @ ( suc @ K3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_decode_aux.simps
% 5.45/5.77 thf(fact_6084_prod__decode__aux_Opelims,axiom,
% 5.45/5.77 ! [X: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.45/5.77 ( ( ( nat_prod_decode_aux @ X @ Xa )
% 5.45/5.77 = Y )
% 5.45/5.77 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.45/5.77 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X )
% 5.45/5.77 => ( Y
% 5.45/5.77 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X @ Xa ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_eq_nat @ Xa @ X )
% 5.45/5.77 => ( Y
% 5.45/5.77 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa @ ( suc @ X ) ) ) ) ) )
% 5.45/5.77 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_decode_aux.pelims
% 5.45/5.77 thf(fact_6085_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_int,Ys3: list_int] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr4439495888332055232nt_int @ ( product_int_int @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_int_int @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) @ ( nth_int @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6086_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_int,Ys3: list_nat] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr8617346907841251940nt_nat @ ( product_int_nat @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_int_nat @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) @ ( nth_nat @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6087_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_int,Ys3: list_o] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_int @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr7514405829937366042_int_o @ ( product_int_o @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_int_o @ ( nth_int @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) @ ( nth_o @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6088_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_nat,Ys3: list_int] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr3440142176431000676at_int @ ( product_nat_int @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_nat_int @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) @ ( nth_int @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6089_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_nat,Ys3: list_nat] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr7617993195940197384at_nat @ ( product_nat_nat @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_nat_nat @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) @ ( nth_nat @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6090_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_nat,Ys3: list_o] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_nat_o @ ( nth_nat @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) @ ( nth_o @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6091_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_o,Ys3: list_int] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) @ ( nth_int @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6092_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_o,Ys3: list_nat] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) @ ( nth_nat @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6093_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_o,Ys3: list_o] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) @ ( nth_o @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6094_product__nth,axiom,
% 5.45/5.77 ! [N2: nat,Xs: list_a,Ys3: list_P131111800688179804it_nat] :
% 5.45/5.77 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_a @ Xs ) @ ( size_s341701280123345136it_nat @ Ys3 ) ) )
% 5.45/5.77 => ( ( nth_Pr8687047199098054322it_nat @ ( produc6966004487978991557it_nat @ Xs @ Ys3 ) @ N2 )
% 5.45/5.77 = ( produc9178034014595674355it_nat @ ( nth_a @ Xs @ ( divide_divide_nat @ N2 @ ( size_s341701280123345136it_nat @ Ys3 ) ) ) @ ( nth_Pr4561283279332054789it_nat @ Ys3 @ ( modulo_modulo_nat @ N2 @ ( size_s341701280123345136it_nat @ Ys3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % product_nth
% 5.45/5.77 thf(fact_6095_translation__subtract__Compl,axiom,
% 5.45/5.77 ! [A: rat,T5: set_rat] :
% 5.45/5.77 ( ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ ( uminus2201863774496077783et_rat @ T5 ) )
% 5.45/5.77 = ( uminus2201863774496077783et_rat
% 5.45/5.77 @ ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_Compl
% 5.45/5.77 thf(fact_6096_translation__subtract__Compl,axiom,
% 5.45/5.77 ! [A: int,T5: set_int] :
% 5.45/5.77 ( ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ ( uminus1532241313380277803et_int @ T5 ) )
% 5.45/5.77 = ( uminus1532241313380277803et_int
% 5.45/5.77 @ ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_Compl
% 5.45/5.77 thf(fact_6097_translation__subtract__diff,axiom,
% 5.45/5.77 ! [A: rat,S2: set_rat,T5: set_rat] :
% 5.45/5.77 ( ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ ( minus_minus_set_rat @ S2 @ T5 ) )
% 5.45/5.77 = ( minus_minus_set_rat
% 5.45/5.77 @ ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ S2 )
% 5.45/5.77 @ ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_diff
% 5.45/5.77 thf(fact_6098_translation__subtract__diff,axiom,
% 5.45/5.77 ! [A: int,S2: set_int,T5: set_int] :
% 5.45/5.77 ( ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ ( minus_minus_set_int @ S2 @ T5 ) )
% 5.45/5.77 = ( minus_minus_set_int
% 5.45/5.77 @ ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ S2 )
% 5.45/5.77 @ ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_diff
% 5.45/5.77 thf(fact_6099_translation__subtract__Int,axiom,
% 5.45/5.77 ! [A: rat,S2: set_rat,T5: set_rat] :
% 5.45/5.77 ( ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ ( inf_inf_set_rat @ S2 @ T5 ) )
% 5.45/5.77 = ( inf_inf_set_rat
% 5.45/5.77 @ ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ S2 )
% 5.45/5.77 @ ( image_rat_rat
% 5.45/5.77 @ ^ [X4: rat] : ( minus_minus_rat @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_Int
% 5.45/5.77 thf(fact_6100_translation__subtract__Int,axiom,
% 5.45/5.77 ! [A: int,S2: set_int,T5: set_int] :
% 5.45/5.77 ( ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ ( inf_inf_set_int @ S2 @ T5 ) )
% 5.45/5.77 = ( inf_inf_set_int
% 5.45/5.77 @ ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ S2 )
% 5.45/5.77 @ ( image_int_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ X4 @ A )
% 5.45/5.77 @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_subtract_Int
% 5.45/5.77 thf(fact_6101_sum__gp,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,X: rat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = zero_zero_rat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( ( X = one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.45/5.77 & ( ( X != one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp
% 5.45/5.77 thf(fact_6102_of__nat__sum,axiom,
% 5.45/5.77 ! [F: int > nat,A3: set_int] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_sum
% 5.45/5.77 thf(fact_6103_of__nat__sum,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_sum
% 5.45/5.77 thf(fact_6104_of__nat__sum,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri4939895301339042750nteger @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [X4: nat] : ( semiri4939895301339042750nteger @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_sum
% 5.45/5.77 thf(fact_6105_of__nat__sum,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1316708129612266289at_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_sum
% 5.45/5.77 thf(fact_6106_of__int__sum,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( ring_1_of_int_rat @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.45/5.77 = ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [X4: int] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_sum
% 5.45/5.77 thf(fact_6107_of__int__sum,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( ring_1_of_int_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_sum
% 5.45/5.77 thf(fact_6108_sum_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_z3403309356797280102nteger ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.cl_ivl_Suc
% 5.45/5.77 thf(fact_6109_sum_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_z1048942125864253310at_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.cl_ivl_Suc
% 5.45/5.77 thf(fact_6110_sum_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_rat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.cl_ivl_Suc
% 5.45/5.77 thf(fact_6111_sum_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_int ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.cl_ivl_Suc
% 5.45/5.77 thf(fact_6112_sum_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.cl_ivl_Suc
% 5.45/5.77 thf(fact_6113_mod__sum__eq,axiom,
% 5.45/5.77 ! [F: nat > nat,A: nat,A3: set_nat] :
% 5.45/5.77 ( ( modulo_modulo_nat
% 5.45/5.77 @ ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ A )
% 5.45/5.77 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ A ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod_sum_eq
% 5.45/5.77 thf(fact_6114_mod__sum__eq,axiom,
% 5.45/5.77 ! [F: int > int,A: int,A3: set_int] :
% 5.45/5.77 ( ( modulo_modulo_int
% 5.45/5.77 @ ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ A )
% 5.45/5.77 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ A ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod_sum_eq
% 5.45/5.77 thf(fact_6115_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.45/5.77 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.shift_bounds_cl_Suc_ivl
% 5.45/5.77 thf(fact_6116_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.45/5.77 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.shift_bounds_cl_nat_ivl
% 5.45/5.77 thf(fact_6117_sum_OatLeastAtMost__rev,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atLeastAtMost_rev
% 5.45/5.77 thf(fact_6118_sum_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( G @ ( suc @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6119_sum_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6120_sum_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6121_sum_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6122_sum_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( G @ M ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6123_sum_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6124_sum_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6125_sum_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6126_sum_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( G @ M )
% 5.45/5.77 @ ( groups6857163185585827899at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6127_sum_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( G @ M )
% 5.45/5.77 @ ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6128_sum_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( G @ M )
% 5.45/5.77 @ ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6129_sum_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( G @ M )
% 5.45/5.77 @ ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6130_sum__Suc__diff,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_Suc_diff
% 5.45/5.77 thf(fact_6131_sum__Suc__diff,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_Suc_diff
% 5.45/5.77 thf(fact_6132_sum__power__add,axiom,
% 5.45/5.77 ! [X: code_integer,M: nat,I5: set_nat] :
% 5.45/5.77 ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [I4: nat] : ( power_8256067586552552935nteger @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ I5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_add
% 5.45/5.77 thf(fact_6133_sum__power__add,axiom,
% 5.45/5.77 ! [X: rat,M: nat,I5: set_nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_add
% 5.45/5.77 thf(fact_6134_sum__power__add,axiom,
% 5.45/5.77 ! [X: int,M: nat,I5: set_nat] :
% 5.45/5.77 ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_add
% 5.45/5.77 thf(fact_6135_sum__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > code_integer,A: nat,B: nat] :
% 5.45/5.77 ( ( groups7501900531339628137nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo1084959871951514735nteger
% 5.45/5.77 @ ^ [A5: nat] : ( plus_p5714425477246183910nteger @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_atLeastAtMost_code
% 5.45/5.77 thf(fact_6136_sum__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > multis2468970476368604999at_nat,A: nat,B: nat] :
% 5.45/5.77 ( ( groups6857163185585827899at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo4497565046347964853at_nat
% 5.45/5.77 @ ^ [A5: nat] : ( plus_p7104986032573967614at_nat @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ zero_z1048942125864253310at_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_atLeastAtMost_code
% 5.45/5.77 thf(fact_6137_sum__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > rat,A: nat,B: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo1949268297981939178at_rat
% 5.45/5.77 @ ^ [A5: nat] : ( plus_plus_rat @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_atLeastAtMost_code
% 5.45/5.77 thf(fact_6138_sum__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > int,A: nat,B: nat] :
% 5.45/5.77 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo2581907887559384638at_int
% 5.45/5.77 @ ^ [A5: nat] : ( plus_plus_int @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_atLeastAtMost_code
% 5.45/5.77 thf(fact_6139_sum__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > nat,A: nat,B: nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo2584398358068434914at_nat
% 5.45/5.77 @ ^ [A5: nat] : ( plus_plus_nat @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ zero_zero_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_atLeastAtMost_code
% 5.45/5.77 thf(fact_6140_sum_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.ub_add_nat
% 5.45/5.77 thf(fact_6141_sum_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.ub_add_nat
% 5.45/5.77 thf(fact_6142_sum_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.ub_add_nat
% 5.45/5.77 thf(fact_6143_sum_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.ub_add_nat
% 5.45/5.77 thf(fact_6144_sum__natinterval__diff,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > code_integer] :
% 5.45/5.77 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( minus_8373710615458151222nteger @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( minus_8373710615458151222nteger @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( minus_8373710615458151222nteger @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_natinterval_diff
% 5.45/5.77 thf(fact_6145_sum__natinterval__diff,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > rat] :
% 5.45/5.77 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = zero_zero_rat ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_natinterval_diff
% 5.45/5.77 thf(fact_6146_sum__natinterval__diff,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > int] :
% 5.45/5.77 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.45/5.77 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = zero_zero_int ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_natinterval_diff
% 5.45/5.77 thf(fact_6147_sum__telescope_H_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.45/5.77 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_telescope''
% 5.45/5.77 thf(fact_6148_sum__telescope_H_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,F: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.45/5.77 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_telescope''
% 5.45/5.77 thf(fact_6149_sum__gp__multiplied,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.45/5.77 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_multiplied
% 5.45/5.77 thf(fact_6150_sum__gp__multiplied,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.45/5.77 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_multiplied
% 5.45/5.77 thf(fact_6151_sum__gp__multiplied,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.45/5.77 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_multiplied
% 5.45/5.77 thf(fact_6152_gbinomial__sum__up__index,axiom,
% 5.45/5.77 ! [K: nat,N2: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.77 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_sum_up_index
% 5.45/5.77 thf(fact_6153_sum__gp__offset,axiom,
% 5.45/5.77 ! [X: rat,M: nat,N2: nat] :
% 5.45/5.77 ( ( ( X = one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 5.45/5.77 & ( ( X != one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.45/5.77 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_offset
% 5.45/5.77 thf(fact_6154_translation__Int,axiom,
% 5.45/5.77 ! [A: rat,S2: set_rat,T5: set_rat] :
% 5.45/5.77 ( ( image_rat_rat @ ( plus_plus_rat @ A ) @ ( inf_inf_set_rat @ S2 @ T5 ) )
% 5.45/5.77 = ( inf_inf_set_rat @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ S2 ) @ ( image_rat_rat @ ( plus_plus_rat @ A ) @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_Int
% 5.45/5.77 thf(fact_6155_translation__Int,axiom,
% 5.45/5.77 ! [A: int,S2: set_int,T5: set_int] :
% 5.45/5.77 ( ( image_int_int @ ( plus_plus_int @ A ) @ ( inf_inf_set_int @ S2 @ T5 ) )
% 5.45/5.77 = ( inf_inf_set_int @ ( image_int_int @ ( plus_plus_int @ A ) @ S2 ) @ ( image_int_int @ ( plus_plus_int @ A ) @ T5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % translation_Int
% 5.45/5.77 thf(fact_6156_sum__abs__ge__zero,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ord_less_eq_int @ zero_zero_int
% 5.45/5.77 @ ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_abs_ge_zero
% 5.45/5.77 thf(fact_6157_sum__abs,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.45/5.77 @ ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( abs_abs_int @ ( F @ I4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_abs
% 5.45/5.77 thf(fact_6158_sum_Oempty,axiom,
% 5.45/5.77 ! [G: $o > code_integer] :
% 5.45/5.77 ( ( groups4406642042086082107nteger @ G @ bot_bot_set_o )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6159_sum_Oempty,axiom,
% 5.45/5.77 ! [G: $o > rat] :
% 5.45/5.77 ( ( groups7872700643590313910_o_rat @ G @ bot_bot_set_o )
% 5.45/5.77 = zero_zero_rat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6160_sum_Oempty,axiom,
% 5.45/5.77 ! [G: $o > nat] :
% 5.45/5.77 ( ( groups8507830703676809646_o_nat @ G @ bot_bot_set_o )
% 5.45/5.77 = zero_zero_nat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6161_sum_Oempty,axiom,
% 5.45/5.77 ! [G: $o > int] :
% 5.45/5.77 ( ( groups8505340233167759370_o_int @ G @ bot_bot_set_o )
% 5.45/5.77 = zero_zero_int ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6162_sum_Oempty,axiom,
% 5.45/5.77 ! [G: nat > code_integer] :
% 5.45/5.77 ( ( groups7501900531339628137nteger @ G @ bot_bot_set_nat )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6163_sum_Oempty,axiom,
% 5.45/5.77 ! [G: nat > rat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 5.45/5.77 = zero_zero_rat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6164_sum_Oempty,axiom,
% 5.45/5.77 ! [G: nat > int] :
% 5.45/5.77 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 5.45/5.77 = zero_zero_int ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6165_sum_Oempty,axiom,
% 5.45/5.77 ! [G: int > code_integer] :
% 5.45/5.77 ( ( groups7873554091576472773nteger @ G @ bot_bot_set_int )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6166_sum_Oempty,axiom,
% 5.45/5.77 ! [G: int > rat] :
% 5.45/5.77 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 5.45/5.77 = zero_zero_rat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6167_sum_Oempty,axiom,
% 5.45/5.77 ! [G: int > nat] :
% 5.45/5.77 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 5.45/5.77 = zero_zero_nat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.empty
% 5.45/5.77 thf(fact_6168_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_o,X: $o > code_integer,A: $o > code_integer,B: code_integer,Delta: code_integer] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups4406642042086082107nteger @ X @ I5 )
% 5.45/5.77 = one_one_Code_integer )
% 5.45/5.77 => ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger
% 5.45/5.77 @ ( abs_abs_Code_integer
% 5.45/5.77 @ ( minus_8373710615458151222nteger
% 5.45/5.77 @ ( groups4406642042086082107nteger
% 5.45/5.77 @ ^ [I4: $o] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6169_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups7501900531339628137nteger @ X @ I5 )
% 5.45/5.77 = one_one_Code_integer )
% 5.45/5.77 => ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger
% 5.45/5.77 @ ( abs_abs_Code_integer
% 5.45/5.77 @ ( minus_8373710615458151222nteger
% 5.45/5.77 @ ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6170_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups7873554091576472773nteger @ X @ I5 )
% 5.45/5.77 = one_one_Code_integer )
% 5.45/5.77 => ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger
% 5.45/5.77 @ ( abs_abs_Code_integer
% 5.45/5.77 @ ( minus_8373710615458151222nteger
% 5.45/5.77 @ ( groups7873554091576472773nteger
% 5.45/5.77 @ ^ [I4: int] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6171_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_o,X: $o > rat,A: $o > rat,B: rat,Delta: rat] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups7872700643590313910_o_rat @ X @ I5 )
% 5.45/5.77 = one_one_rat )
% 5.45/5.77 => ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_rat
% 5.45/5.77 @ ( abs_abs_rat
% 5.45/5.77 @ ( minus_minus_rat
% 5.45/5.77 @ ( groups7872700643590313910_o_rat
% 5.45/5.77 @ ^ [I4: $o] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6172_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups2906978787729119204at_rat @ X @ I5 )
% 5.45/5.77 = one_one_rat )
% 5.45/5.77 => ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_rat
% 5.45/5.77 @ ( abs_abs_rat
% 5.45/5.77 @ ( minus_minus_rat
% 5.45/5.77 @ ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6173_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_int,X: int > rat,A: int > rat,B: rat,Delta: rat] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups3906332499630173760nt_rat @ X @ I5 )
% 5.45/5.77 = one_one_rat )
% 5.45/5.77 => ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_rat
% 5.45/5.77 @ ( abs_abs_rat
% 5.45/5.77 @ ( minus_minus_rat
% 5.45/5.77 @ ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [I4: int] : ( times_times_rat @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6174_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_o,X: $o > int,A: $o > int,B: int,Delta: int] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups8505340233167759370_o_int @ X @ I5 )
% 5.45/5.77 = one_one_int )
% 5.45/5.77 => ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_int
% 5.45/5.77 @ ( abs_abs_int
% 5.45/5.77 @ ( minus_minus_int
% 5.45/5.77 @ ( groups8505340233167759370_o_int
% 5.45/5.77 @ ^ [I4: $o] : ( times_times_int @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6175_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_nat,X: nat > int,A: nat > int,B: int,Delta: int] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups3539618377306564664at_int @ X @ I5 )
% 5.45/5.77 = one_one_int )
% 5.45/5.77 => ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_int
% 5.45/5.77 @ ( abs_abs_int
% 5.45/5.77 @ ( minus_minus_int
% 5.45/5.77 @ ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_int @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6176_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_int,X: int > int,A: int > int,B: int,Delta: int] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups4538972089207619220nt_int @ X @ I5 )
% 5.45/5.77 = one_one_int )
% 5.45/5.77 => ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ I5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_less_eq_int
% 5.45/5.77 @ ( abs_abs_int
% 5.45/5.77 @ ( minus_minus_int
% 5.45/5.77 @ ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( times_times_int @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6177_convex__sum__bound__le,axiom,
% 5.45/5.77 ! [I5: set_set_nat,X: set_nat > code_integer,A: set_nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.45/5.77 ( ! [I3: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I3 ) ) )
% 5.45/5.77 => ( ( ( groups9190459664516455967nteger @ X @ I5 )
% 5.45/5.77 = one_one_Code_integer )
% 5.45/5.77 => ( ! [I3: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ I3 @ I5 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I3 ) @ B ) ) @ Delta ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger
% 5.45/5.77 @ ( abs_abs_Code_integer
% 5.45/5.77 @ ( minus_8373710615458151222nteger
% 5.45/5.77 @ ( groups9190459664516455967nteger
% 5.45/5.77 @ ^ [I4: set_nat] : ( times_3573771949741848930nteger @ ( A @ I4 ) @ ( X @ I4 ) )
% 5.45/5.77 @ I5 )
% 5.45/5.77 @ B ) )
% 5.45/5.77 @ Delta ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % convex_sum_bound_le
% 5.45/5.77 thf(fact_6178_abs__sum__abs,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( abs_abs_int
% 5.45/5.77 @ ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [A5: int] : ( abs_abs_int @ ( F @ A5 ) )
% 5.45/5.77 @ A3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [A5: int] : ( abs_abs_int @ ( F @ A5 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % abs_sum_abs
% 5.45/5.77 thf(fact_6179_sum_Oneutral__const,axiom,
% 5.45/5.77 ! [A3: set_nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [Uu2: nat] : zero_zero_nat
% 5.45/5.77 @ A3 )
% 5.45/5.77 = zero_zero_nat ) ).
% 5.45/5.77
% 5.45/5.77 % sum.neutral_const
% 5.45/5.77 thf(fact_6180_sum_Oneutral__const,axiom,
% 5.45/5.77 ! [A3: set_int] :
% 5.45/5.77 ( ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [Uu2: int] : zero_zero_int
% 5.45/5.77 @ A3 )
% 5.45/5.77 = zero_zero_int ) ).
% 5.45/5.77
% 5.45/5.77 % sum.neutral_const
% 5.45/5.77 thf(fact_6181_int__sum,axiom,
% 5.45/5.77 ! [F: int > nat,A3: set_int] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % int_sum
% 5.45/5.77 thf(fact_6182_int__sum,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % int_sum
% 5.45/5.77 thf(fact_6183_sum__subtractf__nat,axiom,
% 5.45/5.77 ! [A3: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.45/5.77 ( ! [X3: product_prod_nat_nat] :
% 5.45/5.77 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ( groups977919841031483927at_nat
% 5.45/5.77 @ ^ [X4: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( groups977919841031483927at_nat @ G @ A3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf_nat
% 5.45/5.77 thf(fact_6184_sum__subtractf__nat,axiom,
% 5.45/5.77 ! [A3: set_o,G: $o > nat,F: $o > nat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ( groups8507830703676809646_o_nat
% 5.45/5.77 @ ^ [X4: $o] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( groups8507830703676809646_o_nat @ G @ A3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf_nat
% 5.45/5.77 thf(fact_6185_sum__subtractf__nat,axiom,
% 5.45/5.77 ! [A3: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.45/5.77 ( ! [X3: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ( groups8294997508430121362at_nat
% 5.45/5.77 @ ^ [X4: set_nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( groups8294997508430121362at_nat @ G @ A3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf_nat
% 5.45/5.77 thf(fact_6186_sum__subtractf__nat,axiom,
% 5.45/5.77 ! [A3: set_int,G: int > nat,F: int > nat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ( groups4541462559716669496nt_nat
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf_nat
% 5.45/5.77 thf(fact_6187_sum__subtractf__nat,axiom,
% 5.45/5.77 ! [A3: set_nat,G: nat > nat,F: nat > nat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( G @ X3 ) @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( minus_minus_nat @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf_nat
% 5.45/5.77 thf(fact_6188_sum__SucD,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat,N2: nat] :
% 5.45/5.77 ( ( ( groups3542108847815614940at_nat @ F @ A3 )
% 5.45/5.77 = ( suc @ N2 ) )
% 5.45/5.77 => ? [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 & ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_SucD
% 5.45/5.77 thf(fact_6189_sum_Oswap,axiom,
% 5.45/5.77 ! [G: nat > nat > nat,B3: set_nat,A3: set_nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [J3: nat] :
% 5.45/5.77 ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.swap
% 5.45/5.77 thf(fact_6190_sum_Oswap,axiom,
% 5.45/5.77 ! [G: int > int > int,B3: set_int,A3: set_int] :
% 5.45/5.77 ( ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( groups4538972089207619220nt_int @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [J3: int] :
% 5.45/5.77 ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.swap
% 5.45/5.77 thf(fact_6191_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_o,F: $o > rat,G: $o > rat] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ K5 ) @ ( groups7872700643590313910_o_rat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6192_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6193_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6194_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_o,F: $o > nat,G: $o > nat] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ K5 ) @ ( groups8507830703676809646_o_nat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6195_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6196_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_o,F: $o > int,G: $o > int] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ K5 ) @ ( groups8505340233167759370_o_int @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6197_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6198_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_nat,F: nat > nat,G: nat > nat] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ K5 ) @ ( groups3542108847815614940at_nat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6199_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_int,F: int > int,G: int > int] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups4538972089207619220nt_int @ F @ K5 ) @ ( groups4538972089207619220nt_int @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6200_sum__mono,axiom,
% 5.45/5.77 ! [K5: set_set_nat,F: set_nat > rat,G: set_nat > rat] :
% 5.45/5.77 ( ! [I3: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ I3 @ K5 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups7659867448343625626at_rat @ F @ K5 ) @ ( groups7659867448343625626at_rat @ G @ K5 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_mono
% 5.45/5.77 thf(fact_6201_sum_Odistrib,axiom,
% 5.45/5.77 ! [G: nat > nat,H: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( plus_plus_nat @ ( G @ X4 ) @ ( H @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A3 ) @ ( groups3542108847815614940at_nat @ H @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.distrib
% 5.45/5.77 thf(fact_6202_sum_Odistrib,axiom,
% 5.45/5.77 ! [G: int > int,H: int > int,A3: set_int] :
% 5.45/5.77 ( ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( plus_plus_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A3 ) @ ( groups4538972089207619220nt_int @ H @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.distrib
% 5.45/5.77 thf(fact_6203_sum__product,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat,G: nat > nat,B3: set_nat] :
% 5.45/5.77 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] :
% 5.45/5.77 ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.45/5.77 @ B3 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_product
% 5.45/5.77 thf(fact_6204_sum__product,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int,G: int > int,B3: set_int] :
% 5.45/5.77 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [I4: int] :
% 5.45/5.77 ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [J3: int] : ( times_times_int @ ( F @ I4 ) @ ( G @ J3 ) )
% 5.45/5.77 @ B3 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_product
% 5.45/5.77 thf(fact_6205_sum__distrib__right,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat,R3: nat] :
% 5.45/5.77 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ R3 )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [N: nat] : ( times_times_nat @ ( F @ N ) @ R3 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_distrib_right
% 5.45/5.77 thf(fact_6206_sum__distrib__right,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int,R3: int] :
% 5.45/5.77 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ R3 )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [N: int] : ( times_times_int @ ( F @ N ) @ R3 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_distrib_right
% 5.45/5.77 thf(fact_6207_sum__distrib__left,axiom,
% 5.45/5.77 ! [R3: nat,F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( times_times_nat @ R3 @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [N: nat] : ( times_times_nat @ R3 @ ( F @ N ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_distrib_left
% 5.45/5.77 thf(fact_6208_sum__distrib__left,axiom,
% 5.45/5.77 ! [R3: int,F: int > int,A3: set_int] :
% 5.45/5.77 ( ( times_times_int @ R3 @ ( groups4538972089207619220nt_int @ F @ A3 ) )
% 5.45/5.77 = ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [N: int] : ( times_times_int @ R3 @ ( F @ N ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_distrib_left
% 5.45/5.77 thf(fact_6209_sum__subtractf,axiom,
% 5.45/5.77 ! [F: int > int,G: int > int,A3: set_int] :
% 5.45/5.77 ( ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( minus_minus_int @ ( F @ X4 ) @ ( G @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_subtractf
% 5.45/5.77 thf(fact_6210_sum__negf,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( groups4538972089207619220nt_int
% 5.45/5.77 @ ^ [X4: int] : ( uminus_uminus_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( uminus_uminus_int @ ( groups4538972089207619220nt_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_negf
% 5.45/5.77 thf(fact_6211_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6212_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6213_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6214_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > rat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6215_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > rat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6216_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > rat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6217_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > nat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6218_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6219_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > int] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( groups8505340233167759370_o_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6220_sum__nonneg,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > int] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( groups3539618377306564664at_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonneg
% 5.45/5.77 thf(fact_6221_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups4406642042086082107nteger @ F @ A3 ) @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6222_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ A3 ) @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6223_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ zero_z3403309356797280102nteger ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ A3 ) @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6224_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > rat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6225_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > rat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6226_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > rat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ ( F @ X3 ) @ zero_zero_rat ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6227_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > nat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6228_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ ( F @ X3 ) @ zero_zero_nat ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ zero_zero_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6229_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > int] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ zero_zero_int ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6230_sum__nonpos,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > int] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ ( F @ X3 ) @ zero_zero_int ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_nonpos
% 5.45/5.77 thf(fact_6231_gbinomial__partial__sum__poly__xpos,axiom,
% 5.45/5.77 ! [M: nat,A: rat,X: rat,Y: rat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.77 = ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [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 @ M @ K3 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_partial_sum_poly_xpos
% 5.45/5.77 thf(fact_6232_sum__gp0,axiom,
% 5.45/5.77 ! [X: rat,N2: nat] :
% 5.45/5.77 ( ( ( X = one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.45/5.77 & ( ( X != one_one_rat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp0
% 5.45/5.77 thf(fact_6233_divmod__nat__def,axiom,
% 5.45/5.77 ( divmod_nat
% 5.45/5.77 = ( ^ [M3: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N ) @ ( modulo_modulo_nat @ M3 @ N ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % divmod_nat_def
% 5.45/5.77 thf(fact_6234_sorted__in__between,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,L: list_o,X: $o] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ L ) )
% 5.45/5.77 => ( ( sorted_wrt_o @ ord_less_eq_o @ L )
% 5.45/5.77 => ( ( ord_less_eq_o @ ( nth_o @ L @ I2 ) @ X )
% 5.45/5.77 => ( ( ord_less_o @ X @ ( nth_o @ L @ J ) )
% 5.45/5.77 => ~ ! [K2: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ K2 )
% 5.45/5.77 => ( ( ord_less_nat @ K2 @ J )
% 5.45/5.77 => ( ( ord_less_eq_o @ ( nth_o @ L @ K2 ) @ X )
% 5.45/5.77 => ~ ( ord_less_o @ X @ ( nth_o @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_in_between
% 5.45/5.77 thf(fact_6235_sorted__in__between,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,L: list_rat,X: rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ L ) )
% 5.45/5.77 => ( ( sorted_wrt_rat @ ord_less_eq_rat @ L )
% 5.45/5.77 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ I2 ) @ X )
% 5.45/5.77 => ( ( ord_less_rat @ X @ ( nth_rat @ L @ J ) )
% 5.45/5.77 => ~ ! [K2: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ K2 )
% 5.45/5.77 => ( ( ord_less_nat @ K2 @ J )
% 5.45/5.77 => ( ( ord_less_eq_rat @ ( nth_rat @ L @ K2 ) @ X )
% 5.45/5.77 => ~ ( ord_less_rat @ X @ ( nth_rat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_in_between
% 5.45/5.77 thf(fact_6236_sorted__in__between,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,L: list_num,X: num] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_num @ L ) )
% 5.45/5.77 => ( ( sorted_wrt_num @ ord_less_eq_num @ L )
% 5.45/5.77 => ( ( ord_less_eq_num @ ( nth_num @ L @ I2 ) @ X )
% 5.45/5.77 => ( ( ord_less_num @ X @ ( nth_num @ L @ J ) )
% 5.45/5.77 => ~ ! [K2: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ K2 )
% 5.45/5.77 => ( ( ord_less_nat @ K2 @ J )
% 5.45/5.77 => ( ( ord_less_eq_num @ ( nth_num @ L @ K2 ) @ X )
% 5.45/5.77 => ~ ( ord_less_num @ X @ ( nth_num @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_in_between
% 5.45/5.77 thf(fact_6237_sorted__in__between,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,L: list_nat,X: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ L ) )
% 5.45/5.77 => ( ( sorted_wrt_nat @ ord_less_eq_nat @ L )
% 5.45/5.77 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ I2 ) @ X )
% 5.45/5.77 => ( ( ord_less_nat @ X @ ( nth_nat @ L @ J ) )
% 5.45/5.77 => ~ ! [K2: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ K2 )
% 5.45/5.77 => ( ( ord_less_nat @ K2 @ J )
% 5.45/5.77 => ( ( ord_less_eq_nat @ ( nth_nat @ L @ K2 ) @ X )
% 5.45/5.77 => ~ ( ord_less_nat @ X @ ( nth_nat @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_in_between
% 5.45/5.77 thf(fact_6238_sorted__in__between,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,L: list_int,X: int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ I2 )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ L ) )
% 5.45/5.77 => ( ( sorted_wrt_int @ ord_less_eq_int @ L )
% 5.45/5.77 => ( ( ord_less_eq_int @ ( nth_int @ L @ I2 ) @ X )
% 5.45/5.77 => ( ( ord_less_int @ X @ ( nth_int @ L @ J ) )
% 5.45/5.77 => ~ ! [K2: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ K2 )
% 5.45/5.77 => ( ( ord_less_nat @ K2 @ J )
% 5.45/5.77 => ( ( ord_less_eq_int @ ( nth_int @ L @ K2 ) @ X )
% 5.45/5.77 => ~ ( ord_less_int @ X @ ( nth_int @ L @ ( plus_plus_nat @ K2 @ one_one_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_in_between
% 5.45/5.77 thf(fact_6239_gbinomial__Suc,axiom,
% 5.45/5.77 ! [A: rat,K: nat] :
% 5.45/5.77 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.45/5.77 = ( divide_divide_rat
% 5.45/5.77 @ ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.45/5.77 @ ( semiri773545260158071498ct_rat @ ( suc @ K ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_Suc
% 5.45/5.77 thf(fact_6240_gbinomial__Suc,axiom,
% 5.45/5.77 ! [A: code_natural,K: nat] :
% 5.45/5.77 ( ( gbinom7368847122466276068atural @ A @ ( suc @ K ) )
% 5.45/5.77 = ( divide5121882707175180666atural
% 5.45/5.77 @ ( groups2279045934846249631atural
% 5.45/5.77 @ ^ [I4: nat] : ( minus_7197305767214868737atural @ A @ ( semiri3763490453095760265atural @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.45/5.77 @ ( semiri2447717529341329178atural @ ( suc @ K ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_Suc
% 5.45/5.77 thf(fact_6241_gbinomial__Suc,axiom,
% 5.45/5.77 ! [A: code_integer,K: nat] :
% 5.45/5.77 ( ( gbinom8545251970709558553nteger @ A @ ( suc @ K ) )
% 5.45/5.77 = ( divide6298287555418463151nteger
% 5.45/5.77 @ ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( minus_8373710615458151222nteger @ A @ ( semiri4939895301339042750nteger @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.45/5.77 @ ( semiri3624122377584611663nteger @ ( suc @ K ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_Suc
% 5.45/5.77 thf(fact_6242_gbinomial__Suc,axiom,
% 5.45/5.77 ! [A: nat,K: nat] :
% 5.45/5.77 ( ( gbinomial_nat @ A @ ( suc @ K ) )
% 5.45/5.77 = ( divide_divide_nat
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.45/5.77 @ ( semiri1408675320244567234ct_nat @ ( suc @ K ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_Suc
% 5.45/5.77 thf(fact_6243_gbinomial__Suc,axiom,
% 5.45/5.77 ! [A: int,K: nat] :
% 5.45/5.77 ( ( gbinomial_int @ A @ ( suc @ K ) )
% 5.45/5.77 = ( divide_divide_int
% 5.45/5.77 @ ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) )
% 5.45/5.77 @ ( semiri1406184849735516958ct_int @ ( suc @ K ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_Suc
% 5.45/5.77 thf(fact_6244_gbinomial__partial__sum__poly,axiom,
% 5.45/5.77 ! [M: nat,A: rat,X: rat,Y: rat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.77 = ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [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 @ M @ K3 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_partial_sum_poly
% 5.45/5.77 thf(fact_6245_atMost__iff,axiom,
% 5.45/5.77 ! [I2: $o,K: $o] :
% 5.45/5.77 ( ( member_o @ I2 @ ( set_ord_atMost_o @ K ) )
% 5.45/5.77 = ( ord_less_eq_o @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6246_atMost__iff,axiom,
% 5.45/5.77 ! [I2: set_nat,K: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ I2 @ ( set_or4236626031148496127et_nat @ K ) )
% 5.45/5.77 = ( ord_less_eq_set_nat @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6247_atMost__iff,axiom,
% 5.45/5.77 ! [I2: set_int,K: set_int] :
% 5.45/5.77 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 5.45/5.77 = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6248_atMost__iff,axiom,
% 5.45/5.77 ! [I2: rat,K: rat] :
% 5.45/5.77 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.45/5.77 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6249_atMost__iff,axiom,
% 5.45/5.77 ! [I2: num,K: num] :
% 5.45/5.77 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.45/5.77 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6250_atMost__iff,axiom,
% 5.45/5.77 ! [I2: nat,K: nat] :
% 5.45/5.77 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.45/5.77 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6251_atMost__iff,axiom,
% 5.45/5.77 ! [I2: int,K: int] :
% 5.45/5.77 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.45/5.77 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_iff
% 5.45/5.77 thf(fact_6252_prod_Oneutral__const,axiom,
% 5.45/5.77 ! [A3: set_nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [Uu2: nat] : one_one_nat
% 5.45/5.77 @ A3 )
% 5.45/5.77 = one_one_nat ) ).
% 5.45/5.77
% 5.45/5.77 % prod.neutral_const
% 5.45/5.77 thf(fact_6253_prod_Oneutral__const,axiom,
% 5.45/5.77 ! [A3: set_nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [Uu2: nat] : one_one_int
% 5.45/5.77 @ A3 )
% 5.45/5.77 = one_one_int ) ).
% 5.45/5.77
% 5.45/5.77 % prod.neutral_const
% 5.45/5.77 thf(fact_6254_prod_Oneutral__const,axiom,
% 5.45/5.77 ! [A3: set_int] :
% 5.45/5.77 ( ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [Uu2: int] : one_one_int
% 5.45/5.77 @ A3 )
% 5.45/5.77 = one_one_int ) ).
% 5.45/5.77
% 5.45/5.77 % prod.neutral_const
% 5.45/5.77 thf(fact_6255_of__nat__prod,axiom,
% 5.45/5.77 ! [F: int > nat,A3: set_int] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_prod
% 5.45/5.77 thf(fact_6256_of__nat__prod,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [X4: nat] : ( semiri4939895301339042750nteger @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_prod
% 5.45/5.77 thf(fact_6257_of__nat__prod,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1316708129612266289at_nat @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_prod
% 5.45/5.77 thf(fact_6258_of__nat__prod,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_nat_prod
% 5.45/5.77 thf(fact_6259_of__int__prod,axiom,
% 5.45/5.77 ! [F: nat > int,A3: set_nat] :
% 5.45/5.77 ( ( ring_1_of_int_rat @ ( groups705719431365010083at_int @ F @ A3 ) )
% 5.45/5.77 = ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [X4: nat] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_prod
% 5.45/5.77 thf(fact_6260_of__int__prod,axiom,
% 5.45/5.77 ! [F: nat > int,A3: set_nat] :
% 5.45/5.77 ( ( ring_1_of_int_int @ ( groups705719431365010083at_int @ F @ A3 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [X4: nat] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_prod
% 5.45/5.77 thf(fact_6261_of__int__prod,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( ring_1_of_int_rat @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 5.45/5.77 = ( groups1072433553688619179nt_rat
% 5.45/5.77 @ ^ [X4: int] : ( ring_1_of_int_rat @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_prod
% 5.45/5.77 thf(fact_6262_of__int__prod,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int] :
% 5.45/5.77 ( ( ring_1_of_int_int @ ( groups1705073143266064639nt_int @ F @ A3 ) )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [X4: int] : ( ring_1_of_int_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % of_int_prod
% 5.45/5.77 thf(fact_6263_prod_Oempty,axiom,
% 5.45/5.77 ! [G: $o > code_integer] :
% 5.45/5.77 ( ( groups7694694392188491536nteger @ G @ bot_bot_set_o )
% 5.45/5.77 = one_one_Code_integer ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6264_prod_Oempty,axiom,
% 5.45/5.77 ! [G: $o > assn] :
% 5.45/5.77 ( ( groups5301882518646026715o_assn @ G @ bot_bot_set_o )
% 5.45/5.77 = one_one_assn ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6265_prod_Oempty,axiom,
% 5.45/5.77 ! [G: $o > rat] :
% 5.45/5.77 ( ( groups2869687844427037835_o_rat @ G @ bot_bot_set_o )
% 5.45/5.77 = one_one_rat ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6266_prod_Oempty,axiom,
% 5.45/5.77 ! [G: $o > nat] :
% 5.45/5.77 ( ( groups3504817904513533571_o_nat @ G @ bot_bot_set_o )
% 5.45/5.77 = one_one_nat ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6267_prod_Oempty,axiom,
% 5.45/5.77 ! [G: $o > int] :
% 5.45/5.77 ( ( groups3502327434004483295_o_int @ G @ bot_bot_set_o )
% 5.45/5.77 = one_one_int ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6268_prod_Oempty,axiom,
% 5.45/5.77 ! [G: nat > code_integer] :
% 5.45/5.77 ( ( groups3455450783089532116nteger @ G @ bot_bot_set_nat )
% 5.45/5.77 = one_one_Code_integer ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6269_prod_Oempty,axiom,
% 5.45/5.77 ! [G: nat > assn] :
% 5.45/5.77 ( ( groups6906906614972039071t_assn @ G @ bot_bot_set_nat )
% 5.45/5.77 = one_one_assn ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6270_prod_Oempty,axiom,
% 5.45/5.77 ! [G: nat > rat] :
% 5.45/5.77 ( ( groups73079841787564623at_rat @ G @ bot_bot_set_nat )
% 5.45/5.77 = one_one_rat ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6271_prod_Oempty,axiom,
% 5.45/5.77 ! [G: int > code_integer] :
% 5.45/5.77 ( ( groups3827104343326376752nteger @ G @ bot_bot_set_int )
% 5.45/5.77 = one_one_Code_integer ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6272_prod_Oempty,axiom,
% 5.45/5.77 ! [G: int > assn] :
% 5.45/5.77 ( ( groups7882442080178216443t_assn @ G @ bot_bot_set_int )
% 5.45/5.77 = one_one_assn ) ).
% 5.45/5.77
% 5.45/5.77 % prod.empty
% 5.45/5.77 thf(fact_6273_atMost__subset__iff,axiom,
% 5.45/5.77 ! [X: set_int,Y: set_int] :
% 5.45/5.77 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X ) @ ( set_or58775011639299419et_int @ Y ) )
% 5.45/5.77 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_subset_iff
% 5.45/5.77 thf(fact_6274_atMost__subset__iff,axiom,
% 5.45/5.77 ! [X: rat,Y: rat] :
% 5.45/5.77 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X ) @ ( set_ord_atMost_rat @ Y ) )
% 5.45/5.77 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_subset_iff
% 5.45/5.77 thf(fact_6275_atMost__subset__iff,axiom,
% 5.45/5.77 ! [X: num,Y: num] :
% 5.45/5.77 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X ) @ ( set_ord_atMost_num @ Y ) )
% 5.45/5.77 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_subset_iff
% 5.45/5.77 thf(fact_6276_atMost__subset__iff,axiom,
% 5.45/5.77 ! [X: nat,Y: nat] :
% 5.45/5.77 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X ) @ ( set_ord_atMost_nat @ Y ) )
% 5.45/5.77 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_subset_iff
% 5.45/5.77 thf(fact_6277_atMost__subset__iff,axiom,
% 5.45/5.77 ! [X: int,Y: int] :
% 5.45/5.77 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X ) @ ( set_ord_atMost_int @ Y ) )
% 5.45/5.77 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_subset_iff
% 5.45/5.77 thf(fact_6278_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: set_int,H: set_int,H3: set_int] :
% 5.45/5.77 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H ) @ ( set_or58775011639299419et_int @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_less_eq_set_int @ L @ H )
% 5.45/5.77 | ( ord_less_eq_set_int @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6279_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: rat,H: rat,H3: rat] :
% 5.45/5.77 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_less_eq_rat @ L @ H )
% 5.45/5.77 | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6280_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: num,H: num,H3: num] :
% 5.45/5.77 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_less_eq_num @ L @ H )
% 5.45/5.77 | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6281_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: int,H: int,H3: int] :
% 5.45/5.77 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_less_eq_int @ L @ H )
% 5.45/5.77 | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6282_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: nat,H: nat,H3: nat] :
% 5.45/5.77 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_less_eq_nat @ L @ H )
% 5.45/5.77 | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6283_Icc__subset__Iic__iff,axiom,
% 5.45/5.77 ! [L: code_integer,H: code_integer,H3: code_integer] :
% 5.45/5.77 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ L @ H ) @ ( set_or9101266186257409494nteger @ H3 ) )
% 5.45/5.77 = ( ~ ( ord_le3102999989581377725nteger @ L @ H )
% 5.45/5.77 | ( ord_le3102999989581377725nteger @ H @ H3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % Icc_subset_Iic_iff
% 5.45/5.77 thf(fact_6284_prod_OatMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > code_integer,N2: nat] :
% 5.45/5.77 ( ( groups3455450783089532116nteger @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc
% 5.45/5.77 thf(fact_6285_prod_OatMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > assn,N2: nat] :
% 5.45/5.77 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc
% 5.45/5.77 thf(fact_6286_prod_OatMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > rat,N2: nat] :
% 5.45/5.77 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc
% 5.45/5.77 thf(fact_6287_prod_OatMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc
% 5.45/5.77 thf(fact_6288_prod_OatMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > int,N2: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc
% 5.45/5.77 thf(fact_6289_prod_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_Code_integer ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.cl_ivl_Suc
% 5.45/5.77 thf(fact_6290_prod_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > assn] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_assn ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.cl_ivl_Suc
% 5.45/5.77 thf(fact_6291_prod_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_rat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.cl_ivl_Suc
% 5.45/5.77 thf(fact_6292_prod_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.cl_ivl_Suc
% 5.45/5.77 thf(fact_6293_prod_Ocl__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.77 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_int ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.cl_ivl_Suc
% 5.45/5.77 thf(fact_6294_prod_Oswap,axiom,
% 5.45/5.77 ! [G: nat > nat > nat,B3: set_nat,A3: set_nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [J3: nat] :
% 5.45/5.77 ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.swap
% 5.45/5.77 thf(fact_6295_prod_Oswap,axiom,
% 5.45/5.77 ! [G: nat > nat > int,B3: set_nat,A3: set_nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [J3: nat] :
% 5.45/5.77 ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.swap
% 5.45/5.77 thf(fact_6296_prod_Oswap,axiom,
% 5.45/5.77 ! [G: nat > int > int,B3: set_int,A3: set_nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( groups1705073143266064639nt_int @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [J3: int] :
% 5.45/5.77 ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.swap
% 5.45/5.77 thf(fact_6297_prod_Oswap,axiom,
% 5.45/5.77 ! [G: int > nat > int,B3: set_nat,A3: set_int] :
% 5.45/5.77 ( ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [I4: int] : ( groups705719431365010083at_int @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [J3: nat] :
% 5.45/5.77 ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.swap
% 5.45/5.77 thf(fact_6298_prod_Oswap,axiom,
% 5.45/5.77 ! [G: int > int > int,B3: set_int,A3: set_int] :
% 5.45/5.77 ( ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [I4: int] : ( groups1705073143266064639nt_int @ ( G @ I4 ) @ B3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [J3: int] :
% 5.45/5.77 ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [I4: int] : ( G @ I4 @ J3 )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ B3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.swap
% 5.45/5.77 thf(fact_6299_sorted__wrt__true,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( sorted_wrt_nat
% 5.45/5.77 @ ^ [Uu2: nat,Uv: nat] : $true
% 5.45/5.77 @ Xs ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_true
% 5.45/5.77 thf(fact_6300_sorted__wrt__true,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( sorted_wrt_int
% 5.45/5.77 @ ^ [Uu2: int,Uv: int] : $true
% 5.45/5.77 @ Xs ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_true
% 5.45/5.77 thf(fact_6301_not__empty__eq__Iic__eq__empty,axiom,
% 5.45/5.77 ! [H: $o] :
% 5.45/5.77 ( bot_bot_set_o
% 5.45/5.77 != ( set_ord_atMost_o @ H ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_empty_eq_Iic_eq_empty
% 5.45/5.77 thf(fact_6302_not__empty__eq__Iic__eq__empty,axiom,
% 5.45/5.77 ! [H: nat] :
% 5.45/5.77 ( bot_bot_set_nat
% 5.45/5.77 != ( set_ord_atMost_nat @ H ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_empty_eq_Iic_eq_empty
% 5.45/5.77 thf(fact_6303_not__empty__eq__Iic__eq__empty,axiom,
% 5.45/5.77 ! [H: int] :
% 5.45/5.77 ( bot_bot_set_int
% 5.45/5.77 != ( set_ord_atMost_int @ H ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_empty_eq_Iic_eq_empty
% 5.45/5.77 thf(fact_6304_prod_Odistrib,axiom,
% 5.45/5.77 ! [G: nat > nat,H: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( times_times_nat @ ( G @ X4 ) @ ( H @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ A3 ) @ ( groups708209901874060359at_nat @ H @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.distrib
% 5.45/5.77 thf(fact_6305_prod_Odistrib,axiom,
% 5.45/5.77 ! [G: nat > int,H: nat > int,A3: set_nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [X4: nat] : ( times_times_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ A3 ) @ ( groups705719431365010083at_int @ H @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.distrib
% 5.45/5.77 thf(fact_6306_prod_Odistrib,axiom,
% 5.45/5.77 ! [G: int > int,H: int > int,A3: set_int] :
% 5.45/5.77 ( ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [X4: int] : ( times_times_int @ ( G @ X4 ) @ ( H @ X4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( times_times_int @ ( groups1705073143266064639nt_int @ G @ A3 ) @ ( groups1705073143266064639nt_int @ H @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.distrib
% 5.45/5.77 thf(fact_6307_prod__power__distrib,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat,N2: nat] :
% 5.45/5.77 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ N2 )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : ( power_power_nat @ ( F @ X4 ) @ N2 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_power_distrib
% 5.45/5.77 thf(fact_6308_prod__power__distrib,axiom,
% 5.45/5.77 ! [F: nat > int,A3: set_nat,N2: nat] :
% 5.45/5.77 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A3 ) @ N2 )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [X4: nat] : ( power_power_int @ ( F @ X4 ) @ N2 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_power_distrib
% 5.45/5.77 thf(fact_6309_prod__power__distrib,axiom,
% 5.45/5.77 ! [F: int > int,A3: set_int,N2: nat] :
% 5.45/5.77 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ N2 )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [X4: int] : ( power_power_int @ ( F @ X4 ) @ N2 )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_power_distrib
% 5.45/5.77 thf(fact_6310_mod__prod__eq,axiom,
% 5.45/5.77 ! [F: nat > nat,A: nat,A3: set_nat] :
% 5.45/5.77 ( ( modulo_modulo_nat
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( modulo_modulo_nat @ ( F @ I4 ) @ A )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ A )
% 5.45/5.77 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ A ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod_prod_eq
% 5.45/5.77 thf(fact_6311_mod__prod__eq,axiom,
% 5.45/5.77 ! [F: nat > int,A: int,A3: set_nat] :
% 5.45/5.77 ( ( modulo_modulo_int
% 5.45/5.77 @ ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ A )
% 5.45/5.77 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A3 ) @ A ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod_prod_eq
% 5.45/5.77 thf(fact_6312_mod__prod__eq,axiom,
% 5.45/5.77 ! [F: int > int,A: int,A3: set_int] :
% 5.45/5.77 ( ( modulo_modulo_int
% 5.45/5.77 @ ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [I4: int] : ( modulo_modulo_int @ ( F @ I4 ) @ A )
% 5.45/5.77 @ A3 )
% 5.45/5.77 @ A )
% 5.45/5.77 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ A ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod_prod_eq
% 5.45/5.77 thf(fact_6313_prod_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > code_integer,N2: nat] :
% 5.45/5.77 ( ( groups3455450783089532116nteger @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc_shift
% 5.45/5.77 thf(fact_6314_prod_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > assn,N2: nat] :
% 5.45/5.77 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc_shift
% 5.45/5.77 thf(fact_6315_prod_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > rat,N2: nat] :
% 5.45/5.77 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc_shift
% 5.45/5.77 thf(fact_6316_prod_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc_shift
% 5.45/5.77 thf(fact_6317_prod_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > int,N2: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atMost_Suc_shift
% 5.45/5.77 thf(fact_6318_atMost__def,axiom,
% 5.45/5.77 ( set_or4236626031148496127et_nat
% 5.45/5.77 = ( ^ [U2: set_nat] :
% 5.45/5.77 ( collect_set_nat
% 5.45/5.77 @ ^ [X4: set_nat] : ( ord_less_eq_set_nat @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6319_atMost__def,axiom,
% 5.45/5.77 ( set_or58775011639299419et_int
% 5.45/5.77 = ( ^ [U2: set_int] :
% 5.45/5.77 ( collect_set_int
% 5.45/5.77 @ ^ [X4: set_int] : ( ord_less_eq_set_int @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6320_atMost__def,axiom,
% 5.45/5.77 ( set_ord_atMost_rat
% 5.45/5.77 = ( ^ [U2: rat] :
% 5.45/5.77 ( collect_rat
% 5.45/5.77 @ ^ [X4: rat] : ( ord_less_eq_rat @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6321_atMost__def,axiom,
% 5.45/5.77 ( set_ord_atMost_num
% 5.45/5.77 = ( ^ [U2: num] :
% 5.45/5.77 ( collect_num
% 5.45/5.77 @ ^ [X4: num] : ( ord_less_eq_num @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6322_atMost__def,axiom,
% 5.45/5.77 ( set_ord_atMost_nat
% 5.45/5.77 = ( ^ [U2: nat] :
% 5.45/5.77 ( collect_nat
% 5.45/5.77 @ ^ [X4: nat] : ( ord_less_eq_nat @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6323_atMost__def,axiom,
% 5.45/5.77 ( set_ord_atMost_int
% 5.45/5.77 = ( ^ [U2: int] :
% 5.45/5.77 ( collect_int
% 5.45/5.77 @ ^ [X4: int] : ( ord_less_eq_int @ X4 @ U2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atMost_def
% 5.45/5.77 thf(fact_6324_strict__sorted__imp__sorted,axiom,
% 5.45/5.77 ! [Xs: list_rat] :
% 5.45/5.77 ( ( sorted_wrt_rat @ ord_less_rat @ Xs )
% 5.45/5.77 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % strict_sorted_imp_sorted
% 5.45/5.77 thf(fact_6325_strict__sorted__imp__sorted,axiom,
% 5.45/5.77 ! [Xs: list_num] :
% 5.45/5.77 ( ( sorted_wrt_num @ ord_less_num @ Xs )
% 5.45/5.77 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % strict_sorted_imp_sorted
% 5.45/5.77 thf(fact_6326_strict__sorted__imp__sorted,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_nat @ Xs )
% 5.45/5.77 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % strict_sorted_imp_sorted
% 5.45/5.77 thf(fact_6327_strict__sorted__imp__sorted,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( ( sorted_wrt_int @ ord_less_int @ Xs )
% 5.45/5.77 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % strict_sorted_imp_sorted
% 5.45/5.77 thf(fact_6328_prod__nonneg,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_nonneg
% 5.45/5.77 thf(fact_6329_prod__nonneg,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > int] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_nonneg
% 5.45/5.77 thf(fact_6330_prod__nonneg,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > int] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_nonneg
% 5.45/5.77 thf(fact_6331_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > code_integer,G: $o > code_integer] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A3 ) @ ( groups7694694392188491536nteger @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6332_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A3 ) @ ( groups3455450783089532116nteger @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6333_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > code_integer,G: int > code_integer] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A3 ) @ ( groups3827104343326376752nteger @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6334_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > rat,G: $o > rat] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A3 ) @ ( groups2869687844427037835_o_rat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6335_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6336_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6337_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > nat,G: $o > nat] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A3 ) @ ( groups3504817904513533571_o_nat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6338_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat,G: int > nat] :
% 5.45/5.77 ( ! [I3: int] :
% 5.45/5.77 ( ( member_int @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6339_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > int,G: $o > int] :
% 5.45/5.77 ( ! [I3: $o] :
% 5.45/5.77 ( ( member_o @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A3 ) @ ( groups3502327434004483295_o_int @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6340_prod__mono,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat,G: nat > nat] :
% 5.45/5.77 ( ! [I3: nat] :
% 5.45/5.77 ( ( member_nat @ I3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ ( groups708209901874060359at_nat @ G @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_mono
% 5.45/5.77 thf(fact_6341_prod__pos,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos
% 5.45/5.77 thf(fact_6342_prod__pos,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > int] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos
% 5.45/5.77 thf(fact_6343_prod__pos,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > int] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos
% 5.45/5.77 thf(fact_6344_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6345_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6346_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6347_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > rat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6348_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > rat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6349_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > rat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6350_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > nat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( groups3504817904513533571_o_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6351_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6352_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > int] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_int @ one_one_int @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6353_prod__ge__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( F @ X3 ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ one_one_nat @ ( groups708209901874060359at_nat @ F @ A3 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_ge_1
% 5.45/5.77 thf(fact_6354_sorted__wrt__less__idx,axiom,
% 5.45/5.77 ! [Ns: list_nat,I2: nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.45/5.77 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_less_idx
% 5.45/5.77 thf(fact_6355_not__Iic__le__Icc,axiom,
% 5.45/5.77 ! [H: int,L3: int,H3: int] :
% 5.45/5.77 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_Iic_le_Icc
% 5.45/5.77 thf(fact_6356_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.45/5.77 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.shift_bounds_cl_Suc_ivl
% 5.45/5.77 thf(fact_6357_prod_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.45/5.77 ! [G: nat > int,M: nat,N2: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.shift_bounds_cl_Suc_ivl
% 5.45/5.77 thf(fact_6358_power__sum,axiom,
% 5.45/5.77 ! [C: nat,F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( power_power_nat @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [A5: nat] : ( power_power_nat @ C @ ( F @ A5 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % power_sum
% 5.45/5.77 thf(fact_6359_power__sum,axiom,
% 5.45/5.77 ! [C: int,F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( power_power_int @ C @ ( groups3542108847815614940at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [A5: nat] : ( power_power_int @ C @ ( F @ A5 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % power_sum
% 5.45/5.77 thf(fact_6360_power__sum,axiom,
% 5.45/5.77 ! [C: int,F: int > nat,A3: set_int] :
% 5.45/5.77 ( ( power_power_int @ C @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [A5: int] : ( power_power_int @ C @ ( F @ A5 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % power_sum
% 5.45/5.77 thf(fact_6361_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.45/5.77 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.shift_bounds_cl_nat_ivl
% 5.45/5.77 thf(fact_6362_prod_Oshift__bounds__cl__nat__ivl,axiom,
% 5.45/5.77 ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.shift_bounds_cl_nat_ivl
% 5.45/5.77 thf(fact_6363_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A3 ) @ one_one_Code_integer ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6364_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A3 ) @ one_one_Code_integer ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6365_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ one_one_Code_integer ) ) )
% 5.45/5.77 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A3 ) @ one_one_Code_integer ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6366_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > rat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6367_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > rat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6368_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > rat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_rat @ ( F @ X3 ) @ one_one_rat ) ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ one_one_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6369_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > nat] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups3504817904513533571_o_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6370_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat] :
% 5.45/5.77 ( ! [X3: int] :
% 5.45/5.77 ( ( member_int @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6371_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_o,F: $o > int] :
% 5.45/5.77 ( ! [X3: $o] :
% 5.45/5.77 ( ( member_o @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_int @ ( F @ X3 ) @ one_one_int ) ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A3 ) @ one_one_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6372_prod__le__1,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.77 ( ! [X3: nat] :
% 5.45/5.77 ( ( member_nat @ X3 @ A3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) )
% 5.45/5.77 & ( ord_less_eq_nat @ ( F @ X3 ) @ one_one_nat ) ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ one_one_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_le_1
% 5.45/5.77 thf(fact_6373_sorted__wrt__iff__nth__less,axiom,
% 5.45/5.77 ( sorted_wrt_int
% 5.45/5.77 = ( ^ [P4: int > int > $o,Xs3: list_int] :
% 5.45/5.77 ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs3 ) )
% 5.45/5.77 => ( P4 @ ( nth_int @ Xs3 @ I4 ) @ ( nth_int @ Xs3 @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_iff_nth_less
% 5.45/5.77 thf(fact_6374_sorted__wrt__iff__nth__less,axiom,
% 5.45/5.77 ( sorted_wrt_nat
% 5.45/5.77 = ( ^ [P4: nat > nat > $o,Xs3: list_nat] :
% 5.45/5.77 ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs3 ) )
% 5.45/5.77 => ( P4 @ ( nth_nat @ Xs3 @ I4 ) @ ( nth_nat @ Xs3 @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_iff_nth_less
% 5.45/5.77 thf(fact_6375_sorted__wrt__iff__nth__less,axiom,
% 5.45/5.77 ( sorted_wrt_o
% 5.45/5.77 = ( ^ [P4: $o > $o > $o,Xs3: list_o] :
% 5.45/5.77 ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs3 ) )
% 5.45/5.77 => ( P4 @ ( nth_o @ Xs3 @ I4 ) @ ( nth_o @ Xs3 @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_iff_nth_less
% 5.45/5.77 thf(fact_6376_sorted__wrt__nth__less,axiom,
% 5.45/5.77 ! [P: int > int > $o,Xs: list_int,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_int @ P @ Xs )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( P @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_nth_less
% 5.45/5.77 thf(fact_6377_sorted__wrt__nth__less,axiom,
% 5.45/5.77 ! [P: nat > nat > $o,Xs: list_nat,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ P @ Xs )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( P @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_nth_less
% 5.45/5.77 thf(fact_6378_sorted__wrt__nth__less,axiom,
% 5.45/5.77 ! [P: $o > $o > $o,Xs: list_o,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_o @ P @ Xs )
% 5.45/5.77 => ( ( ord_less_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( P @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt_nth_less
% 5.45/5.77 thf(fact_6379_sorted__wrt01,axiom,
% 5.45/5.77 ! [Xs: list_int,P: int > int > $o] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_int @ P @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt01
% 5.45/5.77 thf(fact_6380_sorted__wrt01,axiom,
% 5.45/5.77 ! [Xs: list_nat,P: nat > nat > $o] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_nat @ P @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt01
% 5.45/5.77 thf(fact_6381_sorted__wrt01,axiom,
% 5.45/5.77 ! [Xs: list_o,P: $o > $o > $o] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_o @ P @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_wrt01
% 5.45/5.77 thf(fact_6382_prod_OatLeastAtMost__rev,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeastAtMost_rev
% 5.45/5.77 thf(fact_6383_prod_OatLeastAtMost__rev,axiom,
% 5.45/5.77 ! [G: nat > int,N2: nat,M: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeastAtMost_rev
% 5.45/5.77 thf(fact_6384_prod_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > code_integer,H: nat > code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ one_one_Code_integer @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.zero_middle
% 5.45/5.77 thf(fact_6385_prod_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > assn,H: nat > assn] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_assn @ ( J3 = K ) @ one_one_assn @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [J3: nat] : ( if_assn @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.zero_middle
% 5.45/5.77 thf(fact_6386_prod_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > rat,H: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ one_one_rat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.zero_middle
% 5.45/5.77 thf(fact_6387_prod_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > nat,H: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ one_one_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.zero_middle
% 5.45/5.77 thf(fact_6388_prod_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > int,H: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ one_one_int @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.zero_middle
% 5.45/5.77 thf(fact_6389_sorted__iff__nth__mono__less,axiom,
% 5.45/5.77 ! [Xs: list_o] :
% 5.45/5.77 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_o @ ( nth_o @ Xs @ I4 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono_less
% 5.45/5.77 thf(fact_6390_sorted__iff__nth__mono__less,axiom,
% 5.45/5.77 ! [Xs: list_rat] :
% 5.45/5.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I4 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono_less
% 5.45/5.77 thf(fact_6391_sorted__iff__nth__mono__less,axiom,
% 5.45/5.77 ! [Xs: list_num] :
% 5.45/5.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_num @ ( nth_num @ Xs @ I4 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono_less
% 5.45/5.77 thf(fact_6392_sorted__iff__nth__mono__less,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono_less
% 5.45/5.77 thf(fact_6393_sorted__iff__nth__mono__less,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono_less
% 5.45/5.77 thf(fact_6394_sorted01,axiom,
% 5.45/5.77 ! [Xs: list_o] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_o @ ord_less_eq_o @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted01
% 5.45/5.77 thf(fact_6395_sorted01,axiom,
% 5.45/5.77 ! [Xs: list_rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_rat @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_rat @ ord_less_eq_rat @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted01
% 5.45/5.77 thf(fact_6396_sorted01,axiom,
% 5.45/5.77 ! [Xs: list_num] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_num @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_num @ ord_less_eq_num @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted01
% 5.45/5.77 thf(fact_6397_sorted01,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_nat @ ord_less_eq_nat @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted01
% 5.45/5.77 thf(fact_6398_sorted01,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ one_one_nat )
% 5.45/5.77 => ( sorted_wrt_int @ ord_less_eq_int @ Xs ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted01
% 5.45/5.77 thf(fact_6399_prod_OatLeast0__atMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > code_integer,N2: nat] :
% 5.45/5.77 ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast0_atMost_Suc
% 5.45/5.77 thf(fact_6400_prod_OatLeast0__atMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > assn,N2: nat] :
% 5.45/5.77 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast0_atMost_Suc
% 5.45/5.77 thf(fact_6401_prod_OatLeast0__atMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > rat,N2: nat] :
% 5.45/5.77 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast0_atMost_Suc
% 5.45/5.77 thf(fact_6402_prod_OatLeast0__atMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast0_atMost_Suc
% 5.45/5.77 thf(fact_6403_prod_OatLeast0__atMost__Suc,axiom,
% 5.45/5.77 ! [G: nat > int,N2: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast0_atMost_Suc
% 5.45/5.77 thf(fact_6404_prod_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( G @ ( suc @ N2 ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6405_prod_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > assn] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( G @ ( suc @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6406_prod_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( G @ ( suc @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6407_prod_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( G @ ( suc @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6408_prod_Onat__ivl__Suc_H,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( G @ ( suc @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.nat_ivl_Suc'
% 5.45/5.77 thf(fact_6409_prod_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( G @ M ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6410_prod_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > assn] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_assn @ ( G @ M ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6411_prod_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6412_prod_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6413_prod_OatLeast__Suc__atMost,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.atLeast_Suc_atMost
% 5.45/5.77 thf(fact_6414_prod_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( G @ M )
% 5.45/5.77 @ ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6415_prod_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > assn] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( G @ M )
% 5.45/5.77 @ ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6416_prod_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( G @ M )
% 5.45/5.77 @ ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6417_prod_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( G @ M )
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6418_prod_OSuc__reindex__ivl,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( G @ M )
% 5.45/5.77 @ ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.Suc_reindex_ivl
% 5.45/5.77 thf(fact_6419_sum_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 5.45/5.77 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups6857163185585827899at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atMost_Suc_shift
% 5.45/5.77 thf(fact_6420_sum_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > rat,N2: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atMost_Suc_shift
% 5.45/5.77 thf(fact_6421_sum_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > int,N2: nat] :
% 5.45/5.77 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atMost_Suc_shift
% 5.45/5.77 thf(fact_6422_sum_OatMost__Suc__shift,axiom,
% 5.45/5.77 ! [G: nat > nat,N2: nat] :
% 5.45/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.45/5.77 @ ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.atMost_Suc_shift
% 5.45/5.77 thf(fact_6423_sum__telescope,axiom,
% 5.45/5.77 ! [F: nat > rat,I2: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ I2 ) )
% 5.45/5.77 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_telescope
% 5.45/5.77 thf(fact_6424_sum__telescope,axiom,
% 5.45/5.77 ! [F: nat > int,I2: nat] :
% 5.45/5.77 ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ I4 ) @ ( F @ ( suc @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ I2 ) )
% 5.45/5.77 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_telescope
% 5.45/5.77 thf(fact_6425_fact__prod,axiom,
% 5.45/5.77 ( semiri1406184849735516958ct_int
% 5.45/5.77 = ( ^ [N: nat] :
% 5.45/5.77 ( semiri1314217659103216013at_int
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : X4
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % fact_prod
% 5.45/5.77 thf(fact_6426_fact__prod,axiom,
% 5.45/5.77 ( semiri3624122377584611663nteger
% 5.45/5.77 = ( ^ [N: nat] :
% 5.45/5.77 ( semiri4939895301339042750nteger
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : X4
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % fact_prod
% 5.45/5.77 thf(fact_6427_fact__prod,axiom,
% 5.45/5.77 ( semiri1408675320244567234ct_nat
% 5.45/5.77 = ( ^ [N: nat] :
% 5.45/5.77 ( semiri1316708129612266289at_nat
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : X4
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % fact_prod
% 5.45/5.77 thf(fact_6428_prod__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > code_integer,A: nat,B: nat] :
% 5.45/5.77 ( ( groups3455450783089532116nteger @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo1084959871951514735nteger
% 5.45/5.77 @ ^ [A5: nat] : ( times_3573771949741848930nteger @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ one_one_Code_integer ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_atLeastAtMost_code
% 5.45/5.77 thf(fact_6429_prod__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > assn,A: nat,B: nat] :
% 5.45/5.77 ( ( groups6906906614972039071t_assn @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo1959793692361082170t_assn
% 5.45/5.77 @ ^ [A5: nat] : ( times_times_assn @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ one_one_assn ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_atLeastAtMost_code
% 5.45/5.77 thf(fact_6430_prod__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > rat,A: nat,B: nat] :
% 5.45/5.77 ( ( groups73079841787564623at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo1949268297981939178at_rat
% 5.45/5.77 @ ^ [A5: nat] : ( times_times_rat @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ one_one_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_atLeastAtMost_code
% 5.45/5.77 thf(fact_6431_prod__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > nat,A: nat,B: nat] :
% 5.45/5.77 ( ( groups708209901874060359at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo2584398358068434914at_nat
% 5.45/5.77 @ ^ [A5: nat] : ( times_times_nat @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ one_one_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_atLeastAtMost_code
% 5.45/5.77 thf(fact_6432_prod__atLeastAtMost__code,axiom,
% 5.45/5.77 ! [F: nat > int,A: nat,B: nat] :
% 5.45/5.77 ( ( groups705719431365010083at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.45/5.77 = ( set_fo2581907887559384638at_int
% 5.45/5.77 @ ^ [A5: nat] : ( times_times_int @ ( F @ A5 ) )
% 5.45/5.77 @ A
% 5.45/5.77 @ B
% 5.45/5.77 @ one_one_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_atLeastAtMost_code
% 5.45/5.77 thf(fact_6433_sorted__iff__nth__Suc,axiom,
% 5.45/5.77 ! [Xs: list_o] :
% 5.45/5.77 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 5.45/5.77 = ( ! [I4: nat] :
% 5.45/5.77 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_o @ ( nth_o @ Xs @ I4 ) @ ( nth_o @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_Suc
% 5.45/5.77 thf(fact_6434_sorted__iff__nth__Suc,axiom,
% 5.45/5.77 ! [Xs: list_rat] :
% 5.45/5.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 5.45/5.77 = ( ! [I4: nat] :
% 5.45/5.77 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_rat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I4 ) @ ( nth_rat @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_Suc
% 5.45/5.77 thf(fact_6435_sorted__iff__nth__Suc,axiom,
% 5.45/5.77 ! [Xs: list_num] :
% 5.45/5.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 5.45/5.77 = ( ! [I4: nat] :
% 5.45/5.77 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_num @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_num @ ( nth_num @ Xs @ I4 ) @ ( nth_num @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_Suc
% 5.45/5.77 thf(fact_6436_sorted__iff__nth__Suc,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 5.45/5.77 = ( ! [I4: nat] :
% 5.45/5.77 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_Suc
% 5.45/5.77 thf(fact_6437_sorted__iff__nth__Suc,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 5.45/5.77 = ( ! [I4: nat] :
% 5.45/5.77 ( ( ord_less_nat @ ( suc @ I4 ) @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ ( suc @ I4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_Suc
% 5.45/5.77 thf(fact_6438_sorted__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_o,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 5.45/5.77 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_o @ ( nth_o @ Xs @ I2 ) @ ( nth_o @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_nth_mono
% 5.45/5.77 thf(fact_6439_sorted__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_rat,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 5.45/5.77 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_rat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I2 ) @ ( nth_rat @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_nth_mono
% 5.45/5.77 thf(fact_6440_sorted__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_num,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 5.45/5.77 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_num @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_num @ ( nth_num @ Xs @ I2 ) @ ( nth_num @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_nth_mono
% 5.45/5.77 thf(fact_6441_sorted__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_nat,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 5.45/5.77 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I2 ) @ ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_nth_mono
% 5.45/5.77 thf(fact_6442_sorted__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_int,I2: nat,J: nat] :
% 5.45/5.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 5.45/5.77 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.77 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( nth_int @ Xs @ I2 ) @ ( nth_int @ Xs @ J ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_nth_mono
% 5.45/5.77 thf(fact_6443_sorted__iff__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_o] :
% 5.45/5.77 ( ( sorted_wrt_o @ ord_less_eq_o @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_o @ ( nth_o @ Xs @ I4 ) @ ( nth_o @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono
% 5.45/5.77 thf(fact_6444_sorted__iff__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_rat] :
% 5.45/5.77 ( ( sorted_wrt_rat @ ord_less_eq_rat @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_rat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_rat @ ( nth_rat @ Xs @ I4 ) @ ( nth_rat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono
% 5.45/5.77 thf(fact_6445_sorted__iff__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_num] :
% 5.45/5.77 ( ( sorted_wrt_num @ ord_less_eq_num @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_num @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_num @ ( nth_num @ Xs @ I4 ) @ ( nth_num @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono
% 5.45/5.77 thf(fact_6446_sorted__iff__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_nat] :
% 5.45/5.77 ( ( sorted_wrt_nat @ ord_less_eq_nat @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_nat @ ( nth_nat @ Xs @ I4 ) @ ( nth_nat @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono
% 5.45/5.77 thf(fact_6447_sorted__iff__nth__mono,axiom,
% 5.45/5.77 ! [Xs: list_int] :
% 5.45/5.77 ( ( sorted_wrt_int @ ord_less_eq_int @ Xs )
% 5.45/5.77 = ( ! [I4: nat,J3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I4 @ J3 )
% 5.45/5.77 => ( ( ord_less_nat @ J3 @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ord_less_eq_int @ ( nth_int @ Xs @ I4 ) @ ( nth_int @ Xs @ J3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sorted_iff_nth_mono
% 5.45/5.77 thf(fact_6448_prod_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > code_integer,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.ub_add_nat
% 5.45/5.77 thf(fact_6449_prod_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > assn,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.ub_add_nat
% 5.45/5.77 thf(fact_6450_prod_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > rat,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.ub_add_nat
% 5.45/5.77 thf(fact_6451_prod_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > nat,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.ub_add_nat
% 5.45/5.77 thf(fact_6452_prod_Oub__add__nat,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,G: nat > int,P3: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P3 ) ) )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P3 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.ub_add_nat
% 5.45/5.77 thf(fact_6453_gbinomial__parallel__sum,axiom,
% 5.45/5.77 ! [A: rat,N2: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_parallel_sum
% 5.45/5.77 thf(fact_6454_fact__eq__fact__times,axiom,
% 5.45/5.77 ! [N2: nat,M: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.77 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.45/5.77 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : X4
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % fact_eq_fact_times
% 5.45/5.77 thf(fact_6455_sum__gp__basic,axiom,
% 5.45/5.77 ! [X: code_integer,N2: nat] :
% 5.45/5.77 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.77 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_basic
% 5.45/5.77 thf(fact_6456_sum__gp__basic,axiom,
% 5.45/5.77 ! [X: rat,N2: nat] :
% 5.45/5.77 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.77 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_basic
% 5.45/5.77 thf(fact_6457_sum__gp__basic,axiom,
% 5.45/5.77 ! [X: int,N2: nat] :
% 5.45/5.77 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.77 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ ( suc @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_gp_basic
% 5.45/5.77 thf(fact_6458_pochhammer__Suc__prod,axiom,
% 5.45/5.77 ! [A: rat,N2: nat] :
% 5.45/5.77 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod
% 5.45/5.77 thf(fact_6459_pochhammer__Suc__prod,axiom,
% 5.45/5.77 ! [A: code_integer,N2: nat] :
% 5.45/5.77 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod
% 5.45/5.77 thf(fact_6460_pochhammer__Suc__prod,axiom,
% 5.45/5.77 ! [A: nat,N2: nat] :
% 5.45/5.77 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod
% 5.45/5.77 thf(fact_6461_pochhammer__Suc__prod,axiom,
% 5.45/5.77 ! [A: int,N2: nat] :
% 5.45/5.77 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod
% 5.45/5.77 thf(fact_6462_sum__power__shift,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ M ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_shift
% 5.45/5.77 thf(fact_6463_sum__power__shift,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_shift
% 5.45/5.77 thf(fact_6464_sum__power__shift,axiom,
% 5.45/5.77 ! [M: nat,N2: nat,X: int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.77 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_power_shift
% 5.45/5.77 thf(fact_6465_pochhammer__prod__rev,axiom,
% 5.45/5.77 ( comm_s4028243227959126397er_rat
% 5.45/5.77 = ( ^ [A5: rat,N: nat] :
% 5.45/5.77 ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_prod_rev
% 5.45/5.77 thf(fact_6466_pochhammer__prod__rev,axiom,
% 5.45/5.77 ( comm_s8582702949713902594nteger
% 5.45/5.77 = ( ^ [A5: code_integer,N: nat] :
% 5.45/5.77 ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_prod_rev
% 5.45/5.77 thf(fact_6467_pochhammer__prod__rev,axiom,
% 5.45/5.77 ( comm_s4663373288045622133er_nat
% 5.45/5.77 = ( ^ [A5: nat,N: nat] :
% 5.45/5.77 ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_prod_rev
% 5.45/5.77 thf(fact_6468_pochhammer__prod__rev,axiom,
% 5.45/5.77 ( comm_s4660882817536571857er_int
% 5.45/5.77 = ( ^ [A5: int,N: nat] :
% 5.45/5.77 ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_prod_rev
% 5.45/5.77 thf(fact_6469_fact__div__fact,axiom,
% 5.45/5.77 ! [N2: nat,M: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.77 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [X4: nat] : X4
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % fact_div_fact
% 5.45/5.77 thf(fact_6470_gbinomial__sum__lower__neg,axiom,
% 5.45/5.77 ! [A: rat,M: nat] :
% 5.45/5.77 ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.77 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_sum_lower_neg
% 5.45/5.77 thf(fact_6471_pochhammer__Suc__prod__rev,axiom,
% 5.45/5.77 ! [A: rat,N2: nat] :
% 5.45/5.77 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod_rev
% 5.45/5.77 thf(fact_6472_pochhammer__Suc__prod__rev,axiom,
% 5.45/5.77 ! [A: code_integer,N2: nat] :
% 5.45/5.77 ( ( comm_s8582702949713902594nteger @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A @ ( semiri4939895301339042750nteger @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod_rev
% 5.45/5.77 thf(fact_6473_pochhammer__Suc__prod__rev,axiom,
% 5.45/5.77 ! [A: nat,N2: nat] :
% 5.45/5.77 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod_rev
% 5.45/5.77 thf(fact_6474_pochhammer__Suc__prod__rev,axiom,
% 5.45/5.77 ! [A: int,N2: nat] :
% 5.45/5.77 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_Suc_prod_rev
% 5.45/5.77 thf(fact_6475_sum_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > code_integer,H: nat > code_integer] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_Code_integer @ ( J3 = K ) @ zero_z3403309356797280102nteger @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [J3: nat] : ( if_Code_integer @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.zero_middle
% 5.45/5.77 thf(fact_6476_sum_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > multis2468970476368604999at_nat,H: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_mul8430962117462786573at_nat @ ( J3 = K ) @ zero_z1048942125864253310at_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups6857163185585827899at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_mul8430962117462786573at_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.zero_middle
% 5.45/5.77 thf(fact_6477_sum_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > rat,H: nat > rat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.zero_middle
% 5.45/5.77 thf(fact_6478_sum_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > int,H: nat > int] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.zero_middle
% 5.45/5.77 thf(fact_6479_sum_Ozero__middle,axiom,
% 5.45/5.77 ! [P3: nat,K: nat,G: nat > nat,H: nat > nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ one_one_nat @ P3 )
% 5.45/5.77 => ( ( ord_less_eq_nat @ K @ P3 )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ P3 ) )
% 5.45/5.77 = ( groups3542108847815614940at_nat
% 5.45/5.77 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P3 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.zero_middle
% 5.45/5.77 thf(fact_6480_choose__alternating__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_sum
% 5.45/5.77 thf(fact_6481_choose__alternating__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_sum
% 5.45/5.77 thf(fact_6482_choose__alternating__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_sum
% 5.45/5.77 thf(fact_6483_choose__alternating__linear__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( N2 != one_one_nat )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I4 ) @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_linear_sum
% 5.45/5.77 thf(fact_6484_choose__alternating__linear__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( N2 != one_one_nat )
% 5.45/5.77 => ( ( groups3539618377306564664at_int
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I4 ) @ ( semiri1314217659103216013at_int @ I4 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_linear_sum
% 5.45/5.77 thf(fact_6485_choose__alternating__linear__sum,axiom,
% 5.45/5.77 ! [N2: nat] :
% 5.45/5.77 ( ( N2 != one_one_nat )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I4 ) @ ( semiri4939895301339042750nteger @ I4 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I4 ) ) )
% 5.45/5.77 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % choose_alternating_linear_sum
% 5.45/5.77 thf(fact_6486_pochhammer__times__pochhammer__half,axiom,
% 5.45/5.77 ! [Z: rat,N2: nat] :
% 5.45/5.77 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % pochhammer_times_pochhammer_half
% 5.45/5.77 thf(fact_6487_sum__zero__power_H,axiom,
% 5.45/5.77 ! [A3: set_nat,C: nat > rat,D2: nat > rat] :
% 5.45/5.77 ( ( ( ( finite_finite_nat @ A3 )
% 5.45/5.77 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D2 @ zero_zero_nat ) ) ) )
% 5.45/5.77 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.45/5.77 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) ) @ ( D2 @ I4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = zero_zero_rat ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_zero_power'
% 5.45/5.77 thf(fact_6488_nth__enumerate__eq,axiom,
% 5.45/5.77 ! [M: nat,Xs: list_int,N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ M @ ( size_size_list_int @ Xs ) )
% 5.45/5.77 => ( ( nth_Pr3440142176431000676at_int @ ( enumerate_int @ N2 @ Xs ) @ M )
% 5.45/5.77 = ( product_Pair_nat_int @ ( plus_plus_nat @ N2 @ M ) @ ( nth_int @ Xs @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_enumerate_eq
% 5.45/5.77 thf(fact_6489_nth__enumerate__eq,axiom,
% 5.45/5.77 ! [M: nat,Xs: list_nat,N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ M @ ( size_size_list_nat @ Xs ) )
% 5.45/5.77 => ( ( nth_Pr7617993195940197384at_nat @ ( enumerate_nat @ N2 @ Xs ) @ M )
% 5.45/5.77 = ( product_Pair_nat_nat @ ( plus_plus_nat @ N2 @ M ) @ ( nth_nat @ Xs @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_enumerate_eq
% 5.45/5.77 thf(fact_6490_nth__enumerate__eq,axiom,
% 5.45/5.77 ! [M: nat,Xs: list_o,N2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ M @ ( size_size_list_o @ Xs ) )
% 5.45/5.77 => ( ( nth_Pr112076138515278198_nat_o @ ( enumerate_o @ N2 @ Xs ) @ M )
% 5.45/5.77 = ( product_Pair_nat_o @ ( plus_plus_nat @ N2 @ M ) @ ( nth_o @ Xs @ M ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % nth_enumerate_eq
% 5.45/5.77 thf(fact_6491_gbinomial__prod__rev,axiom,
% 5.45/5.77 ( gbinomial_rat
% 5.45/5.77 = ( ^ [A5: rat,K3: nat] :
% 5.45/5.77 ( divide_divide_rat
% 5.45/5.77 @ ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 5.45/5.77 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_prod_rev
% 5.45/5.77 thf(fact_6492_gbinomial__prod__rev,axiom,
% 5.45/5.77 ( gbinom7368847122466276068atural
% 5.45/5.77 = ( ^ [A5: code_natural,K3: nat] :
% 5.45/5.77 ( divide5121882707175180666atural
% 5.45/5.77 @ ( groups2279045934846249631atural
% 5.45/5.77 @ ^ [I4: nat] : ( minus_7197305767214868737atural @ A5 @ ( semiri3763490453095760265atural @ I4 ) )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 5.45/5.77 @ ( semiri2447717529341329178atural @ K3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_prod_rev
% 5.45/5.77 thf(fact_6493_gbinomial__prod__rev,axiom,
% 5.45/5.77 ( gbinom8545251970709558553nteger
% 5.45/5.77 = ( ^ [A5: code_integer,K3: nat] :
% 5.45/5.77 ( divide6298287555418463151nteger
% 5.45/5.77 @ ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [I4: nat] : ( minus_8373710615458151222nteger @ A5 @ ( semiri4939895301339042750nteger @ I4 ) )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 5.45/5.77 @ ( semiri3624122377584611663nteger @ K3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_prod_rev
% 5.45/5.77 thf(fact_6494_gbinomial__prod__rev,axiom,
% 5.45/5.77 ( gbinomial_nat
% 5.45/5.77 = ( ^ [A5: nat,K3: nat] :
% 5.45/5.77 ( divide_divide_nat
% 5.45/5.77 @ ( groups708209901874060359at_nat
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 5.45/5.77 @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_prod_rev
% 5.45/5.77 thf(fact_6495_gbinomial__prod__rev,axiom,
% 5.45/5.77 ( gbinomial_int
% 5.45/5.77 = ( ^ [A5: int,K3: nat] :
% 5.45/5.77 ( divide_divide_int
% 5.45/5.77 @ ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [I4: nat] : ( minus_minus_int @ A5 @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) )
% 5.45/5.77 @ ( semiri1406184849735516958ct_int @ K3 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % gbinomial_prod_rev
% 5.45/5.77 thf(fact_6496_semiring__norm_I78_J,axiom,
% 5.45/5.77 ! [M: num,N2: num] :
% 5.45/5.77 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ M @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(78)
% 5.45/5.77 thf(fact_6497_semiring__norm_I71_J,axiom,
% 5.45/5.77 ! [M: num,N2: num] :
% 5.45/5.77 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.45/5.77 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(71)
% 5.45/5.77 thf(fact_6498_semiring__norm_I75_J,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ~ ( ord_less_num @ M @ one ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(75)
% 5.45/5.77 thf(fact_6499_semiring__norm_I68_J,axiom,
% 5.45/5.77 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(68)
% 5.45/5.77 thf(fact_6500_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: $o,L: $o,U: $o] :
% 5.45/5.77 ( ( member_o @ I2 @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_o @ L @ I2 )
% 5.45/5.77 & ( ord_less_o @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6501_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: set_nat,L: set_nat,U: set_nat] :
% 5.45/5.77 ( ( member_set_nat @ I2 @ ( set_or3540276404033026485et_nat @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_set_nat @ L @ I2 )
% 5.45/5.77 & ( ord_less_set_nat @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6502_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: assn,L: assn,U: assn] :
% 5.45/5.77 ( ( member_assn @ I2 @ ( set_or5523502641901747543n_assn @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_assn @ L @ I2 )
% 5.45/5.77 & ( ord_less_assn @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6503_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: set_int,L: set_int,U: set_int] :
% 5.45/5.77 ( ( member_set_int @ I2 @ ( set_or8585797421378605585et_int @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_set_int @ L @ I2 )
% 5.45/5.77 & ( ord_less_set_int @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6504_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: rat,L: rat,U: rat] :
% 5.45/5.77 ( ( member_rat @ I2 @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_rat @ L @ I2 )
% 5.45/5.77 & ( ord_less_rat @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6505_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: num,L: num,U: num] :
% 5.45/5.77 ( ( member_num @ I2 @ ( set_or1222409239386451017an_num @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_num @ L @ I2 )
% 5.45/5.77 & ( ord_less_num @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6506_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: nat,L: nat,U: nat] :
% 5.45/5.77 ( ( member_nat @ I2 @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_nat @ L @ I2 )
% 5.45/5.77 & ( ord_less_nat @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6507_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: int,L: int,U: int] :
% 5.45/5.77 ( ( member_int @ I2 @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.45/5.77 = ( ( ord_less_eq_int @ L @ I2 )
% 5.45/5.77 & ( ord_less_int @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6508_atLeastLessThan__iff,axiom,
% 5.45/5.77 ! [I2: code_integer,L: code_integer,U: code_integer] :
% 5.45/5.77 ( ( member_Code_integer @ I2 @ ( set_or8404916559141939852nteger @ L @ U ) )
% 5.45/5.77 = ( ( ord_le3102999989581377725nteger @ L @ I2 )
% 5.45/5.77 & ( ord_le6747313008572928689nteger @ I2 @ U ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_iff
% 5.45/5.77 thf(fact_6509_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: $o,A: $o] :
% 5.45/5.77 ( ( ord_less_eq_o @ B @ A )
% 5.45/5.77 => ( ( set_or7139685690850216873Than_o @ A @ B )
% 5.45/5.77 = bot_bot_set_o ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6510_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: set_int,A: set_int] :
% 5.45/5.77 ( ( ord_less_eq_set_int @ B @ A )
% 5.45/5.77 => ( ( set_or8585797421378605585et_int @ A @ B )
% 5.45/5.77 = bot_bot_set_set_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6511_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: rat,A: rat] :
% 5.45/5.77 ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.77 => ( ( set_or4029947393144176647an_rat @ A @ B )
% 5.45/5.77 = bot_bot_set_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6512_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: num,A: num] :
% 5.45/5.77 ( ( ord_less_eq_num @ B @ A )
% 5.45/5.77 => ( ( set_or1222409239386451017an_num @ A @ B )
% 5.45/5.77 = bot_bot_set_num ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6513_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: nat,A: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.77 => ( ( set_or4665077453230672383an_nat @ A @ B )
% 5.45/5.77 = bot_bot_set_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6514_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: int,A: int] :
% 5.45/5.77 ( ( ord_less_eq_int @ B @ A )
% 5.45/5.77 => ( ( set_or4662586982721622107an_int @ A @ B )
% 5.45/5.77 = bot_bot_set_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6515_atLeastLessThan__empty,axiom,
% 5.45/5.77 ! [B: code_integer,A: code_integer] :
% 5.45/5.77 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.77 => ( ( set_or8404916559141939852nteger @ A @ B )
% 5.45/5.77 = bot_bo3990330152332043303nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty
% 5.45/5.77 thf(fact_6516_infinite__Icc__iff,axiom,
% 5.45/5.77 ! [A: rat,B: rat] :
% 5.45/5.77 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.45/5.77 = ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.77
% 5.45/5.77 % infinite_Icc_iff
% 5.45/5.77 thf(fact_6517_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: $o,B: $o] :
% 5.45/5.77 ( ( bot_bot_set_o
% 5.45/5.77 = ( set_or7139685690850216873Than_o @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6518_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: assn,B: assn] :
% 5.45/5.77 ( ( bot_bot_set_assn
% 5.45/5.77 = ( set_or5523502641901747543n_assn @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_assn @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6519_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: rat,B: rat] :
% 5.45/5.77 ( ( bot_bot_set_rat
% 5.45/5.77 = ( set_or4029947393144176647an_rat @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6520_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: num,B: num] :
% 5.45/5.77 ( ( bot_bot_set_num
% 5.45/5.77 = ( set_or1222409239386451017an_num @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6521_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: nat,B: nat] :
% 5.45/5.77 ( ( bot_bot_set_nat
% 5.45/5.77 = ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6522_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: int,B: int] :
% 5.45/5.77 ( ( bot_bot_set_int
% 5.45/5.77 = ( set_or4662586982721622107an_int @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6523_atLeastLessThan__empty__iff2,axiom,
% 5.45/5.77 ! [A: code_integer,B: code_integer] :
% 5.45/5.77 ( ( bot_bo3990330152332043303nteger
% 5.45/5.77 = ( set_or8404916559141939852nteger @ A @ B ) )
% 5.45/5.77 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff2
% 5.45/5.77 thf(fact_6524_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: $o,B: $o] :
% 5.45/5.77 ( ( ( set_or7139685690850216873Than_o @ A @ B )
% 5.45/5.77 = bot_bot_set_o )
% 5.45/5.77 = ( ~ ( ord_less_o @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6525_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: assn,B: assn] :
% 5.45/5.77 ( ( ( set_or5523502641901747543n_assn @ A @ B )
% 5.45/5.77 = bot_bot_set_assn )
% 5.45/5.77 = ( ~ ( ord_less_assn @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6526_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: rat,B: rat] :
% 5.45/5.77 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 5.45/5.77 = bot_bot_set_rat )
% 5.45/5.77 = ( ~ ( ord_less_rat @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6527_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: num,B: num] :
% 5.45/5.77 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 5.45/5.77 = bot_bot_set_num )
% 5.45/5.77 = ( ~ ( ord_less_num @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6528_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: nat,B: nat] :
% 5.45/5.77 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 5.45/5.77 = bot_bot_set_nat )
% 5.45/5.77 = ( ~ ( ord_less_nat @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6529_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: int,B: int] :
% 5.45/5.77 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 5.45/5.77 = bot_bot_set_int )
% 5.45/5.77 = ( ~ ( ord_less_int @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6530_atLeastLessThan__empty__iff,axiom,
% 5.45/5.77 ! [A: code_integer,B: code_integer] :
% 5.45/5.77 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 5.45/5.77 = bot_bo3990330152332043303nteger )
% 5.45/5.77 = ( ~ ( ord_le6747313008572928689nteger @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_empty_iff
% 5.45/5.77 thf(fact_6531_infinite__Ico__iff,axiom,
% 5.45/5.77 ! [A: rat,B: rat] :
% 5.45/5.77 ( ( ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) )
% 5.45/5.77 = ( ord_less_rat @ A @ B ) ) ).
% 5.45/5.77
% 5.45/5.77 % infinite_Ico_iff
% 5.45/5.77 thf(fact_6532_ivl__subset,axiom,
% 5.45/5.77 ! [I2: rat,J: rat,M: rat,N2: rat] :
% 5.45/5.77 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ I2 @ J ) @ ( set_or4029947393144176647an_rat @ M @ N2 ) )
% 5.45/5.77 = ( ( ord_less_eq_rat @ J @ I2 )
% 5.45/5.77 | ( ( ord_less_eq_rat @ M @ I2 )
% 5.45/5.77 & ( ord_less_eq_rat @ J @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_subset
% 5.45/5.77 thf(fact_6533_ivl__subset,axiom,
% 5.45/5.77 ! [I2: num,J: num,M: num,N2: num] :
% 5.45/5.77 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ I2 @ J ) @ ( set_or1222409239386451017an_num @ M @ N2 ) )
% 5.45/5.77 = ( ( ord_less_eq_num @ J @ I2 )
% 5.45/5.77 | ( ( ord_less_eq_num @ M @ I2 )
% 5.45/5.77 & ( ord_less_eq_num @ J @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_subset
% 5.45/5.77 thf(fact_6534_ivl__subset,axiom,
% 5.45/5.77 ! [I2: nat,J: nat,M: nat,N2: nat] :
% 5.45/5.77 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.77 = ( ( ord_less_eq_nat @ J @ I2 )
% 5.45/5.77 | ( ( ord_less_eq_nat @ M @ I2 )
% 5.45/5.77 & ( ord_less_eq_nat @ J @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_subset
% 5.45/5.77 thf(fact_6535_ivl__subset,axiom,
% 5.45/5.77 ! [I2: int,J: int,M: int,N2: int] :
% 5.45/5.77 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ I2 @ J ) @ ( set_or4662586982721622107an_int @ M @ N2 ) )
% 5.45/5.77 = ( ( ord_less_eq_int @ J @ I2 )
% 5.45/5.77 | ( ( ord_less_eq_int @ M @ I2 )
% 5.45/5.77 & ( ord_less_eq_int @ J @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_subset
% 5.45/5.77 thf(fact_6536_ivl__subset,axiom,
% 5.45/5.77 ! [I2: code_integer,J: code_integer,M: code_integer,N2: code_integer] :
% 5.45/5.77 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ I2 @ J ) @ ( set_or8404916559141939852nteger @ M @ N2 ) )
% 5.45/5.77 = ( ( ord_le3102999989581377725nteger @ J @ I2 )
% 5.45/5.77 | ( ( ord_le3102999989581377725nteger @ M @ I2 )
% 5.45/5.77 & ( ord_le3102999989581377725nteger @ J @ N2 ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_subset
% 5.45/5.77 thf(fact_6537_ivl__diff,axiom,
% 5.45/5.77 ! [I2: rat,N2: rat,M: rat] :
% 5.45/5.77 ( ( ord_less_eq_rat @ I2 @ N2 )
% 5.45/5.77 => ( ( minus_minus_set_rat @ ( set_or4029947393144176647an_rat @ I2 @ M ) @ ( set_or4029947393144176647an_rat @ I2 @ N2 ) )
% 5.45/5.77 = ( set_or4029947393144176647an_rat @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_diff
% 5.45/5.77 thf(fact_6538_ivl__diff,axiom,
% 5.45/5.77 ! [I2: num,N2: num,M: num] :
% 5.45/5.77 ( ( ord_less_eq_num @ I2 @ N2 )
% 5.45/5.77 => ( ( minus_minus_set_num @ ( set_or1222409239386451017an_num @ I2 @ M ) @ ( set_or1222409239386451017an_num @ I2 @ N2 ) )
% 5.45/5.77 = ( set_or1222409239386451017an_num @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_diff
% 5.45/5.77 thf(fact_6539_ivl__diff,axiom,
% 5.45/5.77 ! [I2: nat,N2: nat,M: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.45/5.77 => ( ( minus_minus_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ M ) @ ( set_or4665077453230672383an_nat @ I2 @ N2 ) )
% 5.45/5.77 = ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_diff
% 5.45/5.77 thf(fact_6540_ivl__diff,axiom,
% 5.45/5.77 ! [I2: int,N2: int,M: int] :
% 5.45/5.77 ( ( ord_less_eq_int @ I2 @ N2 )
% 5.45/5.77 => ( ( minus_minus_set_int @ ( set_or4662586982721622107an_int @ I2 @ M ) @ ( set_or4662586982721622107an_int @ I2 @ N2 ) )
% 5.45/5.77 = ( set_or4662586982721622107an_int @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_diff
% 5.45/5.77 thf(fact_6541_ivl__diff,axiom,
% 5.45/5.77 ! [I2: code_integer,N2: code_integer,M: code_integer] :
% 5.45/5.77 ( ( ord_le3102999989581377725nteger @ I2 @ N2 )
% 5.45/5.77 => ( ( minus_2355218937544613996nteger @ ( set_or8404916559141939852nteger @ I2 @ M ) @ ( set_or8404916559141939852nteger @ I2 @ N2 ) )
% 5.45/5.77 = ( set_or8404916559141939852nteger @ N2 @ M ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % ivl_diff
% 5.45/5.77 thf(fact_6542_binomial__eq__0__iff,axiom,
% 5.45/5.77 ! [N2: nat,K: nat] :
% 5.45/5.77 ( ( ( binomial @ N2 @ K )
% 5.45/5.77 = zero_zero_nat )
% 5.45/5.77 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.45/5.77
% 5.45/5.77 % binomial_eq_0_iff
% 5.45/5.77 thf(fact_6543_semiring__norm_I69_J,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(69)
% 5.45/5.77 thf(fact_6544_semiring__norm_I76_J,axiom,
% 5.45/5.77 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % semiring_norm(76)
% 5.45/5.77 thf(fact_6545_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > code_integer] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups4406642042086082107nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups4406642042086082107nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6546_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6547_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > code_integer] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7873554091576472773nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7873554091576472773nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6548_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups879477027807139574nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups879477027807139574nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6549_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > rat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7872700643590313910_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7872700643590313910_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6550_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > rat] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6551_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > rat] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [K3: int] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6552_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups6602215022474089585er_rat
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups6602215022474089585er_rat
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6553_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > nat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups8507830703676809646_o_nat
% 5.45/5.77 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups8507830703676809646_o_nat
% 5.45/5.77 @ ^ [K3: $o] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_nat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6554_sum_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > nat] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups4541462559716669496nt_nat
% 5.45/5.77 @ ^ [K3: int] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups4541462559716669496nt_nat
% 5.45/5.77 @ ^ [K3: int] : ( if_nat @ ( A = K3 ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_nat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta'
% 5.45/5.77 thf(fact_6555_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > code_integer] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups4406642042086082107nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups4406642042086082107nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6556_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups7501900531339628137nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6557_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > code_integer] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7873554091576472773nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7873554091576472773nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6558_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups879477027807139574nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups879477027807139574nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_z3403309356797280102nteger ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6559_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > rat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7872700643590313910_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7872700643590313910_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6560_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > rat] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6561_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > rat] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3906332499630173760nt_rat
% 5.45/5.77 @ ^ [K3: int] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6562_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > rat] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups6602215022474089585er_rat
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups6602215022474089585er_rat
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6563_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > nat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups8507830703676809646_o_nat
% 5.45/5.77 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups8507830703676809646_o_nat
% 5.45/5.77 @ ^ [K3: $o] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_nat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6564_sum_Odelta,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > nat] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups4541462559716669496nt_nat
% 5.45/5.77 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups4541462559716669496nt_nat
% 5.45/5.77 @ ^ [K3: int] : ( if_nat @ ( K3 = A ) @ ( B @ K3 ) @ zero_zero_nat )
% 5.45/5.77 @ S )
% 5.45/5.77 = zero_zero_nat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.delta
% 5.45/5.77 thf(fact_6565_image__add__atLeastLessThan_H,axiom,
% 5.45/5.77 ! [K: rat,I2: rat,J: rat] :
% 5.45/5.77 ( ( image_rat_rat
% 5.45/5.77 @ ^ [N: rat] : ( plus_plus_rat @ N @ K )
% 5.45/5.77 @ ( set_or4029947393144176647an_rat @ I2 @ J ) )
% 5.45/5.77 = ( set_or4029947393144176647an_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ K ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_add_atLeastLessThan'
% 5.45/5.77 thf(fact_6566_image__add__atLeastLessThan_H,axiom,
% 5.45/5.77 ! [K: nat,I2: nat,J: nat] :
% 5.45/5.77 ( ( image_nat_nat
% 5.45/5.77 @ ^ [N: nat] : ( plus_plus_nat @ N @ K )
% 5.45/5.77 @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.45/5.77 = ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_add_atLeastLessThan'
% 5.45/5.77 thf(fact_6567_image__add__atLeastLessThan_H,axiom,
% 5.45/5.77 ! [K: int,I2: int,J: int] :
% 5.45/5.77 ( ( image_int_int
% 5.45/5.77 @ ^ [N: int] : ( plus_plus_int @ N @ K )
% 5.45/5.77 @ ( set_or4662586982721622107an_int @ I2 @ J ) )
% 5.45/5.77 = ( set_or4662586982721622107an_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_add_atLeastLessThan'
% 5.45/5.77 thf(fact_6568_image__add__atLeastLessThan_H,axiom,
% 5.45/5.77 ! [K: code_integer,I2: code_integer,J: code_integer] :
% 5.45/5.77 ( ( image_4470545334726330049nteger
% 5.45/5.77 @ ^ [N: code_integer] : ( plus_p5714425477246183910nteger @ N @ K )
% 5.45/5.77 @ ( set_or8404916559141939852nteger @ I2 @ J ) )
% 5.45/5.77 = ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ I2 @ K ) @ ( plus_p5714425477246183910nteger @ J @ K ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % image_add_atLeastLessThan'
% 5.45/5.77 thf(fact_6569_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > code_integer] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7694694392188491536nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7694694392188491536nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6570_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6571_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > code_integer] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3827104343326376752nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3827104343326376752nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6572_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups3674199335183972705nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups3674199335183972705nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( A = K3 ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6573_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > assn] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups5301882518646026715o_assn
% 5.45/5.77 @ ^ [K3: $o] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups5301882518646026715o_assn
% 5.45/5.77 @ ^ [K3: $o] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6574_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > assn] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [K3: nat] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6575_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > assn] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7882442080178216443t_assn
% 5.45/5.77 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7882442080178216443t_assn
% 5.45/5.77 @ ^ [K3: int] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6576_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups1304777262505850412r_assn
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups1304777262505850412r_assn
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_assn @ ( A = K3 ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6577_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > rat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups2869687844427037835_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups2869687844427037835_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6578_prod_Odelta_H,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > rat] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( A = K3 ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta'
% 5.45/5.77 thf(fact_6579_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > code_integer] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7694694392188491536nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups7694694392188491536nteger
% 5.45/5.77 @ ^ [K3: $o] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6580_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > code_integer] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups3455450783089532116nteger
% 5.45/5.77 @ ^ [K3: nat] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6581_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > code_integer] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3827104343326376752nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups3827104343326376752nteger
% 5.45/5.77 @ ^ [K3: int] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6582_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > code_integer] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups3674199335183972705nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups3674199335183972705nteger
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = A ) @ ( B @ K3 ) @ one_one_Code_integer )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_Code_integer ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6583_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > assn] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups5301882518646026715o_assn
% 5.45/5.77 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups5301882518646026715o_assn
% 5.45/5.77 @ ^ [K3: $o] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6584_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > assn] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn
% 5.45/5.77 @ ^ [K3: nat] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6585_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_int,A: int,B: int > assn] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( ( ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7882442080178216443t_assn
% 5.45/5.77 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_int @ A @ S )
% 5.45/5.77 => ( ( groups7882442080178216443t_assn
% 5.45/5.77 @ ^ [K3: int] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6586_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_Code_integer,A: code_integer,B: code_integer > assn] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( ( ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups1304777262505850412r_assn
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_Code_integer @ A @ S )
% 5.45/5.77 => ( ( groups1304777262505850412r_assn
% 5.45/5.77 @ ^ [K3: code_integer] : ( if_assn @ ( K3 = A ) @ ( B @ K3 ) @ one_one_assn )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_assn ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6587_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_o,A: $o,B: $o > rat] :
% 5.45/5.77 ( ( finite_finite_o @ S )
% 5.45/5.77 => ( ( ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups2869687844427037835_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_o @ A @ S )
% 5.45/5.77 => ( ( groups2869687844427037835_o_rat
% 5.45/5.77 @ ^ [K3: $o] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6588_prod_Odelta,axiom,
% 5.45/5.77 ! [S: set_nat,A: nat,B: nat > rat] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( ( ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = ( B @ A ) ) )
% 5.45/5.77 & ( ~ ( member_nat @ A @ S )
% 5.45/5.77 => ( ( groups73079841787564623at_rat
% 5.45/5.77 @ ^ [K3: nat] : ( if_rat @ ( K3 = A ) @ ( B @ K3 ) @ one_one_rat )
% 5.45/5.77 @ S )
% 5.45/5.77 = one_one_rat ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.delta
% 5.45/5.77 thf(fact_6589_zero__less__binomial__iff,axiom,
% 5.45/5.77 ! [N2: nat,K: nat] :
% 5.45/5.77 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.45/5.77 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % zero_less_binomial_iff
% 5.45/5.77 thf(fact_6590_prod__pos__nat__iff,axiom,
% 5.45/5.77 ! [A3: set_int,F: int > nat] :
% 5.45/5.77 ( ( finite_finite_int @ A3 )
% 5.45/5.77 => ( ( ord_less_nat @ zero_zero_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( ! [X4: int] :
% 5.45/5.77 ( ( member_int @ X4 @ A3 )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos_nat_iff
% 5.45/5.77 thf(fact_6591_prod__pos__nat__iff,axiom,
% 5.45/5.77 ! [A3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.77 => ( ( ord_less_nat @ zero_zero_nat @ ( groups3190895334310489300er_nat @ F @ A3 ) )
% 5.45/5.77 = ( ! [X4: code_integer] :
% 5.45/5.77 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos_nat_iff
% 5.45/5.77 thf(fact_6592_prod__pos__nat__iff,axiom,
% 5.45/5.77 ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.45/5.77 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.77 => ( ( ord_less_nat @ zero_zero_nat @ ( groups4077766827762148844at_nat @ F @ A3 ) )
% 5.45/5.77 = ( ! [X4: product_prod_nat_nat] :
% 5.45/5.77 ( ( member8440522571783428010at_nat @ X4 @ A3 )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos_nat_iff
% 5.45/5.77 thf(fact_6593_prod__pos__nat__iff,axiom,
% 5.45/5.77 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.77 ( ( finite_finite_nat @ A3 )
% 5.45/5.77 => ( ( ord_less_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.45/5.77 = ( ! [X4: nat] :
% 5.45/5.77 ( ( member_nat @ X4 @ A3 )
% 5.45/5.77 => ( ord_less_nat @ zero_zero_nat @ ( F @ X4 ) ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod_pos_nat_iff
% 5.45/5.77 thf(fact_6594_not__neg__one__le__neg__numeral__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_neg_one_le_neg_numeral_iff
% 5.45/5.77 thf(fact_6595_not__neg__one__le__neg__numeral__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_neg_one_le_neg_numeral_iff
% 5.45/5.77 thf(fact_6596_not__neg__one__le__neg__numeral__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % not_neg_one_le_neg_numeral_iff
% 5.45/5.77 thf(fact_6597_neg__numeral__less__neg__one__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % neg_numeral_less_neg_one_iff
% 5.45/5.77 thf(fact_6598_neg__numeral__less__neg__one__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % neg_numeral_less_neg_one_iff
% 5.45/5.77 thf(fact_6599_neg__numeral__less__neg__one__iff,axiom,
% 5.45/5.77 ! [M: num] :
% 5.45/5.77 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.45/5.77 = ( M != one ) ) ).
% 5.45/5.77
% 5.45/5.77 % neg_numeral_less_neg_one_iff
% 5.45/5.77 thf(fact_6600_numeral__le__one__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ N2 ) @ one_one_Code_integer )
% 5.45/5.77 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.45/5.77
% 5.45/5.77 % numeral_le_one_iff
% 5.45/5.77 thf(fact_6601_numeral__le__one__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_le1926595141338095240atural @ ( numera5444537566228673987atural @ N2 ) @ one_one_Code_natural )
% 5.45/5.77 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.45/5.77
% 5.45/5.77 % numeral_le_one_iff
% 5.45/5.77 thf(fact_6602_numeral__le__one__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.45/5.77 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.45/5.77
% 5.45/5.77 % numeral_le_one_iff
% 5.45/5.77 thf(fact_6603_numeral__le__one__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.45/5.77 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.45/5.77
% 5.45/5.77 % numeral_le_one_iff
% 5.45/5.77 thf(fact_6604_numeral__le__one__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.45/5.77 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.45/5.77
% 5.45/5.77 % numeral_le_one_iff
% 5.45/5.77 thf(fact_6605_one__less__numeral__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ one @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_numeral_iff
% 5.45/5.77 thf(fact_6606_one__less__numeral__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ one @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_numeral_iff
% 5.45/5.77 thf(fact_6607_one__less__numeral__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ one @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_numeral_iff
% 5.45/5.77 thf(fact_6608_one__less__numeral__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ one @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_numeral_iff
% 5.45/5.77 thf(fact_6609_one__less__numeral__iff,axiom,
% 5.45/5.77 ! [N2: num] :
% 5.45/5.77 ( ( ord_le5570908160329646204atural @ one_one_Code_natural @ ( numera5444537566228673987atural @ N2 ) )
% 5.45/5.77 = ( ord_less_num @ one @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_numeral_iff
% 5.45/5.77 thf(fact_6610_power2__less__eq__zero__iff,axiom,
% 5.45/5.77 ! [A: code_integer] :
% 5.45/5.77 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.77 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_less_eq_zero_iff
% 5.45/5.77 thf(fact_6611_power2__less__eq__zero__iff,axiom,
% 5.45/5.77 ! [A: rat] :
% 5.45/5.77 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.45/5.77 = ( A = zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_less_eq_zero_iff
% 5.45/5.77 thf(fact_6612_power2__less__eq__zero__iff,axiom,
% 5.45/5.77 ! [A: int] :
% 5.45/5.77 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.45/5.77 = ( A = zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_less_eq_zero_iff
% 5.45/5.77 thf(fact_6613_power2__eq__iff__nonneg,axiom,
% 5.45/5.77 ! [X: code_integer,Y: code_integer] :
% 5.45/5.77 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.77 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.77 => ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.77 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( X = Y ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_eq_iff_nonneg
% 5.45/5.77 thf(fact_6614_power2__eq__iff__nonneg,axiom,
% 5.45/5.77 ! [X: rat,Y: rat] :
% 5.45/5.77 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.77 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.77 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( X = Y ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_eq_iff_nonneg
% 5.45/5.77 thf(fact_6615_power2__eq__iff__nonneg,axiom,
% 5.45/5.77 ! [X: nat,Y: nat] :
% 5.45/5.77 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.45/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.45/5.77 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.77 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( X = Y ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_eq_iff_nonneg
% 5.45/5.77 thf(fact_6616_power2__eq__iff__nonneg,axiom,
% 5.45/5.77 ! [X: int,Y: int] :
% 5.45/5.77 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.77 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.77 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( X = Y ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % power2_eq_iff_nonneg
% 5.45/5.77 thf(fact_6617_zero__less__power2,axiom,
% 5.45/5.77 ! [A: code_integer] :
% 5.45/5.77 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.45/5.77
% 5.45/5.77 % zero_less_power2
% 5.45/5.77 thf(fact_6618_zero__less__power2,axiom,
% 5.45/5.77 ! [A: rat] :
% 5.45/5.77 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( A != zero_zero_rat ) ) ).
% 5.45/5.77
% 5.45/5.77 % zero_less_power2
% 5.45/5.77 thf(fact_6619_zero__less__power2,axiom,
% 5.45/5.77 ! [A: int] :
% 5.45/5.77 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( A != zero_zero_int ) ) ).
% 5.45/5.77
% 5.45/5.77 % zero_less_power2
% 5.45/5.77 thf(fact_6620_sum_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_z3403309356797280102nteger ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.op_ivl_Suc
% 5.45/5.77 thf(fact_6621_sum_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_z1048942125864253310at_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.op_ivl_Suc
% 5.45/5.77 thf(fact_6622_sum_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_rat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.op_ivl_Suc
% 5.45/5.77 thf(fact_6623_sum_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_int ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.op_ivl_Suc
% 5.45/5.77 thf(fact_6624_sum_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = zero_zero_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum.op_ivl_Suc
% 5.45/5.77 thf(fact_6625_prod_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_Code_integer ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.op_ivl_Suc
% 5.45/5.77 thf(fact_6626_prod_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > assn] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_assn ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.op_ivl_Suc
% 5.45/5.77 thf(fact_6627_prod_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_rat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.op_ivl_Suc
% 5.45/5.77 thf(fact_6628_prod_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_nat ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.op_ivl_Suc
% 5.45/5.77 thf(fact_6629_prod_Oop__ivl__Suc,axiom,
% 5.45/5.77 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.77 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = one_one_int ) )
% 5.45/5.77 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.77 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) ) )
% 5.45/5.77 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % prod.op_ivl_Suc
% 5.45/5.77 thf(fact_6630_sum__zero__power,axiom,
% 5.45/5.77 ! [A3: set_nat,C: nat > rat] :
% 5.45/5.77 ( ( ( ( finite_finite_nat @ A3 )
% 5.45/5.77 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = ( C @ zero_zero_nat ) ) )
% 5.45/5.77 & ( ~ ( ( finite_finite_nat @ A3 )
% 5.45/5.77 & ( member_nat @ zero_zero_nat @ A3 ) )
% 5.45/5.77 => ( ( groups2906978787729119204at_rat
% 5.45/5.77 @ ^ [I4: nat] : ( times_times_rat @ ( C @ I4 ) @ ( power_power_rat @ zero_zero_rat @ I4 ) )
% 5.45/5.77 @ A3 )
% 5.45/5.77 = zero_zero_rat ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % sum_zero_power
% 5.45/5.77 thf(fact_6631_one__less__floor,axiom,
% 5.45/5.77 ! [X: rat] :
% 5.45/5.77 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X ) )
% 5.45/5.77 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) ) ).
% 5.45/5.77
% 5.45/5.77 % one_less_floor
% 5.45/5.77 thf(fact_6632_floor__le__one,axiom,
% 5.45/5.77 ! [X: rat] :
% 5.45/5.77 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ one_one_int )
% 5.45/5.77 = ( ord_less_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % floor_le_one
% 5.45/5.77 thf(fact_6633_mod2__gr__0,axiom,
% 5.45/5.77 ! [M: nat] :
% 5.45/5.77 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.77 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.77 = one_one_nat ) ) ).
% 5.45/5.77
% 5.45/5.77 % mod2_gr_0
% 5.45/5.77 thf(fact_6634_int__prod,axiom,
% 5.45/5.77 ! [F: int > nat,A3: set_int] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups1707563613775114915nt_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups1705073143266064639nt_int
% 5.45/5.77 @ ^ [X4: int] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % int_prod
% 5.45/5.77 thf(fact_6635_int__prod,axiom,
% 5.45/5.77 ! [F: nat > nat,A3: set_nat] :
% 5.45/5.77 ( ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ F @ A3 ) )
% 5.45/5.77 = ( groups705719431365010083at_int
% 5.45/5.77 @ ^ [X4: nat] : ( semiri1314217659103216013at_int @ ( F @ X4 ) )
% 5.45/5.77 @ A3 ) ) ).
% 5.45/5.77
% 5.45/5.77 % int_prod
% 5.45/5.77 thf(fact_6636_finite__if__eq__beyond__finite,axiom,
% 5.45/5.77 ! [S: set_int,S4: set_int] :
% 5.45/5.77 ( ( finite_finite_int @ S )
% 5.45/5.77 => ( finite6197958912794628473et_int
% 5.45/5.77 @ ( collect_set_int
% 5.45/5.77 @ ^ [S6: set_int] :
% 5.45/5.77 ( ( minus_minus_set_int @ S6 @ S )
% 5.45/5.77 = ( minus_minus_set_int @ S4 @ S ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % finite_if_eq_beyond_finite
% 5.45/5.77 thf(fact_6637_finite__if__eq__beyond__finite,axiom,
% 5.45/5.77 ! [S: set_Code_integer,S4: set_Code_integer] :
% 5.45/5.77 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.77 => ( finite6931041176100689706nteger
% 5.45/5.77 @ ( collec574505750873337192nteger
% 5.45/5.77 @ ^ [S6: set_Code_integer] :
% 5.45/5.77 ( ( minus_2355218937544613996nteger @ S6 @ S )
% 5.45/5.77 = ( minus_2355218937544613996nteger @ S4 @ S ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % finite_if_eq_beyond_finite
% 5.45/5.77 thf(fact_6638_finite__if__eq__beyond__finite,axiom,
% 5.45/5.77 ! [S: set_Pr1261947904930325089at_nat,S4: set_Pr1261947904930325089at_nat] :
% 5.45/5.77 ( ( finite6177210948735845034at_nat @ S )
% 5.45/5.77 => ( finite9047747110432174090at_nat
% 5.45/5.77 @ ( collec5514110066124741708at_nat
% 5.45/5.77 @ ^ [S6: set_Pr1261947904930325089at_nat] :
% 5.45/5.77 ( ( minus_1356011639430497352at_nat @ S6 @ S )
% 5.45/5.77 = ( minus_1356011639430497352at_nat @ S4 @ S ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % finite_if_eq_beyond_finite
% 5.45/5.77 thf(fact_6639_finite__if__eq__beyond__finite,axiom,
% 5.45/5.77 ! [S: set_nat,S4: set_nat] :
% 5.45/5.77 ( ( finite_finite_nat @ S )
% 5.45/5.77 => ( finite1152437895449049373et_nat
% 5.45/5.77 @ ( collect_set_nat
% 5.45/5.77 @ ^ [S6: set_nat] :
% 5.45/5.77 ( ( minus_minus_set_nat @ S6 @ S )
% 5.45/5.77 = ( minus_minus_set_nat @ S4 @ S ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % finite_if_eq_beyond_finite
% 5.45/5.77 thf(fact_6640_infinite__Ico,axiom,
% 5.45/5.77 ! [A: rat,B: rat] :
% 5.45/5.77 ( ( ord_less_rat @ A @ B )
% 5.45/5.77 => ~ ( finite_finite_rat @ ( set_or4029947393144176647an_rat @ A @ B ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % infinite_Ico
% 5.45/5.77 thf(fact_6641_binomial__le__pow2,axiom,
% 5.45/5.77 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.45/5.77
% 5.45/5.77 % binomial_le_pow2
% 5.45/5.77 thf(fact_6642_atLeastLessThan__eq__iff,axiom,
% 5.45/5.77 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.77 ( ( ord_less_rat @ A @ B )
% 5.45/5.77 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.77 => ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 5.45/5.77 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 5.45/5.77 = ( ( A = C )
% 5.45/5.77 & ( B = D2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_eq_iff
% 5.45/5.77 thf(fact_6643_atLeastLessThan__eq__iff,axiom,
% 5.45/5.77 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.77 ( ( ord_less_num @ A @ B )
% 5.45/5.77 => ( ( ord_less_num @ C @ D2 )
% 5.45/5.77 => ( ( ( set_or1222409239386451017an_num @ A @ B )
% 5.45/5.77 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 5.45/5.77 = ( ( A = C )
% 5.45/5.77 & ( B = D2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_eq_iff
% 5.45/5.77 thf(fact_6644_atLeastLessThan__eq__iff,axiom,
% 5.45/5.77 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.77 ( ( ord_less_nat @ A @ B )
% 5.45/5.77 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.77 => ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 5.45/5.77 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 5.45/5.77 = ( ( A = C )
% 5.45/5.77 & ( B = D2 ) ) ) ) ) ).
% 5.45/5.77
% 5.45/5.77 % atLeastLessThan_eq_iff
% 5.45/5.77 thf(fact_6645_atLeastLessThan__eq__iff,axiom,
% 5.45/5.77 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.77 ( ( ord_less_int @ A @ B )
% 5.45/5.77 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.77 => ( ( ( set_or4662586982721622107an_int @ A @ B )
% 5.45/5.78 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 5.45/5.78 = ( ( A = C )
% 5.45/5.78 & ( B = D2 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_eq_iff
% 5.45/5.78 thf(fact_6646_atLeastLessThan__eq__iff,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.78 => ( ( ( set_or8404916559141939852nteger @ A @ B )
% 5.45/5.78 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 5.45/5.78 = ( ( A = C )
% 5.45/5.78 & ( B = D2 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_eq_iff
% 5.45/5.78 thf(fact_6647_atLeastLessThan__inj_I1_J,axiom,
% 5.45/5.78 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.78 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 5.45/5.78 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_rat @ A @ B )
% 5.45/5.78 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.78 => ( A = C ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(1)
% 5.45/5.78 thf(fact_6648_atLeastLessThan__inj_I1_J,axiom,
% 5.45/5.78 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.78 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 5.45/5.78 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_num @ A @ B )
% 5.45/5.78 => ( ( ord_less_num @ C @ D2 )
% 5.45/5.78 => ( A = C ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(1)
% 5.45/5.78 thf(fact_6649_atLeastLessThan__inj_I1_J,axiom,
% 5.45/5.78 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.78 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 5.45/5.78 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_nat @ A @ B )
% 5.45/5.78 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.78 => ( A = C ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(1)
% 5.45/5.78 thf(fact_6650_atLeastLessThan__inj_I1_J,axiom,
% 5.45/5.78 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.78 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 5.45/5.78 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_int @ A @ B )
% 5.45/5.78 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.78 => ( A = C ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(1)
% 5.45/5.78 thf(fact_6651_atLeastLessThan__inj_I1_J,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.78 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 5.45/5.78 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.78 => ( A = C ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(1)
% 5.45/5.78 thf(fact_6652_atLeastLessThan__inj_I2_J,axiom,
% 5.45/5.78 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.78 ( ( ( set_or4029947393144176647an_rat @ A @ B )
% 5.45/5.78 = ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_rat @ A @ B )
% 5.45/5.78 => ( ( ord_less_rat @ C @ D2 )
% 5.45/5.78 => ( B = D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(2)
% 5.45/5.78 thf(fact_6653_atLeastLessThan__inj_I2_J,axiom,
% 5.45/5.78 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.78 ( ( ( set_or1222409239386451017an_num @ A @ B )
% 5.45/5.78 = ( set_or1222409239386451017an_num @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_num @ A @ B )
% 5.45/5.78 => ( ( ord_less_num @ C @ D2 )
% 5.45/5.78 => ( B = D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(2)
% 5.45/5.78 thf(fact_6654_atLeastLessThan__inj_I2_J,axiom,
% 5.45/5.78 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.78 ( ( ( set_or4665077453230672383an_nat @ A @ B )
% 5.45/5.78 = ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_nat @ A @ B )
% 5.45/5.78 => ( ( ord_less_nat @ C @ D2 )
% 5.45/5.78 => ( B = D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(2)
% 5.45/5.78 thf(fact_6655_atLeastLessThan__inj_I2_J,axiom,
% 5.45/5.78 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.78 ( ( ( set_or4662586982721622107an_int @ A @ B )
% 5.45/5.78 = ( set_or4662586982721622107an_int @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_int @ A @ B )
% 5.45/5.78 => ( ( ord_less_int @ C @ D2 )
% 5.45/5.78 => ( B = D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(2)
% 5.45/5.78 thf(fact_6656_atLeastLessThan__inj_I2_J,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.78 ( ( ( set_or8404916559141939852nteger @ A @ B )
% 5.45/5.78 = ( set_or8404916559141939852nteger @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ C @ D2 )
% 5.45/5.78 => ( B = D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_inj(2)
% 5.45/5.78 thf(fact_6657_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.45/5.78 ! [N7: set_nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.78 => ( finite_finite_nat @ N7 ) ) ).
% 5.45/5.78
% 5.45/5.78 % subset_eq_atLeast0_lessThan_finite
% 5.45/5.78 thf(fact_6658_choose__row__sum,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_row_sum
% 5.45/5.78 thf(fact_6659_finite__nat__set__iff__bounded,axiom,
% 5.45/5.78 ( finite_finite_nat
% 5.45/5.78 = ( ^ [N8: set_nat] :
% 5.45/5.78 ? [M3: nat] :
% 5.45/5.78 ! [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ N8 )
% 5.45/5.78 => ( ord_less_nat @ X4 @ M3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % finite_nat_set_iff_bounded
% 5.45/5.78 thf(fact_6660_bounded__nat__set__is__finite,axiom,
% 5.45/5.78 ! [N7: set_nat,N2: nat] :
% 5.45/5.78 ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ N7 )
% 5.45/5.78 => ( ord_less_nat @ X3 @ N2 ) )
% 5.45/5.78 => ( finite_finite_nat @ N7 ) ) ).
% 5.45/5.78
% 5.45/5.78 % bounded_nat_set_is_finite
% 5.45/5.78 thf(fact_6661_finite__nat__set__iff__bounded__le,axiom,
% 5.45/5.78 ( finite_finite_nat
% 5.45/5.78 = ( ^ [N8: set_nat] :
% 5.45/5.78 ? [M3: nat] :
% 5.45/5.78 ! [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ N8 )
% 5.45/5.78 => ( ord_less_eq_nat @ X4 @ M3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % finite_nat_set_iff_bounded_le
% 5.45/5.78 thf(fact_6662_choose__square__sum,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.78 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_square_sum
% 5.45/5.78 thf(fact_6663_mult__2,axiom,
% 5.45/5.78 ! [Z: nat] :
% 5.45/5.78 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.45/5.78 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2
% 5.45/5.78 thf(fact_6664_mult__2,axiom,
% 5.45/5.78 ! [Z: int] :
% 5.45/5.78 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.45/5.78 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2
% 5.45/5.78 thf(fact_6665_mult__2,axiom,
% 5.45/5.78 ! [Z: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Z )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2
% 5.45/5.78 thf(fact_6666_mult__2,axiom,
% 5.45/5.78 ! [Z: rat] :
% 5.45/5.78 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.45/5.78 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2
% 5.45/5.78 thf(fact_6667_mult__2,axiom,
% 5.45/5.78 ! [Z: code_natural] :
% 5.45/5.78 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ Z )
% 5.45/5.78 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2
% 5.45/5.78 thf(fact_6668_mult__2__right,axiom,
% 5.45/5.78 ! [Z: nat] :
% 5.45/5.78 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2_right
% 5.45/5.78 thf(fact_6669_mult__2__right,axiom,
% 5.45/5.78 ! [Z: int] :
% 5.45/5.78 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2_right
% 5.45/5.78 thf(fact_6670_mult__2__right,axiom,
% 5.45/5.78 ! [Z: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ Z @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2_right
% 5.45/5.78 thf(fact_6671_mult__2__right,axiom,
% 5.45/5.78 ! [Z: rat] :
% 5.45/5.78 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2_right
% 5.45/5.78 thf(fact_6672_mult__2__right,axiom,
% 5.45/5.78 ! [Z: code_natural] :
% 5.45/5.78 ( ( times_2397367101498566445atural @ Z @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_p4538020629002901425atural @ Z @ Z ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_2_right
% 5.45/5.78 thf(fact_6673_left__add__twice,axiom,
% 5.45/5.78 ! [A: nat,B: nat] :
% 5.45/5.78 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.45/5.78 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % left_add_twice
% 5.45/5.78 thf(fact_6674_left__add__twice,axiom,
% 5.45/5.78 ! [A: int,B: int] :
% 5.45/5.78 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.45/5.78 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % left_add_twice
% 5.45/5.78 thf(fact_6675_left__add__twice,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer] :
% 5.45/5.78 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % left_add_twice
% 5.45/5.78 thf(fact_6676_left__add__twice,axiom,
% 5.45/5.78 ! [A: rat,B: rat] :
% 5.45/5.78 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.45/5.78 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % left_add_twice
% 5.45/5.78 thf(fact_6677_left__add__twice,axiom,
% 5.45/5.78 ! [A: code_natural,B: code_natural] :
% 5.45/5.78 ( ( plus_p4538020629002901425atural @ A @ ( plus_p4538020629002901425atural @ A @ B ) )
% 5.45/5.78 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % left_add_twice
% 5.45/5.78 thf(fact_6678_le__num__One__iff,axiom,
% 5.45/5.78 ! [X: num] :
% 5.45/5.78 ( ( ord_less_eq_num @ X @ one )
% 5.45/5.78 = ( X = one ) ) ).
% 5.45/5.78
% 5.45/5.78 % le_num_One_iff
% 5.45/5.78 thf(fact_6679_power4__eq__xxxx,axiom,
% 5.45/5.78 ! [X: code_integer] :
% 5.45/5.78 ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ X @ X ) @ X ) @ X ) ) ).
% 5.45/5.78
% 5.45/5.78 % power4_eq_xxxx
% 5.45/5.78 thf(fact_6680_power4__eq__xxxx,axiom,
% 5.45/5.78 ! [X: assn] :
% 5.45/5.78 ( ( power_power_assn @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( times_times_assn @ ( times_times_assn @ ( times_times_assn @ X @ X ) @ X ) @ X ) ) ).
% 5.45/5.78
% 5.45/5.78 % power4_eq_xxxx
% 5.45/5.78 thf(fact_6681_power4__eq__xxxx,axiom,
% 5.45/5.78 ! [X: rat] :
% 5.45/5.78 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.45/5.78
% 5.45/5.78 % power4_eq_xxxx
% 5.45/5.78 thf(fact_6682_power4__eq__xxxx,axiom,
% 5.45/5.78 ! [X: nat] :
% 5.45/5.78 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.45/5.78
% 5.45/5.78 % power4_eq_xxxx
% 5.45/5.78 thf(fact_6683_power4__eq__xxxx,axiom,
% 5.45/5.78 ! [X: int] :
% 5.45/5.78 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.45/5.78
% 5.45/5.78 % power4_eq_xxxx
% 5.45/5.78 thf(fact_6684_power2__eq__square,axiom,
% 5.45/5.78 ! [A: code_integer] :
% 5.45/5.78 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_square
% 5.45/5.78 thf(fact_6685_power2__eq__square,axiom,
% 5.45/5.78 ! [A: assn] :
% 5.45/5.78 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( times_times_assn @ A @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_square
% 5.45/5.78 thf(fact_6686_power2__eq__square,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( times_times_rat @ A @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_square
% 5.45/5.78 thf(fact_6687_power2__eq__square,axiom,
% 5.45/5.78 ! [A: nat] :
% 5.45/5.78 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( times_times_nat @ A @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_square
% 5.45/5.78 thf(fact_6688_power2__eq__square,axiom,
% 5.45/5.78 ! [A: int] :
% 5.45/5.78 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( times_times_int @ A @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_square
% 5.45/5.78 thf(fact_6689_finite__M__bounded__by__nat,axiom,
% 5.45/5.78 ! [P: nat > $o,I2: nat] :
% 5.45/5.78 ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [K3: nat] :
% 5.45/5.78 ( ( P @ K3 )
% 5.45/5.78 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % finite_M_bounded_by_nat
% 5.45/5.78 thf(fact_6690_finite__less__ub,axiom,
% 5.45/5.78 ! [F: nat > nat,U: nat] :
% 5.45/5.78 ( ! [N5: nat] : ( ord_less_eq_nat @ N5 @ ( F @ N5 ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % finite_less_ub
% 5.45/5.78 thf(fact_6691_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,B3: set_nat,G: $o > nat > nat,R: $o > nat > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups8507830703676809646_o_nat
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups8507830703676809646_o_nat
% 5.45/5.78 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6692_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_int,B3: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6693_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,B3: set_nat,G: code_integer > nat > nat,R: code_integer > nat > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups7237345082560585321er_nat
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups7237345082560585321er_nat
% 5.45/5.78 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6694_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,B3: set_int,G: $o > int > int,R: $o > int > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups8505340233167759370_o_int
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups8505340233167759370_o_int
% 5.45/5.78 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6695_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_int,G: nat > int > int,R: nat > int > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6696_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,B3: set_int,G: code_integer > int > int,R: code_integer > int > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups7234854612051535045er_int
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups7234854612051535045er_int
% 5.45/5.78 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6697_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_o,G: nat > $o > nat,R: nat > $o > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_o @ B3 )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups8507830703676809646_o_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [Y4: $o] :
% 5.45/5.78 ( ( member_o @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups8507830703676809646_o_nat
% 5.45/5.78 @ ^ [Y4: $o] :
% 5.45/5.78 ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6698_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_int,G: nat > int > nat,R: nat > int > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups4541462559716669496nt_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6699_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_Code_integer,G: nat > code_integer > nat,R: nat > code_integer > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups7237345082560585321er_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups7237345082560585321er_nat
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6700_sum_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_nat,G: nat > nat > nat,R: nat > nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.swap_restrict
% 5.45/5.78 thf(fact_6701_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,B3: set_nat,G: $o > nat > nat,R: $o > nat > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups3504817904513533571_o_nat
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( groups708209901874060359at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3504817904513533571_o_nat
% 5.45/5.78 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6702_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_int,B3: set_nat,G: int > nat > nat,R: int > nat > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups1707563613775114915nt_nat
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( groups708209901874060359at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups1707563613775114915nt_nat
% 5.45/5.78 @ ^ [X4: int] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6703_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,B3: set_nat,G: code_integer > nat > nat,R: code_integer > nat > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups3190895334310489300er_nat
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( groups708209901874060359at_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3190895334310489300er_nat
% 5.45/5.78 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6704_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,B3: set_nat,G: $o > nat > int,R: $o > nat > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups3502327434004483295_o_int
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( groups705719431365010083at_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3502327434004483295_o_int
% 5.45/5.78 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6705_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,B3: set_nat,G: code_integer > nat > int,R: code_integer > nat > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( finite_finite_nat @ B3 )
% 5.45/5.78 => ( ( groups3188404863801439024er_int
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( groups705719431365010083at_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( ( member_nat @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3188404863801439024er_int
% 5.45/5.78 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6706_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,B3: set_int,G: $o > int > int,R: $o > int > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups3502327434004483295_o_int
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups1705073143266064639nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3502327434004483295_o_int
% 5.45/5.78 @ ^ [X4: $o] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6707_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,B3: set_int,G: code_integer > int > int,R: code_integer > int > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups3188404863801439024er_int
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( groups1705073143266064639nt_int @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups1705073143266064639nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3188404863801439024er_int
% 5.45/5.78 @ ^ [X4: code_integer] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6708_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_o,G: nat > $o > nat,R: nat > $o > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_o @ B3 )
% 5.45/5.78 => ( ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups3504817904513533571_o_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [Y4: $o] :
% 5.45/5.78 ( ( member_o @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3504817904513533571_o_nat
% 5.45/5.78 @ ^ [Y4: $o] :
% 5.45/5.78 ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6709_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_int,G: nat > int > nat,R: nat > int > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite_finite_int @ B3 )
% 5.45/5.78 => ( ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups1707563613775114915nt_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( ( member_int @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups1707563613775114915nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6710_prod_Oswap__restrict,axiom,
% 5.45/5.78 ! [A3: set_nat,B3: set_Code_integer,G: nat > code_integer > nat,R: nat > code_integer > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.78 => ( ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( groups3190895334310489300er_nat @ ( G @ X4 )
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Y4 @ B3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ A3 )
% 5.45/5.78 = ( groups3190895334310489300er_nat
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [X4: nat] : ( G @ X4 @ Y4 )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( R @ X4 @ Y4 ) ) ) )
% 5.45/5.78 @ B3 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.swap_restrict
% 5.45/5.78 thf(fact_6711_less__exp,axiom,
% 5.45/5.78 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % less_exp
% 5.45/5.78 thf(fact_6712_self__le__ge2__pow,axiom,
% 5.45/5.78 ! [K: nat,M: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.45/5.78 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % self_le_ge2_pow
% 5.45/5.78 thf(fact_6713_power2__nat__le__eq__le,axiom,
% 5.45/5.78 ! [M: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_nat_le_eq_le
% 5.45/5.78 thf(fact_6714_power2__nat__le__imp__le,axiom,
% 5.45/5.78 ! [M: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.45/5.78 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_nat_le_imp_le
% 5.45/5.78 thf(fact_6715_sum__power2,axiom,
% 5.45/5.78 ! [K: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.45/5.78 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2
% 5.45/5.78 thf(fact_6716_Sum__Ico__nat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : X4
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.78 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % Sum_Ico_nat
% 5.45/5.78 thf(fact_6717_binomial__eq__0,axiom,
% 5.45/5.78 ! [N2: nat,K: nat] :
% 5.45/5.78 ( ( ord_less_nat @ N2 @ K )
% 5.45/5.78 => ( ( binomial @ N2 @ K )
% 5.45/5.78 = zero_zero_nat ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_eq_0
% 5.45/5.78 thf(fact_6718_half__gt__zero__iff,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % half_gt_zero_iff
% 5.45/5.78 thf(fact_6719_half__gt__zero,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.45/5.78 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % half_gt_zero
% 5.45/5.78 thf(fact_6720_atLeastLessThan__subset__iff,axiom,
% 5.45/5.78 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.78 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_eq_rat @ B @ A )
% 5.45/5.78 | ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.78 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_subset_iff
% 5.45/5.78 thf(fact_6721_atLeastLessThan__subset__iff,axiom,
% 5.45/5.78 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.78 ( ( ord_less_eq_set_num @ ( set_or1222409239386451017an_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_eq_num @ B @ A )
% 5.45/5.78 | ( ( ord_less_eq_num @ C @ A )
% 5.45/5.78 & ( ord_less_eq_num @ B @ D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_subset_iff
% 5.45/5.78 thf(fact_6722_atLeastLessThan__subset__iff,axiom,
% 5.45/5.78 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.78 ( ( ord_less_eq_set_nat @ ( set_or4665077453230672383an_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_eq_nat @ B @ A )
% 5.45/5.78 | ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.78 & ( ord_less_eq_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_subset_iff
% 5.45/5.78 thf(fact_6723_atLeastLessThan__subset__iff,axiom,
% 5.45/5.78 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.78 ( ( ord_less_eq_set_int @ ( set_or4662586982721622107an_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_less_eq_int @ B @ A )
% 5.45/5.78 | ( ( ord_less_eq_int @ C @ A )
% 5.45/5.78 & ( ord_less_eq_int @ B @ D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_subset_iff
% 5.45/5.78 thf(fact_6724_atLeastLessThan__subset__iff,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.78 ( ( ord_le7084787975880047091nteger @ ( set_or8404916559141939852nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.45/5.78 | ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ B @ D2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_subset_iff
% 5.45/5.78 thf(fact_6725_zero__le__power2,axiom,
% 5.45/5.78 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_power2
% 5.45/5.78 thf(fact_6726_zero__le__power2,axiom,
% 5.45/5.78 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_power2
% 5.45/5.78 thf(fact_6727_zero__le__power2,axiom,
% 5.45/5.78 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_power2
% 5.45/5.78 thf(fact_6728_power2__eq__imp__eq,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.78 => ( X = Y ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_imp_eq
% 5.45/5.78 thf(fact_6729_power2__eq__imp__eq,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.45/5.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.78 => ( X = Y ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_imp_eq
% 5.45/5.78 thf(fact_6730_power2__eq__imp__eq,axiom,
% 5.45/5.78 ! [X: nat,Y: nat] :
% 5.45/5.78 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.45/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.45/5.78 => ( X = Y ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_imp_eq
% 5.45/5.78 thf(fact_6731_power2__eq__imp__eq,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.78 => ( X = Y ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_eq_imp_eq
% 5.45/5.78 thf(fact_6732_power2__le__imp__le,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_imp_le
% 5.45/5.78 thf(fact_6733_power2__le__imp__le,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.78 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_imp_le
% 5.45/5.78 thf(fact_6734_power2__le__imp__le,axiom,
% 5.45/5.78 ! [X: nat,Y: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.45/5.78 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_imp_le
% 5.45/5.78 thf(fact_6735_power2__le__imp__le,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.78 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_imp_le
% 5.45/5.78 thf(fact_6736_power2__less__0,axiom,
% 5.45/5.78 ! [A: code_integer] :
% 5.45/5.78 ~ ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_0
% 5.45/5.78 thf(fact_6737_power2__less__0,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_0
% 5.45/5.78 thf(fact_6738_power2__less__0,axiom,
% 5.45/5.78 ! [A: int] :
% 5.45/5.78 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_0
% 5.45/5.78 thf(fact_6739_binomial__symmetric,axiom,
% 5.45/5.78 ! [K: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.78 => ( ( binomial @ N2 @ K )
% 5.45/5.78 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_symmetric
% 5.45/5.78 thf(fact_6740_ivl__disj__un__two_I3_J,axiom,
% 5.45/5.78 ! [L: rat,M: rat,U: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_rat @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 5.45/5.78 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(3)
% 5.45/5.78 thf(fact_6741_ivl__disj__un__two_I3_J,axiom,
% 5.45/5.78 ! [L: num,M: num,U: num] :
% 5.45/5.78 ( ( ord_less_eq_num @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_num @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M ) @ ( set_or1222409239386451017an_num @ M @ U ) )
% 5.45/5.78 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(3)
% 5.45/5.78 thf(fact_6742_ivl__disj__un__two_I3_J,axiom,
% 5.45/5.78 ! [L: nat,M: nat,U: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_nat @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 5.45/5.78 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(3)
% 5.45/5.78 thf(fact_6743_ivl__disj__un__two_I3_J,axiom,
% 5.45/5.78 ! [L: int,M: int,U: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_int @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 5.45/5.78 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(3)
% 5.45/5.78 thf(fact_6744_ivl__disj__un__two_I3_J,axiom,
% 5.45/5.78 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ L @ M )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 5.45/5.78 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 5.45/5.78 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(3)
% 5.45/5.78 thf(fact_6745_ex__nat__less__eq,axiom,
% 5.45/5.78 ! [N2: nat,P: nat > $o] :
% 5.45/5.78 ( ( ? [M3: nat] :
% 5.45/5.78 ( ( ord_less_nat @ M3 @ N2 )
% 5.45/5.78 & ( P @ M3 ) ) )
% 5.45/5.78 = ( ? [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.78 & ( P @ X4 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_nat_less_eq
% 5.45/5.78 thf(fact_6746_all__nat__less__eq,axiom,
% 5.45/5.78 ! [N2: nat,P: nat > $o] :
% 5.45/5.78 ( ( ! [M3: nat] :
% 5.45/5.78 ( ( ord_less_nat @ M3 @ N2 )
% 5.45/5.78 => ( P @ M3 ) ) )
% 5.45/5.78 = ( ! [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.78 => ( P @ X4 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % all_nat_less_eq
% 5.45/5.78 thf(fact_6747_less__2__cases__iff,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( ( N2 = zero_zero_nat )
% 5.45/5.78 | ( N2
% 5.45/5.78 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % less_2_cases_iff
% 5.45/5.78 thf(fact_6748_less__2__cases,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 => ( ( N2 = zero_zero_nat )
% 5.45/5.78 | ( N2
% 5.45/5.78 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % less_2_cases
% 5.45/5.78 thf(fact_6749_ivl__disj__int__two_I3_J,axiom,
% 5.45/5.78 ! [L: $o,M: $o,U: $o] :
% 5.45/5.78 ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or7139685690850216873Than_o @ M @ U ) )
% 5.45/5.78 = bot_bot_set_o ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(3)
% 5.45/5.78 thf(fact_6750_ivl__disj__int__two_I3_J,axiom,
% 5.45/5.78 ! [L: nat,M: nat,U: nat] :
% 5.45/5.78 ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 5.45/5.78 = bot_bot_set_nat ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(3)
% 5.45/5.78 thf(fact_6751_ivl__disj__int__two_I3_J,axiom,
% 5.45/5.78 ! [L: int,M: int,U: int] :
% 5.45/5.78 ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 5.45/5.78 = bot_bot_set_int ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(3)
% 5.45/5.78 thf(fact_6752_ivl__disj__int__two_I3_J,axiom,
% 5.45/5.78 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.78 ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 5.45/5.78 = bot_bo3990330152332043303nteger ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(3)
% 5.45/5.78 thf(fact_6753_abs__le__square__iff,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 5.45/5.78 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_le_square_iff
% 5.45/5.78 thf(fact_6754_abs__le__square__iff,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 5.45/5.78 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_le_square_iff
% 5.45/5.78 thf(fact_6755_abs__le__square__iff,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.45/5.78 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_le_square_iff
% 5.45/5.78 thf(fact_6756_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_Code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( S != bot_bo3990330152332043303nteger )
% 5.45/5.78 => ? [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Xa2 @ S )
% 5.45/5.78 & ( ord_le6747313008572928689nteger @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6757_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_o] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_o )
% 5.45/5.78 => ? [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: $o] :
% 5.45/5.78 ( ( member_o @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_o @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6758_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_assn] :
% 5.45/5.78 ( ( finite_finite_assn @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_assn )
% 5.45/5.78 => ? [X3: assn] :
% 5.45/5.78 ( ( member_assn @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: assn] :
% 5.45/5.78 ( ( member_assn @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_assn @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6759_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_rat] :
% 5.45/5.78 ( ( finite_finite_rat @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_rat )
% 5.45/5.78 => ? [X3: rat] :
% 5.45/5.78 ( ( member_rat @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: rat] :
% 5.45/5.78 ( ( member_rat @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_rat @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6760_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_num] :
% 5.45/5.78 ( ( finite_finite_num @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_num )
% 5.45/5.78 => ? [X3: num] :
% 5.45/5.78 ( ( member_num @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: num] :
% 5.45/5.78 ( ( member_num @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_num @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6761_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_nat )
% 5.45/5.78 => ? [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_nat @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6762_ex__min__if__finite,axiom,
% 5.45/5.78 ! [S: set_int] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( S != bot_bot_set_int )
% 5.45/5.78 => ? [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S )
% 5.45/5.78 & ~ ? [Xa2: int] :
% 5.45/5.78 ( ( member_int @ Xa2 @ S )
% 5.45/5.78 & ( ord_less_int @ Xa2 @ X3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_min_if_finite
% 5.45/5.78 thf(fact_6763_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_Code_integer] :
% 5.45/5.78 ( ( X6 != bot_bo3990330152332043303nteger )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_le6747313008572928689nteger @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite6017078050557962740nteger @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6764_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_o] :
% 5.45/5.78 ( ( X6 != bot_bot_set_o )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: $o] :
% 5.45/5.78 ( ( member_o @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_less_o @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite_finite_o @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6765_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_rat] :
% 5.45/5.78 ( ( X6 != bot_bot_set_rat )
% 5.45/5.78 => ( ! [X3: rat] :
% 5.45/5.78 ( ( member_rat @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: rat] :
% 5.45/5.78 ( ( member_rat @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_less_rat @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite_finite_rat @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6766_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_num] :
% 5.45/5.78 ( ( X6 != bot_bot_set_num )
% 5.45/5.78 => ( ! [X3: num] :
% 5.45/5.78 ( ( member_num @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: num] :
% 5.45/5.78 ( ( member_num @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_less_num @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite_finite_num @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6767_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_nat] :
% 5.45/5.78 ( ( X6 != bot_bot_set_nat )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_less_nat @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite_finite_nat @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6768_infinite__growing,axiom,
% 5.45/5.78 ! [X6: set_int] :
% 5.45/5.78 ( ( X6 != bot_bot_set_int )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ X6 )
% 5.45/5.78 => ? [Xa2: int] :
% 5.45/5.78 ( ( member_int @ Xa2 @ X6 )
% 5.45/5.78 & ( ord_less_int @ X3 @ Xa2 ) ) )
% 5.45/5.78 => ~ ( finite_finite_int @ X6 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_growing
% 5.45/5.78 thf(fact_6769_binomial__le__pow,axiom,
% 5.45/5.78 ! [R3: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ R3 @ N2 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( binomial @ N2 @ R3 ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_le_pow
% 5.45/5.78 thf(fact_6770_diff__le__diff__pow,axiom,
% 5.45/5.78 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.45/5.78 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_le_diff_pow
% 5.45/5.78 thf(fact_6771_binomial__r__part__sum,axiom,
% 5.45/5.78 ! [M: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_r_part_sum
% 5.45/5.78 thf(fact_6772_atLeastLessThan0,axiom,
% 5.45/5.78 ! [M: nat] :
% 5.45/5.78 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.45/5.78 = bot_bot_set_nat ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan0
% 5.45/5.78 thf(fact_6773_choose__linear__sum,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_nat @ I4 @ ( binomial @ N2 @ I4 ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.78 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_linear_sum
% 5.45/5.78 thf(fact_6774_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: $o > rat,I5: set_o,G: $o > rat,I2: $o] :
% 5.45/5.78 ( ( ( groups7872700643590313910_o_rat @ F @ I5 )
% 5.45/5.78 = ( groups7872700643590313910_o_rat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_o @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_o @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6775_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: nat > rat,I5: set_nat,G: nat > rat,I2: nat] :
% 5.45/5.78 ( ( ( groups2906978787729119204at_rat @ F @ I5 )
% 5.45/5.78 = ( groups2906978787729119204at_rat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_nat @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6776_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: int > rat,I5: set_int,G: int > rat,I2: int] :
% 5.45/5.78 ( ( ( groups3906332499630173760nt_rat @ F @ I5 )
% 5.45/5.78 = ( groups3906332499630173760nt_rat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_int @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_int @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6777_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: code_integer > rat,I5: set_Code_integer,G: code_integer > rat,I2: code_integer] :
% 5.45/5.78 ( ( ( groups6602215022474089585er_rat @ F @ I5 )
% 5.45/5.78 = ( groups6602215022474089585er_rat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6778_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: $o > nat,I5: set_o,G: $o > nat,I2: $o] :
% 5.45/5.78 ( ( ( groups8507830703676809646_o_nat @ F @ I5 )
% 5.45/5.78 = ( groups8507830703676809646_o_nat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_o @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_o @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6779_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: int > nat,I5: set_int,G: int > nat,I2: int] :
% 5.45/5.78 ( ( ( groups4541462559716669496nt_nat @ F @ I5 )
% 5.45/5.78 = ( groups4541462559716669496nt_nat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_int @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_int @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6780_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: code_integer > nat,I5: set_Code_integer,G: code_integer > nat,I2: code_integer] :
% 5.45/5.78 ( ( ( groups7237345082560585321er_nat @ F @ I5 )
% 5.45/5.78 = ( groups7237345082560585321er_nat @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6781_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: $o > int,I5: set_o,G: $o > int,I2: $o] :
% 5.45/5.78 ( ( ( groups8505340233167759370_o_int @ F @ I5 )
% 5.45/5.78 = ( groups8505340233167759370_o_int @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_o @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_o @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6782_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: nat > int,I5: set_nat,G: nat > int,I2: nat] :
% 5.45/5.78 ( ( ( groups3539618377306564664at_int @ F @ I5 )
% 5.45/5.78 = ( groups3539618377306564664at_int @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.78 => ( ( finite_finite_nat @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6783_sum__mono__inv,axiom,
% 5.45/5.78 ! [F: code_integer > int,I5: set_Code_integer,G: code_integer > int,I2: code_integer] :
% 5.45/5.78 ( ( ( groups7234854612051535045er_int @ F @ I5 )
% 5.45/5.78 = ( groups7234854612051535045er_int @ G @ I5 ) )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ I3 ) @ ( G @ I3 ) ) )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = ( G @ I2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_mono_inv
% 5.45/5.78 thf(fact_6784_infinite__Icc,axiom,
% 5.45/5.78 ! [A: rat,B: rat] :
% 5.45/5.78 ( ( ord_less_rat @ A @ B )
% 5.45/5.78 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % infinite_Icc
% 5.45/5.78 thf(fact_6785_mult__numeral__1__right,axiom,
% 5.45/5.78 ! [A: nat] :
% 5.45/5.78 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1_right
% 5.45/5.78 thf(fact_6786_mult__numeral__1__right,axiom,
% 5.45/5.78 ! [A: int] :
% 5.45/5.78 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1_right
% 5.45/5.78 thf(fact_6787_mult__numeral__1__right,axiom,
% 5.45/5.78 ! [A: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ A @ ( numera6620942414471956472nteger @ one ) )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1_right
% 5.45/5.78 thf(fact_6788_mult__numeral__1__right,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1_right
% 5.45/5.78 thf(fact_6789_mult__numeral__1__right,axiom,
% 5.45/5.78 ! [A: code_natural] :
% 5.45/5.78 ( ( times_2397367101498566445atural @ A @ ( numera5444537566228673987atural @ one ) )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1_right
% 5.45/5.78 thf(fact_6790_mult__numeral__1,axiom,
% 5.45/5.78 ! [A: nat] :
% 5.45/5.78 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1
% 5.45/5.78 thf(fact_6791_mult__numeral__1,axiom,
% 5.45/5.78 ! [A: int] :
% 5.45/5.78 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1
% 5.45/5.78 thf(fact_6792_mult__numeral__1,axiom,
% 5.45/5.78 ! [A: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ one ) @ A )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1
% 5.45/5.78 thf(fact_6793_mult__numeral__1,axiom,
% 5.45/5.78 ! [A: rat] :
% 5.45/5.78 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1
% 5.45/5.78 thf(fact_6794_mult__numeral__1,axiom,
% 5.45/5.78 ! [A: code_natural] :
% 5.45/5.78 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ one ) @ A )
% 5.45/5.78 = A ) ).
% 5.45/5.78
% 5.45/5.78 % mult_numeral_1
% 5.45/5.78 thf(fact_6795_sum__choose__upper,axiom,
% 5.45/5.78 ! [M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.78 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_choose_upper
% 5.45/5.78 thf(fact_6796_sum_Oshift__bounds__Suc__ivl,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.shift_bounds_Suc_ivl
% 5.45/5.78 thf(fact_6797_sum_Oshift__bounds__nat__ivl,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.shift_bounds_nat_ivl
% 5.45/5.78 thf(fact_6798_prod_Oshift__bounds__Suc__ivl,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.shift_bounds_Suc_ivl
% 5.45/5.78 thf(fact_6799_prod_Oshift__bounds__Suc__ivl,axiom,
% 5.45/5.78 ! [G: nat > int,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.shift_bounds_Suc_ivl
% 5.45/5.78 thf(fact_6800_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_p5714425477246183910nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6801_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_p5714425477246183910nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6802_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_p5714425477246183910nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6803_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_p5714425477246183910nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6804_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > rat,Y: $o > rat] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6805_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6806_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_int,X: int > rat,Y: int > rat] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6807_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_Code_integer,X: code_integer > rat,Y: code_integer > rat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_rat ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6808_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > nat,Y: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_nat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_nat ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_nat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6809_sum_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > nat,Y: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != zero_zero_nat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != zero_zero_nat ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( plus_plus_nat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != zero_zero_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.finite_Collect_op
% 5.45/5.78 thf(fact_6810_prod_Oshift__bounds__nat__ivl,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.45/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.shift_bounds_nat_ivl
% 5.45/5.78 thf(fact_6811_prod_Oshift__bounds__nat__ivl,axiom,
% 5.45/5.78 ! [G: nat > int,M: nat,K: nat,N2: nat] :
% 5.45/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [I4: nat] : ( G @ ( plus_plus_nat @ I4 @ K ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.shift_bounds_nat_ivl
% 5.45/5.78 thf(fact_6812_divmod__digit__0_I2_J,axiom,
% 5.45/5.78 ! [B: nat,A: nat] :
% 5.45/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.78 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.45/5.78 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(2)
% 5.45/5.78 thf(fact_6813_divmod__digit__0_I2_J,axiom,
% 5.45/5.78 ! [B: int,A: int] :
% 5.45/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.78 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.45/5.78 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(2)
% 5.45/5.78 thf(fact_6814_divmod__digit__0_I2_J,axiom,
% 5.45/5.78 ! [B: code_integer,A: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.45/5.78 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(2)
% 5.45/5.78 thf(fact_6815_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > code_integer,Y: $o > code_integer] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( times_3573771949741848930nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6816_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > code_integer,Y: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( times_3573771949741848930nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6817_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_int,X: int > code_integer,Y: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( times_3573771949741848930nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6818_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_Code_integer,X: code_integer > code_integer,Y: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_Code_integer ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( times_3573771949741848930nteger @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_Code_integer ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6819_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > assn,Y: $o > assn] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_assn @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_assn ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6820_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > assn,Y: nat > assn] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_assn @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_assn ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6821_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_int,X: int > assn,Y: int > assn] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [I4: int] :
% 5.45/5.78 ( ( member_int @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_assn @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_assn ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6822_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_Code_integer,X: code_integer > assn,Y: code_integer > assn] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_assn ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [I4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_assn @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_assn ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6823_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_o,X: $o > rat,Y: $o > rat] :
% 5.45/5.78 ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_rat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_rat ) ) ) )
% 5.45/5.78 => ( finite_finite_o
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [I4: $o] :
% 5.45/5.78 ( ( member_o @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6824_prod_Ofinite__Collect__op,axiom,
% 5.45/5.78 ! [I5: set_nat,X: nat > rat,Y: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( X @ I4 )
% 5.45/5.78 != one_one_rat ) ) ) )
% 5.45/5.78 => ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( Y @ I4 )
% 5.45/5.78 != one_one_rat ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [I4: nat] :
% 5.45/5.78 ( ( member_nat @ I4 @ I5 )
% 5.45/5.78 & ( ( times_times_rat @ ( X @ I4 ) @ ( Y @ I4 ) )
% 5.45/5.78 != one_one_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.finite_Collect_op
% 5.45/5.78 thf(fact_6825_power2__less__imp__less,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.78 => ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_imp_less
% 5.45/5.78 thf(fact_6826_power2__less__imp__less,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.78 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_imp_less
% 5.45/5.78 thf(fact_6827_power2__less__imp__less,axiom,
% 5.45/5.78 ! [X: nat,Y: nat] :
% 5.45/5.78 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.45/5.78 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_imp_less
% 5.45/5.78 thf(fact_6828_power2__less__imp__less,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.78 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_less_imp_less
% 5.45/5.78 thf(fact_6829_sum__power2__le__zero__iff,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 = ( ( X = zero_z3403309356797280102nteger )
% 5.45/5.78 & ( Y = zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_le_zero_iff
% 5.45/5.78 thf(fact_6830_sum__power2__le__zero__iff,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( 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 )
% 5.45/5.78 = ( ( X = zero_zero_rat )
% 5.45/5.78 & ( Y = zero_zero_rat ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_le_zero_iff
% 5.45/5.78 thf(fact_6831_sum__power2__le__zero__iff,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( 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 )
% 5.45/5.78 = ( ( X = zero_zero_int )
% 5.45/5.78 & ( Y = zero_zero_int ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_le_zero_iff
% 5.45/5.78 thf(fact_6832_sum__power2__ge__zero,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_ge_zero
% 5.45/5.78 thf(fact_6833_sum__power2__ge__zero,axiom,
% 5.45/5.78 ! [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 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_ge_zero
% 5.45/5.78 thf(fact_6834_sum__power2__ge__zero,axiom,
% 5.45/5.78 ! [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 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_ge_zero
% 5.45/5.78 thf(fact_6835_sum__power2__gt__zero__iff,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.45/5.78 = ( ( X != zero_z3403309356797280102nteger )
% 5.45/5.78 | ( Y != zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_gt_zero_iff
% 5.45/5.78 thf(fact_6836_sum__power2__gt__zero__iff,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( 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 ) ) ) ) )
% 5.45/5.78 = ( ( X != zero_zero_rat )
% 5.45/5.78 | ( Y != zero_zero_rat ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_gt_zero_iff
% 5.45/5.78 thf(fact_6837_sum__power2__gt__zero__iff,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( 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 ) ) ) ) )
% 5.45/5.78 = ( ( X != zero_zero_int )
% 5.45/5.78 | ( Y != zero_zero_int ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_power2_gt_zero_iff
% 5.45/5.78 thf(fact_6838_not__sum__power2__lt__zero,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ~ ( ord_le6747313008572928689nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_z3403309356797280102nteger ) ).
% 5.45/5.78
% 5.45/5.78 % not_sum_power2_lt_zero
% 5.45/5.78 thf(fact_6839_not__sum__power2__lt__zero,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ~ ( 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 ) ).
% 5.45/5.78
% 5.45/5.78 % not_sum_power2_lt_zero
% 5.45/5.78 thf(fact_6840_not__sum__power2__lt__zero,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ~ ( 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 ) ).
% 5.45/5.78
% 5.45/5.78 % not_sum_power2_lt_zero
% 5.45/5.78 thf(fact_6841_numeral__code_I2_J,axiom,
% 5.45/5.78 ! [N2: num] :
% 5.45/5.78 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.45/5.78 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % numeral_code(2)
% 5.45/5.78 thf(fact_6842_numeral__code_I2_J,axiom,
% 5.45/5.78 ! [N2: num] :
% 5.45/5.78 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.45/5.78 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % numeral_code(2)
% 5.45/5.78 thf(fact_6843_numeral__code_I2_J,axiom,
% 5.45/5.78 ! [N2: num] :
% 5.45/5.78 ( ( numera6620942414471956472nteger @ ( bit0 @ N2 ) )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % numeral_code(2)
% 5.45/5.78 thf(fact_6844_numeral__code_I2_J,axiom,
% 5.45/5.78 ! [N2: num] :
% 5.45/5.78 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.45/5.78 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % numeral_code(2)
% 5.45/5.78 thf(fact_6845_numeral__code_I2_J,axiom,
% 5.45/5.78 ! [N2: num] :
% 5.45/5.78 ( ( numera5444537566228673987atural @ ( bit0 @ N2 ) )
% 5.45/5.78 = ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % numeral_code(2)
% 5.45/5.78 thf(fact_6846_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > code_integer,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups4406642042086082107nteger @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups4406642042086082107nteger
% 5.45/5.78 @ ^ [X4: $o] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6847_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > code_integer,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups7501900531339628137nteger @ G
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups7501900531339628137nteger
% 5.45/5.78 @ ^ [X4: nat] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6848_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > code_integer,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups7873554091576472773nteger @ G
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups7873554091576472773nteger
% 5.45/5.78 @ ^ [X4: int] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6849_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > code_integer,P: code_integer > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups879477027807139574nteger @ G
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups879477027807139574nteger
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6850_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > rat,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups7872700643590313910_o_rat @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups7872700643590313910_o_rat
% 5.45/5.78 @ ^ [X4: $o] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6851_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > rat,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups2906978787729119204at_rat @ G
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat
% 5.45/5.78 @ ^ [X4: nat] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6852_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > rat,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups3906332499630173760nt_rat @ G
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups3906332499630173760nt_rat
% 5.45/5.78 @ ^ [X4: int] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6853_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > rat,P: code_integer > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups6602215022474089585er_rat @ G
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups6602215022474089585er_rat
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6854_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > nat,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups8507830703676809646_o_nat @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups8507830703676809646_o_nat
% 5.45/5.78 @ ^ [X4: $o] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6855_sum_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > nat,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat @ G
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( G @ X4 ) @ zero_zero_nat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_filter
% 5.45/5.78 thf(fact_6856_power2__sum,axiom,
% 5.45/5.78 ! [X: nat,Y: nat] :
% 5.45/5.78 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( 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 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_sum
% 5.45/5.78 thf(fact_6857_power2__sum,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( 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 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_sum
% 5.45/5.78 thf(fact_6858_power2__sum,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_sum
% 5.45/5.78 thf(fact_6859_power2__sum,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( 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 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_sum
% 5.45/5.78 thf(fact_6860_power2__sum,axiom,
% 5.45/5.78 ! [X: code_natural,Y: code_natural] :
% 5.45/5.78 ( ( power_7079662738309270450atural @ ( plus_p4538020629002901425atural @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( power_7079662738309270450atural @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_7079662738309270450atural @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_2397367101498566445atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_sum
% 5.45/5.78 thf(fact_6861_square__le__1,axiom,
% 5.45/5.78 ! [X: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % square_le_1
% 5.45/5.78 thf(fact_6862_square__le__1,axiom,
% 5.45/5.78 ! [X: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.45/5.78 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.45/5.78 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % square_le_1
% 5.45/5.78 thf(fact_6863_square__le__1,axiom,
% 5.45/5.78 ! [X: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.45/5.78 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.45/5.78 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % square_le_1
% 5.45/5.78 thf(fact_6864_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_int_int > nat,P: product_prod_int_int > $o] :
% 5.45/5.78 ( ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6865_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: list_nat > nat,P: list_nat > $o] :
% 5.45/5.78 ( ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6866_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: set_nat > nat,P: set_nat > $o] :
% 5.45/5.78 ( ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6867_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: nat > nat,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6868_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: int > nat,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6869_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: code_integer > nat,P: code_integer > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6870_filter__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_nat_nat > nat,P: product_prod_nat_nat > $o] :
% 5.45/5.78 ( ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( P @ X4 ) @ ( M6 @ X4 ) @ zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % filter_preserves_multiset
% 5.45/5.78 thf(fact_6871_zero__le__even__power_H,axiom,
% 5.45/5.78 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_even_power'
% 5.45/5.78 thf(fact_6872_zero__le__even__power_H,axiom,
% 5.45/5.78 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_even_power'
% 5.45/5.78 thf(fact_6873_zero__le__even__power_H,axiom,
% 5.45/5.78 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_le_even_power'
% 5.45/5.78 thf(fact_6874_power2__le__iff__abs__le,axiom,
% 5.45/5.78 ! [Y: code_integer,X: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_iff_abs_le
% 5.45/5.78 thf(fact_6875_power2__le__iff__abs__le,axiom,
% 5.45/5.78 ! [Y: rat,X: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.45/5.78 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_iff_abs_le
% 5.45/5.78 thf(fact_6876_power2__le__iff__abs__le,axiom,
% 5.45/5.78 ! [Y: int,X: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.45/5.78 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.78 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_le_iff_abs_le
% 5.45/5.78 thf(fact_6877_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( groups8507830703676809646_o_nat @ H @ S )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups8507830703676809646_o_nat @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_o_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6878_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_int,H: int > nat,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat @ H @ S )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups4541462559716669496nt_nat @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_int_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6879_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( groups7237345082560585321er_nat @ H @ S )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups7237345082560585321er_nat @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_951025933927791156er_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6880_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_o,H: $o > int,G: $o > int] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( groups8505340233167759370_o_int @ H @ S )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups8505340233167759370_o_int @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_o_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6881_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > int,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups3539618377306564664at_int @ H @ S )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3539618377306564664at_int @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6882_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_Code_integer,H: code_integer > int,G: code_integer > int] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( groups7234854612051535045er_int @ H @ S )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups7234854612051535045er_int @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_948535463418740880er_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6883_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > nat,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat @ H @ S )
% 5.45/5.78 = ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6884_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > nat,G: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat @ H @ S )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6885_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_int,H: int > int,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( groups4538972089207619220nt_int @ H @ S )
% 5.45/5.78 = ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_int_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6886_sum_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_int,H: int > int,G: int > int] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( groups4538972089207619220nt_int @ H @ S )
% 5.45/5.78 = ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_int_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.image_gen
% 5.45/5.78 thf(fact_6887_abs__square__le__1,axiom,
% 5.45/5.78 ! [X: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.45/5.78 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_le_1
% 5.45/5.78 thf(fact_6888_abs__square__le__1,axiom,
% 5.45/5.78 ! [X: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.45/5.78 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_le_1
% 5.45/5.78 thf(fact_6889_abs__square__le__1,axiom,
% 5.45/5.78 ! [X: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.45/5.78 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_le_1
% 5.45/5.78 thf(fact_6890_abs__square__less__1,axiom,
% 5.45/5.78 ! [X: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.45/5.78 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_less_1
% 5.45/5.78 thf(fact_6891_abs__square__less__1,axiom,
% 5.45/5.78 ! [X: rat] :
% 5.45/5.78 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.45/5.78 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_less_1
% 5.45/5.78 thf(fact_6892_abs__square__less__1,axiom,
% 5.45/5.78 ! [X: int] :
% 5.45/5.78 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.45/5.78 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.45/5.78
% 5.45/5.78 % abs_square_less_1
% 5.45/5.78 thf(fact_6893_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > code_integer,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups7694694392188491536nteger @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups7694694392188491536nteger
% 5.45/5.78 @ ^ [X4: $o] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6894_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > code_integer,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups3455450783089532116nteger @ G
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups3455450783089532116nteger
% 5.45/5.78 @ ^ [X4: nat] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6895_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > code_integer,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups3827104343326376752nteger @ G
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups3827104343326376752nteger
% 5.45/5.78 @ ^ [X4: int] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6896_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > code_integer,P: code_integer > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups3674199335183972705nteger @ G
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups3674199335183972705nteger
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_Code_integer @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6897_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > assn,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups5301882518646026715o_assn @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups5301882518646026715o_assn
% 5.45/5.78 @ ^ [X4: $o] : ( if_assn @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6898_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > assn,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups6906906614972039071t_assn @ G
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups6906906614972039071t_assn
% 5.45/5.78 @ ^ [X4: nat] : ( if_assn @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6899_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > assn,P: int > $o] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups7882442080178216443t_assn @ G
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups7882442080178216443t_assn
% 5.45/5.78 @ ^ [X4: int] : ( if_assn @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6900_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > assn,P: code_integer > $o] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups1304777262505850412r_assn @ G
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups1304777262505850412r_assn
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_assn @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6901_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > rat,P: $o > $o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups2869687844427037835_o_rat @ G
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups2869687844427037835_o_rat
% 5.45/5.78 @ ^ [X4: $o] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6902_prod_Ointer__filter,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > rat,P: nat > $o] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups73079841787564623at_rat @ G
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 & ( P @ X4 ) ) ) )
% 5.45/5.78 = ( groups73079841787564623at_rat
% 5.45/5.78 @ ^ [X4: nat] : ( if_rat @ ( P @ X4 ) @ ( G @ X4 ) @ one_one_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.inter_filter
% 5.45/5.78 thf(fact_6903_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( groups3504817904513533571_o_nat @ H @ S )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3504817904513533571_o_nat @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_o_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6904_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_int,H: int > nat,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( groups1707563613775114915nt_nat @ H @ S )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups1707563613775114915nt_nat @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_int_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6905_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( groups3190895334310489300er_nat @ H @ S )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3190895334310489300er_nat @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_951025933927791156er_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6906_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_o,H: $o > int,G: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( groups3502327434004483295_o_int @ H @ S )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3502327434004483295_o_int @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_o_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6907_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_Code_integer,H: code_integer > int,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( groups3188404863801439024er_int @ H @ S )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3188404863801439024er_int @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_951025933927791156er_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6908_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_o,H: $o > int,G: $o > int] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( groups3502327434004483295_o_int @ H @ S )
% 5.45/5.78 = ( groups1705073143266064639nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3502327434004483295_o_int @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_o_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6909_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_Code_integer,H: code_integer > int,G: code_integer > int] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( groups3188404863801439024er_int @ H @ S )
% 5.45/5.78 = ( groups1705073143266064639nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3188404863801439024er_int @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_948535463418740880er_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6910_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > nat,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups708209901874060359at_nat @ H @ S )
% 5.45/5.78 = ( groups1707563613775114915nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups708209901874060359at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_int @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6911_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > nat,G: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups708209901874060359at_nat @ H @ S )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups708209901874060359at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6912_prod_Oimage__gen,axiom,
% 5.45/5.78 ! [S: set_nat,H: nat > int,G: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( groups705719431365010083at_int @ H @ S )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups705719431365010083at_int @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ ( image_nat_nat @ G @ S ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.image_gen
% 5.45/5.78 thf(fact_6913_minus__power__mult__self,axiom,
% 5.45/5.78 ! [A: int,N2: nat] :
% 5.45/5.78 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.45/5.78 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % minus_power_mult_self
% 5.45/5.78 thf(fact_6914_minus__power__mult__self,axiom,
% 5.45/5.78 ! [A: code_integer,N2: nat] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.45/5.78 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % minus_power_mult_self
% 5.45/5.78 thf(fact_6915_minus__power__mult__self,axiom,
% 5.45/5.78 ! [A: rat,N2: nat] :
% 5.45/5.78 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.45/5.78 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % minus_power_mult_self
% 5.45/5.78 thf(fact_6916_power__odd__eq,axiom,
% 5.45/5.78 ! [A: code_integer,N2: nat] :
% 5.45/5.78 ( ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.78 = ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power_odd_eq
% 5.45/5.78 thf(fact_6917_power__odd__eq,axiom,
% 5.45/5.78 ! [A: assn,N2: nat] :
% 5.45/5.78 ( ( power_power_assn @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.78 = ( times_times_assn @ A @ ( power_power_assn @ ( power_power_assn @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power_odd_eq
% 5.45/5.78 thf(fact_6918_power__odd__eq,axiom,
% 5.45/5.78 ! [A: rat,N2: nat] :
% 5.45/5.78 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.78 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power_odd_eq
% 5.45/5.78 thf(fact_6919_power__odd__eq,axiom,
% 5.45/5.78 ! [A: nat,N2: nat] :
% 5.45/5.78 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.78 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power_odd_eq
% 5.45/5.78 thf(fact_6920_power__odd__eq,axiom,
% 5.45/5.78 ! [A: int,N2: nat] :
% 5.45/5.78 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.78 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power_odd_eq
% 5.45/5.78 thf(fact_6921_Suc__n__div__2__gt__zero,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.78 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % Suc_n_div_2_gt_zero
% 5.45/5.78 thf(fact_6922_div__2__gt__zero,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.45/5.78 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % div_2_gt_zero
% 5.45/5.78 thf(fact_6923_finite__int__segment,axiom,
% 5.45/5.78 ! [A: rat,B: rat] :
% 5.45/5.78 ( finite_finite_rat
% 5.45/5.78 @ ( collect_rat
% 5.45/5.78 @ ^ [X4: rat] :
% 5.45/5.78 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.45/5.78 & ( ord_less_eq_rat @ A @ X4 )
% 5.45/5.78 & ( ord_less_eq_rat @ X4 @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % finite_int_segment
% 5.45/5.78 thf(fact_6924_zero__less__binomial,axiom,
% 5.45/5.78 ! [K: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.78 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % zero_less_binomial
% 5.45/5.78 thf(fact_6925_sum_Oivl__cong,axiom,
% 5.45/5.78 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H: nat > nat] :
% 5.45/5.78 ( ( A = C )
% 5.45/5.78 => ( ( B = D2 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ C @ X3 )
% 5.45/5.78 => ( ( ord_less_nat @ X3 @ D2 )
% 5.45/5.78 => ( ( G @ X3 )
% 5.45/5.78 = ( H @ X3 ) ) ) )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ H @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.ivl_cong
% 5.45/5.78 thf(fact_6926_sum_Oivl__cong,axiom,
% 5.45/5.78 ! [A: int,C: int,B: int,D2: int,G: int > int,H: int > int] :
% 5.45/5.78 ( ( A = C )
% 5.45/5.78 => ( ( B = D2 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ C @ X3 )
% 5.45/5.78 => ( ( ord_less_int @ X3 @ D2 )
% 5.45/5.78 => ( ( G @ X3 )
% 5.45/5.78 = ( H @ X3 ) ) ) )
% 5.45/5.78 => ( ( groups4538972089207619220nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 5.45/5.78 = ( groups4538972089207619220nt_int @ H @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.ivl_cong
% 5.45/5.78 thf(fact_6927_prod_Oivl__cong,axiom,
% 5.45/5.78 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > nat,H: nat > nat] :
% 5.45/5.78 ( ( A = C )
% 5.45/5.78 => ( ( B = D2 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ C @ X3 )
% 5.45/5.78 => ( ( ord_less_nat @ X3 @ D2 )
% 5.45/5.78 => ( ( G @ X3 )
% 5.45/5.78 = ( H @ X3 ) ) ) )
% 5.45/5.78 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.45/5.78 = ( groups708209901874060359at_nat @ H @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.ivl_cong
% 5.45/5.78 thf(fact_6928_prod_Oivl__cong,axiom,
% 5.45/5.78 ! [A: nat,C: nat,B: nat,D2: nat,G: nat > int,H: nat > int] :
% 5.45/5.78 ( ( A = C )
% 5.45/5.78 => ( ( B = D2 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ C @ X3 )
% 5.45/5.78 => ( ( ord_less_nat @ X3 @ D2 )
% 5.45/5.78 => ( ( G @ X3 )
% 5.45/5.78 = ( H @ X3 ) ) ) )
% 5.45/5.78 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.45/5.78 = ( groups705719431365010083at_int @ H @ ( set_or4665077453230672383an_nat @ C @ D2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.ivl_cong
% 5.45/5.78 thf(fact_6929_prod_Oivl__cong,axiom,
% 5.45/5.78 ! [A: int,C: int,B: int,D2: int,G: int > int,H: int > int] :
% 5.45/5.78 ( ( A = C )
% 5.45/5.78 => ( ( B = D2 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ C @ X3 )
% 5.45/5.78 => ( ( ord_less_int @ X3 @ D2 )
% 5.45/5.78 => ( ( G @ X3 )
% 5.45/5.78 = ( H @ X3 ) ) ) )
% 5.45/5.78 => ( ( groups1705073143266064639nt_int @ G @ ( set_or4662586982721622107an_int @ A @ B ) )
% 5.45/5.78 = ( groups1705073143266064639nt_int @ H @ ( set_or4662586982721622107an_int @ C @ D2 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.ivl_cong
% 5.45/5.78 thf(fact_6930_choose__mult,axiom,
% 5.45/5.78 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ K @ M )
% 5.45/5.78 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.45/5.78 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_mult
% 5.45/5.78 thf(fact_6931_ivl__disj__un__two_I7_J,axiom,
% 5.45/5.78 ! [L: rat,M: rat,U: rat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_rat @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_rat @ ( set_or4029947393144176647an_rat @ L @ M ) @ ( set_or633870826150836451st_rat @ M @ U ) )
% 5.45/5.78 = ( set_or633870826150836451st_rat @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(7)
% 5.45/5.78 thf(fact_6932_ivl__disj__un__two_I7_J,axiom,
% 5.45/5.78 ! [L: num,M: num,U: num] :
% 5.45/5.78 ( ( ord_less_eq_num @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_num @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_num @ ( set_or1222409239386451017an_num @ L @ M ) @ ( set_or7049704709247886629st_num @ M @ U ) )
% 5.45/5.78 = ( set_or7049704709247886629st_num @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(7)
% 5.45/5.78 thf(fact_6933_ivl__disj__un__two_I7_J,axiom,
% 5.45/5.78 ! [L: nat,M: nat,U: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_nat @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 5.45/5.78 = ( set_or1269000886237332187st_nat @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(7)
% 5.45/5.78 thf(fact_6934_ivl__disj__un__two_I7_J,axiom,
% 5.45/5.78 ! [L: int,M: int,U: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ L @ M )
% 5.45/5.78 => ( ( ord_less_eq_int @ M @ U )
% 5.45/5.78 => ( ( sup_sup_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 5.45/5.78 = ( set_or1266510415728281911st_int @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(7)
% 5.45/5.78 thf(fact_6935_ivl__disj__un__two_I7_J,axiom,
% 5.45/5.78 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ L @ M )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ M @ U )
% 5.45/5.78 => ( ( sup_su848401254843788991nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 5.45/5.78 = ( set_or189985376899183464nteger @ L @ U ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_un_two(7)
% 5.45/5.78 thf(fact_6936_binomial__altdef__of__nat,axiom,
% 5.45/5.78 ! [K: nat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.78 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) )
% 5.45/5.78 = ( groups73079841787564623at_rat
% 5.45/5.78 @ ^ [I4: nat] : ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ N2 @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K @ I4 ) ) )
% 5.45/5.78 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_altdef_of_nat
% 5.45/5.78 thf(fact_6937_divmod__digit__0_I1_J,axiom,
% 5.45/5.78 ! [B: nat,A: nat] :
% 5.45/5.78 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.78 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(1)
% 5.45/5.78 thf(fact_6938_divmod__digit__0_I1_J,axiom,
% 5.45/5.78 ! [B: int,A: int] :
% 5.45/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.78 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(1)
% 5.45/5.78 thf(fact_6939_divmod__digit__0_I1_J,axiom,
% 5.45/5.78 ! [B: code_integer,A: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_0(1)
% 5.45/5.78 thf(fact_6940_ivl__disj__int__two_I7_J,axiom,
% 5.45/5.78 ! [L: $o,M: $o,U: $o] :
% 5.45/5.78 ( ( inf_inf_set_o @ ( set_or7139685690850216873Than_o @ L @ M ) @ ( set_or8904488021354931149Most_o @ M @ U ) )
% 5.45/5.78 = bot_bot_set_o ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(7)
% 5.45/5.78 thf(fact_6941_ivl__disj__int__two_I7_J,axiom,
% 5.45/5.78 ! [L: nat,M: nat,U: nat] :
% 5.45/5.78 ( ( inf_inf_set_nat @ ( set_or4665077453230672383an_nat @ L @ M ) @ ( set_or1269000886237332187st_nat @ M @ U ) )
% 5.45/5.78 = bot_bot_set_nat ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(7)
% 5.45/5.78 thf(fact_6942_ivl__disj__int__two_I7_J,axiom,
% 5.45/5.78 ! [L: int,M: int,U: int] :
% 5.45/5.78 ( ( inf_inf_set_int @ ( set_or4662586982721622107an_int @ L @ M ) @ ( set_or1266510415728281911st_int @ M @ U ) )
% 5.45/5.78 = bot_bot_set_int ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(7)
% 5.45/5.78 thf(fact_6943_ivl__disj__int__two_I7_J,axiom,
% 5.45/5.78 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.78 ( ( inf_in1364745209274528805nteger @ ( set_or8404916559141939852nteger @ L @ M ) @ ( set_or189985376899183464nteger @ M @ U ) )
% 5.45/5.78 = bot_bo3990330152332043303nteger ) ).
% 5.45/5.78
% 5.45/5.78 % ivl_disj_int_two(7)
% 5.45/5.78 thf(fact_6944_sum_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6945_sum_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > rat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6946_sum_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > int] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6947_sum_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6948_sum__diff__nat__ivl,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,F: nat > rat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat @ F @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_diff_nat_ivl
% 5.45/5.78 thf(fact_6949_sum__diff__nat__ivl,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,F: nat > int] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) )
% 5.45/5.78 = ( groups3539618377306564664at_int @ F @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_diff_nat_ivl
% 5.45/5.78 thf(fact_6950_power2__diff,axiom,
% 5.45/5.78 ! [X: int,Y: int] :
% 5.45/5.78 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( 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 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_diff
% 5.45/5.78 thf(fact_6951_power2__diff,axiom,
% 5.45/5.78 ! [X: code_integer,Y: code_integer] :
% 5.45/5.78 ( ( power_8256067586552552935nteger @ ( minus_8373710615458151222nteger @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_diff
% 5.45/5.78 thf(fact_6952_power2__diff,axiom,
% 5.45/5.78 ! [X: rat,Y: rat] :
% 5.45/5.78 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 = ( 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 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % power2_diff
% 5.45/5.78 thf(fact_6953_binomial__code,axiom,
% 5.45/5.78 ( binomial
% 5.45/5.78 = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % binomial_code
% 5.45/5.78 thf(fact_6954_prod_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > code_integer] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6955_prod_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > assn] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6956_prod_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > rat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6957_prod_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6958_prod_OatLeastLessThan__concat,axiom,
% 5.45/5.78 ! [M: nat,N2: nat,P3: nat,G: nat > int] :
% 5.45/5.78 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.78 => ( ( ord_less_eq_nat @ N2 @ P3 )
% 5.45/5.78 => ( ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ P3 ) ) )
% 5.45/5.78 = ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ P3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.atLeastLessThan_concat
% 5.45/5.78 thf(fact_6959_odd__0__le__power__imp__0__le,axiom,
% 5.45/5.78 ! [A: code_integer,N2: nat] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_0_le_power_imp_0_le
% 5.45/5.78 thf(fact_6960_odd__0__le__power__imp__0__le,axiom,
% 5.45/5.78 ! [A: rat,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_0_le_power_imp_0_le
% 5.45/5.78 thf(fact_6961_odd__0__le__power__imp__0__le,axiom,
% 5.45/5.78 ! [A: int,N2: nat] :
% 5.45/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_0_le_power_imp_0_le
% 5.45/5.78 thf(fact_6962_odd__power__less__zero,axiom,
% 5.45/5.78 ! [A: code_integer,N2: nat] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.45/5.78 => ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_z3403309356797280102nteger ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_power_less_zero
% 5.45/5.78 thf(fact_6963_odd__power__less__zero,axiom,
% 5.45/5.78 ! [A: rat,N2: nat] :
% 5.45/5.78 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.45/5.78 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_power_less_zero
% 5.45/5.78 thf(fact_6964_odd__power__less__zero,axiom,
% 5.45/5.78 ! [A: int,N2: nat] :
% 5.45/5.78 ( ( ord_less_int @ A @ zero_zero_int )
% 5.45/5.78 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 5.45/5.78
% 5.45/5.78 % odd_power_less_zero
% 5.45/5.78 thf(fact_6965_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups4406642042086082107nteger @ F @ A3 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 = ( ! [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6966_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups7501900531339628137nteger @ F @ A3 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 = ( ! [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6967_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups7873554091576472773nteger @ F @ A3 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 = ( ! [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6968_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups879477027807139574nteger @ F @ A3 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 = ( ! [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6969_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > rat] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups7872700643590313910_o_rat @ F @ A3 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 = ( ! [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6970_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups2906978787729119204at_rat @ F @ A3 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 = ( ! [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6971_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > rat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups3906332499630173760nt_rat @ F @ A3 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 = ( ! [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6972_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups6602215022474089585er_rat @ F @ A3 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 = ( ! [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6973_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups8507830703676809646_o_nat @ F @ A3 )
% 5.45/5.78 = zero_zero_nat )
% 5.45/5.78 = ( ! [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6974_sum__nonneg__eq__0__iff,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.78 => ( ( ( groups4541462559716669496nt_nat @ F @ A3 )
% 5.45/5.78 = zero_zero_nat )
% 5.45/5.78 = ( ! [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ A3 )
% 5.45/5.78 => ( ( F @ X4 )
% 5.45/5.78 = zero_zero_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_eq_0_iff
% 5.45/5.78 thf(fact_6975_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_nat,T5: set_nat,G: nat > code_integer,I2: nat > nat,F: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ( finite_finite_nat @ T5 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6976_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_nat,T5: set_int,G: int > code_integer,I2: int > nat,F: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ( finite_finite_int @ T5 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: int] :
% 5.45/5.78 ( ( member_int @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6977_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_nat,T5: set_Code_integer,G: code_integer > code_integer,I2: code_integer > nat,F: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T5 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6978_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_int,T5: set_nat,G: nat > code_integer,I2: nat > int,F: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ( finite_finite_nat @ T5 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6979_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_int,T5: set_int,G: int > code_integer,I2: int > int,F: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ( finite_finite_int @ T5 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: int] :
% 5.45/5.78 ( ( member_int @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6980_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_int,T5: set_Code_integer,G: code_integer > code_integer,I2: code_integer > int,F: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T5 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups7873554091576472773nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6981_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,T5: set_nat,G: nat > code_integer,I2: nat > code_integer,F: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ( finite_finite_nat @ T5 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups7501900531339628137nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6982_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,T5: set_int,G: int > code_integer,I2: int > code_integer,F: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ( finite_finite_int @ T5 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: int] :
% 5.45/5.78 ( ( member_int @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups7873554091576472773nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6983_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,T5: set_Code_integer,G: code_integer > code_integer,I2: code_integer > code_integer,F: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T5 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ T5 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_le3102999989581377725nteger @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ S2 ) @ ( groups879477027807139574nteger @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6984_sum__le__included,axiom,
% 5.45/5.78 ! [S2: set_nat,T5: set_nat,G: nat > rat,I2: nat > nat,F: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ( finite_finite_nat @ T5 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ T5 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S2 )
% 5.45/5.78 => ? [Xa2: nat] :
% 5.45/5.78 ( ( member_nat @ Xa2 @ T5 )
% 5.45/5.78 & ( ( I2 @ Xa2 )
% 5.45/5.78 = X3 )
% 5.45/5.78 & ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ Xa2 ) ) ) )
% 5.45/5.78 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S2 ) @ ( groups2906978787729119204at_rat @ G @ T5 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_le_included
% 5.45/5.78 thf(fact_6985_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: nat] :
% 5.45/5.78 ( ( member_nat @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_rat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6986_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: int] :
% 5.45/5.78 ( ( member_int @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_rat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6987_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_rat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6988_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > nat,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: int] :
% 5.45/5.78 ( ( member_int @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_nat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6989_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_nat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6990_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > int,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: nat] :
% 5.45/5.78 ( ( member_nat @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_int @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6991_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_int @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6992_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > nat,G: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: nat] :
% 5.45/5.78 ( ( member_nat @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_nat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6993_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > int,G: int > int] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: int] :
% 5.45/5.78 ( ( member_int @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_int @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6994_sum__strict__mono__ex1,axiom,
% 5.45/5.78 ! [A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat,G: product_prod_nat_nat > rat] :
% 5.45/5.78 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.78 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.78 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ? [X7: product_prod_nat_nat] :
% 5.45/5.78 ( ( member8440522571783428010at_nat @ X7 @ A3 )
% 5.45/5.78 & ( ord_less_rat @ ( F @ X7 ) @ ( G @ X7 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups342789780944988191at_rat @ F @ A3 ) @ ( groups342789780944988191at_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono_ex1
% 5.45/5.78 thf(fact_6995_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_6996_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > rat,G: $o > rat] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_o )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_6997_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_6998_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_int )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_rat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_6999_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7000_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > nat,G: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_o )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( groups8507830703676809646_o_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7001_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_int,F: int > nat,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_int )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_nat @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7002_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7003_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_o,F: $o > int,G: $o > int] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_o )
% 5.45/5.78 => ( ! [X3: $o] :
% 5.45/5.78 ( ( member_o @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A3 ) @ ( groups8505340233167759370_o_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7004_sum__strict__mono,axiom,
% 5.45/5.78 ! [A3: set_nat,F: nat > int,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ A3 )
% 5.45/5.78 => ( ord_less_int @ ( F @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ G @ A3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_strict_mono
% 5.45/5.78 thf(fact_7005_prod_Orelated,axiom,
% 5.45/5.78 ! [R: code_integer > code_integer > $o,S: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 5.45/5.78 ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 5.45/5.78 => ( ! [X12: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_3573771949741848930nteger @ X12 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups3455450783089532116nteger @ H @ S ) @ ( groups3455450783089532116nteger @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7006_prod_Orelated,axiom,
% 5.45/5.78 ! [R: code_integer > code_integer > $o,S: set_int,H: int > code_integer,G: int > code_integer] :
% 5.45/5.78 ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 5.45/5.78 => ( ! [X12: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_3573771949741848930nteger @ X12 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups3827104343326376752nteger @ H @ S ) @ ( groups3827104343326376752nteger @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7007_prod_Orelated,axiom,
% 5.45/5.78 ! [R: code_integer > code_integer > $o,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.78 ( ( R @ one_one_Code_integer @ one_one_Code_integer )
% 5.45/5.78 => ( ! [X12: code_integer,Y12: code_integer,X22: code_integer,Y22: code_integer] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_3573771949741848930nteger @ X12 @ Y12 ) @ ( times_3573771949741848930nteger @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups3674199335183972705nteger @ H @ S ) @ ( groups3674199335183972705nteger @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7008_prod_Orelated,axiom,
% 5.45/5.78 ! [R: assn > assn > $o,S: set_nat,H: nat > assn,G: nat > assn] :
% 5.45/5.78 ( ( R @ one_one_assn @ one_one_assn )
% 5.45/5.78 => ( ! [X12: assn,Y12: assn,X22: assn,Y22: assn] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_assn @ X12 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups6906906614972039071t_assn @ H @ S ) @ ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7009_prod_Orelated,axiom,
% 5.45/5.78 ! [R: assn > assn > $o,S: set_int,H: int > assn,G: int > assn] :
% 5.45/5.78 ( ( R @ one_one_assn @ one_one_assn )
% 5.45/5.78 => ( ! [X12: assn,Y12: assn,X22: assn,Y22: assn] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_assn @ X12 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups7882442080178216443t_assn @ H @ S ) @ ( groups7882442080178216443t_assn @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7010_prod_Orelated,axiom,
% 5.45/5.78 ! [R: assn > assn > $o,S: set_Code_integer,H: code_integer > assn,G: code_integer > assn] :
% 5.45/5.78 ( ( R @ one_one_assn @ one_one_assn )
% 5.45/5.78 => ( ! [X12: assn,Y12: assn,X22: assn,Y22: assn] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_assn @ X12 @ Y12 ) @ ( times_times_assn @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups1304777262505850412r_assn @ H @ S ) @ ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7011_prod_Orelated,axiom,
% 5.45/5.78 ! [R: rat > rat > $o,S: set_nat,H: nat > rat,G: nat > rat] :
% 5.45/5.78 ( ( R @ one_one_rat @ one_one_rat )
% 5.45/5.78 => ( ! [X12: rat,Y12: rat,X22: rat,Y22: rat] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_rat @ X12 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ! [X3: nat] :
% 5.45/5.78 ( ( member_nat @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups73079841787564623at_rat @ H @ S ) @ ( groups73079841787564623at_rat @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7012_prod_Orelated,axiom,
% 5.45/5.78 ! [R: rat > rat > $o,S: set_int,H: int > rat,G: int > rat] :
% 5.45/5.78 ( ( R @ one_one_rat @ one_one_rat )
% 5.45/5.78 => ( ! [X12: rat,Y12: rat,X22: rat,Y22: rat] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_rat @ X12 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups1072433553688619179nt_rat @ H @ S ) @ ( groups1072433553688619179nt_rat @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7013_prod_Orelated,axiom,
% 5.45/5.78 ! [R: rat > rat > $o,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.78 ( ( R @ one_one_rat @ one_one_rat )
% 5.45/5.78 => ( ! [X12: rat,Y12: rat,X22: rat,Y22: rat] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_rat @ X12 @ Y12 ) @ ( times_times_rat @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ! [X3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups2555765274223993564er_rat @ H @ S ) @ ( groups2555765274223993564er_rat @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7014_prod_Orelated,axiom,
% 5.45/5.78 ! [R: nat > nat > $o,S: set_int,H: int > nat,G: int > nat] :
% 5.45/5.78 ( ( R @ one_one_nat @ one_one_nat )
% 5.45/5.78 => ( ! [X12: nat,Y12: nat,X22: nat,Y22: nat] :
% 5.45/5.78 ( ( ( R @ X12 @ X22 )
% 5.45/5.78 & ( R @ Y12 @ Y22 ) )
% 5.45/5.78 => ( R @ ( times_times_nat @ X12 @ Y12 ) @ ( times_times_nat @ X22 @ Y22 ) ) )
% 5.45/5.78 => ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ! [X3: int] :
% 5.45/5.78 ( ( member_int @ X3 @ S )
% 5.45/5.78 => ( R @ ( H @ X3 ) @ ( G @ X3 ) ) )
% 5.45/5.78 => ( R @ ( groups1707563613775114915nt_nat @ H @ S ) @ ( groups1707563613775114915nt_nat @ G @ S ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.related
% 5.45/5.78 thf(fact_7015_ex__power__ivl1,axiom,
% 5.45/5.78 ! [B: nat,K: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.45/5.78 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.45/5.78 => ? [N5: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N5 ) @ K )
% 5.45/5.78 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_power_ivl1
% 5.45/5.78 thf(fact_7016_ex__power__ivl2,axiom,
% 5.45/5.78 ! [B: nat,K: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.45/5.78 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.45/5.78 => ? [N5: nat] :
% 5.45/5.78 ( ( ord_less_nat @ ( power_power_nat @ B @ N5 ) @ K )
% 5.45/5.78 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N5 @ one_one_nat ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % ex_power_ivl2
% 5.45/5.78 thf(fact_7017_atLeastLessThan__add__Un,axiom,
% 5.45/5.78 ! [I2: nat,J: nat,K: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ I2 @ J )
% 5.45/5.78 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.45/5.78 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % atLeastLessThan_add_Un
% 5.45/5.78 thf(fact_7018_mask__eq__sum__exp,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.45/5.78 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Q7: nat] : ( ord_less_nat @ Q7 @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mask_eq_sum_exp
% 5.45/5.78 thf(fact_7019_mask__eq__sum__exp,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer )
% 5.45/5.78 = ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Q7: nat] : ( ord_less_nat @ Q7 @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mask_eq_sum_exp
% 5.45/5.78 thf(fact_7020_mask__eq__sum__exp,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_natural )
% 5.45/5.78 = ( groups6325495683096345652atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Q7: nat] : ( ord_less_nat @ Q7 @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mask_eq_sum_exp
% 5.45/5.78 thf(fact_7021_mask__eq__sum__exp,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Q7: nat] : ( ord_less_nat @ Q7 @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mask_eq_sum_exp
% 5.45/5.78 thf(fact_7022_mult__1s__ring__1_I1_J,axiom,
% 5.45/5.78 ! [B: int] :
% 5.45/5.78 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.45/5.78 = ( uminus_uminus_int @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(1)
% 5.45/5.78 thf(fact_7023_mult__1s__ring__1_I1_J,axiom,
% 5.45/5.78 ! [B: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.45/5.78 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(1)
% 5.45/5.78 thf(fact_7024_mult__1s__ring__1_I1_J,axiom,
% 5.45/5.78 ! [B: rat] :
% 5.45/5.78 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.45/5.78 = ( uminus_uminus_rat @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(1)
% 5.45/5.78 thf(fact_7025_mult__1s__ring__1_I2_J,axiom,
% 5.45/5.78 ! [B: int] :
% 5.45/5.78 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.45/5.78 = ( uminus_uminus_int @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(2)
% 5.45/5.78 thf(fact_7026_mult__1s__ring__1_I2_J,axiom,
% 5.45/5.78 ! [B: code_integer] :
% 5.45/5.78 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.45/5.78 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(2)
% 5.45/5.78 thf(fact_7027_mult__1s__ring__1_I2_J,axiom,
% 5.45/5.78 ! [B: rat] :
% 5.45/5.78 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.45/5.78 = ( uminus_uminus_rat @ B ) ) ).
% 5.45/5.78
% 5.45/5.78 % mult_1s_ring_1(2)
% 5.45/5.78 thf(fact_7028_sum_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > multis2468970476368604999at_nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups6857163185585827899at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs
% 5.45/5.78 thf(fact_7029_sum_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > rat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs
% 5.45/5.78 thf(fact_7030_sum_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > int,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs
% 5.45/5.78 thf(fact_7031_sum_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs
% 5.45/5.78 thf(fact_7032_mask__eq__sum__exp__nat,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [Q7: nat] : ( ord_less_nat @ Q7 @ N2 ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mask_eq_sum_exp_nat
% 5.45/5.78 thf(fact_7033_prod_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > code_integer,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3455450783089532116nteger
% 5.45/5.78 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs
% 5.45/5.78 thf(fact_7034_prod_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > assn,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups6906906614972039071t_assn
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs
% 5.45/5.78 thf(fact_7035_prod_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > rat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups73079841787564623at_rat
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs
% 5.45/5.78 thf(fact_7036_prod_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > nat,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs
% 5.45/5.78 thf(fact_7037_prod_Oin__pairs,axiom,
% 5.45/5.78 ! [G: nat > int,M: nat,N2: nat] :
% 5.45/5.78 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs
% 5.45/5.78 thf(fact_7038_gauss__sum__nat,axiom,
% 5.45/5.78 ! [N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [X4: nat] : X4
% 5.45/5.78 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.78 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % gauss_sum_nat
% 5.45/5.78 thf(fact_7039_prod__int__eq,axiom,
% 5.45/5.78 ! [I2: nat,J: nat] :
% 5.45/5.78 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.45/5.78 = ( groups1705073143266064639nt_int
% 5.45/5.78 @ ^ [X4: int] : X4
% 5.45/5.78 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod_int_eq
% 5.45/5.78 thf(fact_7040_sum_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 5.45/5.78 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups6857163185585827899at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_p7104986032573967614at_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs_0
% 5.45/5.78 thf(fact_7041_sum_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > rat,N2: nat] :
% 5.45/5.78 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs_0
% 5.45/5.78 thf(fact_7042_sum_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > int,N2: nat] :
% 5.45/5.78 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs_0
% 5.45/5.78 thf(fact_7043_sum_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.in_pairs_0
% 5.45/5.78 thf(fact_7044_prod_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > code_integer,N2: nat] :
% 5.45/5.78 ( ( groups3455450783089532116nteger @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups3455450783089532116nteger
% 5.45/5.78 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs_0
% 5.45/5.78 thf(fact_7045_prod_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > assn,N2: nat] :
% 5.45/5.78 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups6906906614972039071t_assn
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_assn @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs_0
% 5.45/5.78 thf(fact_7046_prod_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > rat,N2: nat] :
% 5.45/5.78 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups73079841787564623at_rat
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs_0
% 5.45/5.78 thf(fact_7047_prod_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > nat,N2: nat] :
% 5.45/5.78 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups708209901874060359at_nat
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs_0
% 5.45/5.78 thf(fact_7048_prod_Oin__pairs__0,axiom,
% 5.45/5.78 ! [G: nat > int,N2: nat] :
% 5.45/5.78 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.45/5.78 = ( groups705719431365010083at_int
% 5.45/5.78 @ ^ [I4: nat] : ( times_times_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) ) ) )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.in_pairs_0
% 5.45/5.78 thf(fact_7049_sum__choose__lower,axiom,
% 5.45/5.78 ! [R3: nat,N2: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 5.45/5.78 @ ( set_ord_atMost_nat @ N2 ) )
% 5.45/5.78 = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N2 ) ) @ N2 ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_choose_lower
% 5.45/5.78 thf(fact_7050_choose__rising__sum_I2_J,axiom,
% 5.45/5.78 ! [N2: nat,M: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.45/5.78 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.78 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_rising_sum(2)
% 5.45/5.78 thf(fact_7051_choose__rising__sum_I1_J,axiom,
% 5.45/5.78 ! [N2: nat,M: nat] :
% 5.45/5.78 ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.45/5.78 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.78 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % choose_rising_sum(1)
% 5.45/5.78 thf(fact_7052_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > code_integer,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups4406642042086082107nteger @ F @ S2 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7053_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_nat,F: nat > code_integer,I2: nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7501900531339628137nteger @ F @ S2 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 => ( ( member_nat @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7054_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > code_integer,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7873554091576472773nteger @ F @ S2 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7055_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,F: code_integer > code_integer,I2: code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups879477027807139574nteger @ F @ S2 )
% 5.45/5.78 = zero_z3403309356797280102nteger )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7056_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > rat,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7057_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_nat,F: nat > rat,I2: nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 => ( ( member_nat @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7058_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > rat,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7059_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,F: code_integer > rat,I2: code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 5.45/5.78 = zero_zero_rat )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7060_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > nat,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups8507830703676809646_o_nat @ F @ S2 )
% 5.45/5.78 = zero_zero_nat )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7061_sum__nonneg__0,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > nat,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.45/5.78 = zero_zero_nat )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ( F @ I2 )
% 5.45/5.78 = zero_zero_nat ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_0
% 5.45/5.78 thf(fact_7062_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > code_integer,B3: code_integer,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups4406642042086082107nteger @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7063_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_nat,F: nat > code_integer,B3: code_integer,I2: nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7501900531339628137nteger @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_nat @ I2 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7064_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > code_integer,B3: code_integer,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7873554091576472773nteger @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7065_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,F: code_integer > code_integer,B3: code_integer,I2: code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups879477027807139574nteger @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ S2 )
% 5.45/5.78 => ( ord_le3102999989581377725nteger @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7066_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > rat,B3: rat,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups7872700643590313910_o_rat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7067_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_nat,F: nat > rat,B3: rat,I2: nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S2 )
% 5.45/5.78 => ( ! [I3: nat] :
% 5.45/5.78 ( ( member_nat @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups2906978787729119204at_rat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_nat @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7068_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > rat,B3: rat,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups3906332499630173760nt_rat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7069_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_Code_integer,F: code_integer > rat,B3: rat,I2: code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S2 )
% 5.45/5.78 => ( ! [I3: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups6602215022474089585er_rat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_Code_integer @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_rat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7070_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_o,F: $o > nat,B3: nat,I2: $o] :
% 5.45/5.78 ( ( finite_finite_o @ S2 )
% 5.45/5.78 => ( ! [I3: $o] :
% 5.45/5.78 ( ( member_o @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups8507830703676809646_o_nat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_o @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7071_sum__nonneg__leq__bound,axiom,
% 5.45/5.78 ! [S2: set_int,F: int > nat,B3: nat,I2: int] :
% 5.45/5.78 ( ( finite_finite_int @ S2 )
% 5.45/5.78 => ( ! [I3: int] :
% 5.45/5.78 ( ( member_int @ I3 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.78 => ( ( ( groups4541462559716669496nt_nat @ F @ S2 )
% 5.45/5.78 = B3 )
% 5.45/5.78 => ( ( member_int @ I2 @ S2 )
% 5.45/5.78 => ( ord_less_eq_nat @ ( F @ I2 ) @ B3 ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum_nonneg_leq_bound
% 5.45/5.78 thf(fact_7072_mod__double__modulus,axiom,
% 5.45/5.78 ! [M: code_integer,X: code_integer] :
% 5.45/5.78 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.45/5.78 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.45/5.78 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mod_double_modulus
% 5.45/5.78 thf(fact_7073_mod__double__modulus,axiom,
% 5.45/5.78 ! [M: nat,X: nat] :
% 5.45/5.78 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.45/5.78 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( modulo_modulo_nat @ X @ M ) )
% 5.45/5.78 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mod_double_modulus
% 5.45/5.78 thf(fact_7074_mod__double__modulus,axiom,
% 5.45/5.78 ! [M: int,X: int] :
% 5.45/5.78 ( ( ord_less_int @ zero_zero_int @ M )
% 5.45/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.45/5.78 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( modulo_modulo_int @ X @ M ) )
% 5.45/5.78 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.45/5.78 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % mod_double_modulus
% 5.45/5.78 thf(fact_7075_divmod__digit__1_I2_J,axiom,
% 5.45/5.78 ! [A: code_integer,B: code_integer] :
% 5.45/5.78 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.78 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.78 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_1(2)
% 5.45/5.78 thf(fact_7076_divmod__digit__1_I2_J,axiom,
% 5.45/5.78 ! [A: nat,B: nat] :
% 5.45/5.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.78 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.78 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_1(2)
% 5.45/5.78 thf(fact_7077_divmod__digit__1_I2_J,axiom,
% 5.45/5.78 ! [A: int,B: int] :
% 5.45/5.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.78 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.78 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.78 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.45/5.78 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % divmod_digit_1(2)
% 5.45/5.78 thf(fact_7078_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_int_int > nat,A: product_prod_int_int] :
% 5.45/5.78 ( ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7079_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: list_nat > nat,A: list_nat] :
% 5.45/5.78 ( ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7080_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: set_nat > nat,A: set_nat] :
% 5.45/5.78 ( ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7081_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: nat > nat,A: nat] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7082_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: int > nat,A: int] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7083_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: code_integer > nat,A: code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7084_add__mset__in__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_nat_nat > nat,A: product_prod_nat_nat] :
% 5.45/5.78 ( ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( if_nat @ ( X4 = A ) @ ( suc @ ( M6 @ X4 ) ) @ ( M6 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % add_mset_in_multiset
% 5.45/5.78 thf(fact_7085_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > code_integer,B3: set_o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups4406642042086082107nteger @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.78 = ( groups4406642042086082107nteger
% 5.45/5.78 @ ^ [X4: $o] : ( if_Code_integer @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7086_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > code_integer,B3: set_int] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups7873554091576472773nteger @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.78 = ( groups7873554091576472773nteger
% 5.45/5.78 @ ^ [X4: int] : ( if_Code_integer @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7087_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > code_integer,B3: set_Code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups879477027807139574nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.78 = ( groups879477027807139574nteger
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_Code_integer @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ zero_z3403309356797280102nteger )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7088_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > rat,B3: set_o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups7872700643590313910_o_rat @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.78 = ( groups7872700643590313910_o_rat
% 5.45/5.78 @ ^ [X4: $o] : ( if_rat @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7089_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > rat,B3: set_int] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.78 = ( groups3906332499630173760nt_rat
% 5.45/5.78 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7090_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > rat,B3: set_Code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.78 = ( groups6602215022474089585er_rat
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_rat @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_rat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7091_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > nat,B3: set_o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups8507830703676809646_o_nat @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.78 = ( groups8507830703676809646_o_nat
% 5.45/5.78 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_nat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7092_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > nat,B3: set_int] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.78 = ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [X4: int] : ( if_nat @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_nat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7093_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > nat,B3: set_Code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.78 = ( groups7237345082560585321er_nat
% 5.45/5.78 @ ^ [X4: code_integer] : ( if_nat @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_nat )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7094_sum_Ointer__restrict,axiom,
% 5.45/5.78 ! [A3: set_o,G: $o > int,B3: set_o] :
% 5.45/5.78 ( ( finite_finite_o @ A3 )
% 5.45/5.78 => ( ( groups8505340233167759370_o_int @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.78 = ( groups8505340233167759370_o_int
% 5.45/5.78 @ ^ [X4: $o] : ( if_int @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ zero_zero_int )
% 5.45/5.78 @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.inter_restrict
% 5.45/5.78 thf(fact_7095_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_Code_integer,G: nat > code_integer,H: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T )
% 5.45/5.78 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups7237345082560585321er_nat
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7096_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_int,G: nat > int,H: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite_finite_int @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7097_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_int,T: set_nat,G: int > nat,H: int > int] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( finite_finite_nat @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3539618377306564664at_int
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups4538972089207619220nt_int @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7098_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_int,T: set_Code_integer,G: int > code_integer,H: int > int] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T )
% 5.45/5.78 => ( ( ord_le7084787975880047091nteger @ ( image_1587234942943678608nteger @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups7234854612051535045er_int
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups4538972089207619220nt_int @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups4538972089207619220nt_int @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7099_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_o,T: set_nat,G: $o > nat,H: $o > nat] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( finite_finite_nat @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_nat @ ( image_o_nat @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups8507830703676809646_o_nat @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups8507830703676809646_o_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7100_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_int,T: set_nat,G: int > nat,H: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( finite_finite_nat @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups4541462559716669496nt_nat @ H
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( member_int @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups4541462559716669496nt_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7101_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_Code_integer,T: set_nat,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.78 => ( ( finite_finite_nat @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_nat @ ( image_951025933927791156er_nat @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups7237345082560585321er_nat @ H
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups7237345082560585321er_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7102_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_nat,G: nat > nat,H: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite_finite_nat @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3542108847815614940at_nat
% 5.45/5.78 @ ^ [Y4: nat] :
% 5.45/5.78 ( groups3542108847815614940at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups3542108847815614940at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7103_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_o,T: set_int,G: $o > int,H: $o > int] :
% 5.45/5.78 ( ( finite_finite_o @ S )
% 5.45/5.78 => ( ( finite_finite_int @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_int @ ( image_o_int @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups8505340233167759370_o_int @ H
% 5.45/5.78 @ ( collect_o
% 5.45/5.78 @ ^ [X4: $o] :
% 5.45/5.78 ( ( member_o @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups8505340233167759370_o_int @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7104_sum_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_int,G: nat > int,H: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite_finite_int @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups4538972089207619220nt_int
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups3539618377306564664at_int @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups3539618377306564664at_int @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.group
% 5.45/5.78 thf(fact_7105_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > code_integer] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups7873554091576472773nteger @ G
% 5.45/5.78 @ ( minus_minus_set_int @ A3
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 = ( groups7873554091576472773nteger @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7106_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups879477027807139574nteger @ G
% 5.45/5.78 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 = ( groups879477027807139574nteger @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7107_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > rat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups3906332499630173760nt_rat @ G
% 5.45/5.78 @ ( minus_minus_set_int @ A3
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) )
% 5.45/5.78 = ( groups3906332499630173760nt_rat @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7108_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups6602215022474089585er_rat @ G
% 5.45/5.78 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) )
% 5.45/5.78 = ( groups6602215022474089585er_rat @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7109_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_int,G: int > nat] :
% 5.45/5.78 ( ( finite_finite_int @ A3 )
% 5.45/5.78 => ( ( groups4541462559716669496nt_nat @ G
% 5.45/5.78 @ ( minus_minus_set_int @ A3
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_nat ) ) ) )
% 5.45/5.78 = ( groups4541462559716669496nt_nat @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7110_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups7237345082560585321er_nat @ G
% 5.45/5.78 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_nat ) ) ) )
% 5.45/5.78 = ( groups7237345082560585321er_nat @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7111_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_Code_integer,G: code_integer > int] :
% 5.45/5.78 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.78 => ( ( groups7234854612051535045er_int @ G
% 5.45/5.78 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_int ) ) ) )
% 5.45/5.78 = ( groups7234854612051535045er_int @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7112_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > code_integer] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups7501900531339628137nteger @ G
% 5.45/5.78 @ ( minus_minus_set_nat @ A3
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_z3403309356797280102nteger ) ) ) )
% 5.45/5.78 = ( groups7501900531339628137nteger @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7113_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > rat] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups2906978787729119204at_rat @ G
% 5.45/5.78 @ ( minus_minus_set_nat @ A3
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_rat ) ) ) )
% 5.45/5.78 = ( groups2906978787729119204at_rat @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7114_sum_Osetdiff__irrelevant,axiom,
% 5.45/5.78 ! [A3: set_nat,G: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ A3 )
% 5.45/5.78 => ( ( groups3539618377306564664at_int @ G
% 5.45/5.78 @ ( minus_minus_set_nat @ A3
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( G @ X4 )
% 5.45/5.78 = zero_zero_int ) ) ) )
% 5.45/5.78 = ( groups3539618377306564664at_int @ G @ A3 ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % sum.setdiff_irrelevant
% 5.45/5.78 thf(fact_7115_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_int_int > nat,N7: product_prod_int_int > nat] :
% 5.45/5.78 ( ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite2998713641127702882nt_int
% 5.45/5.78 @ ( collec213857154873943460nt_int
% 5.45/5.78 @ ^ [X4: product_prod_int_int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7116_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: list_nat > nat,N7: list_nat > nat] :
% 5.45/5.78 ( ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite8100373058378681591st_nat
% 5.45/5.78 @ ( collect_list_nat
% 5.45/5.78 @ ^ [X4: list_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7117_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: set_nat > nat,N7: set_nat > nat] :
% 5.45/5.78 ( ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite1152437895449049373et_nat
% 5.45/5.78 @ ( collect_set_nat
% 5.45/5.78 @ ^ [X4: set_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7118_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: nat > nat,N7: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_nat
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7119_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: int > nat,N7: int > nat] :
% 5.45/5.78 ( ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite_finite_int
% 5.45/5.78 @ ( collect_int
% 5.45/5.78 @ ^ [X4: int] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7120_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: code_integer > nat,N7: code_integer > nat] :
% 5.45/5.78 ( ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6017078050557962740nteger
% 5.45/5.78 @ ( collect_Code_integer
% 5.45/5.78 @ ^ [X4: code_integer] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7121_diff__preserves__multiset,axiom,
% 5.45/5.78 ! [M6: product_prod_nat_nat > nat,N7: product_prod_nat_nat > nat] :
% 5.45/5.78 ( ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( M6 @ X4 ) ) ) )
% 5.45/5.78 => ( finite6177210948735845034at_nat
% 5.45/5.78 @ ( collec3392354462482085612at_nat
% 5.45/5.78 @ ^ [X4: product_prod_nat_nat] : ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( M6 @ X4 ) @ ( N7 @ X4 ) ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % diff_preserves_multiset
% 5.45/5.78 thf(fact_7122_prod_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_Code_integer,G: nat > code_integer,H: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T )
% 5.45/5.78 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3190895334310489300er_nat
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups708209901874060359at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups708209901874060359at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.group
% 5.45/5.78 thf(fact_7123_prod_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_int,G: nat > int,H: nat > nat] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite_finite_int @ T )
% 5.45/5.78 => ( ( ord_less_eq_set_int @ ( image_nat_int @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups1707563613775114915nt_nat
% 5.45/5.78 @ ^ [Y4: int] :
% 5.45/5.78 ( groups708209901874060359at_nat @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups708209901874060359at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.group
% 5.45/5.78 thf(fact_7124_prod_Ogroup,axiom,
% 5.45/5.78 ! [S: set_nat,T: set_Code_integer,G: nat > code_integer,H: nat > int] :
% 5.45/5.78 ( ( finite_finite_nat @ S )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T )
% 5.45/5.78 => ( ( ord_le7084787975880047091nteger @ ( image_1215581382706833972nteger @ G @ S ) @ T )
% 5.45/5.78 => ( ( groups3188404863801439024er_int
% 5.45/5.78 @ ^ [Y4: code_integer] :
% 5.45/5.78 ( groups705719431365010083at_int @ H
% 5.45/5.78 @ ( collect_nat
% 5.45/5.78 @ ^ [X4: nat] :
% 5.45/5.78 ( ( member_nat @ X4 @ S )
% 5.45/5.78 & ( ( G @ X4 )
% 5.45/5.78 = Y4 ) ) ) )
% 5.45/5.78 @ T )
% 5.45/5.78 = ( groups705719431365010083at_int @ H @ S ) ) ) ) ) ).
% 5.45/5.78
% 5.45/5.78 % prod.group
% 5.45/5.78 thf(fact_7125_prod_Ogroup,axiom,
% 5.45/5.78 ! [S: set_int,T: set_Code_integer,G: int > code_integer,H: int > int] :
% 5.45/5.78 ( ( finite_finite_int @ S )
% 5.45/5.78 => ( ( finite6017078050557962740nteger @ T )
% 5.45/5.78 => ( ( ord_le7084787975880047091nteger @ ( image_1587234942943678608nteger @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups3188404863801439024er_int
% 5.45/5.79 @ ^ [Y4: code_integer] :
% 5.45/5.79 ( groups1705073143266064639nt_int @ H
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( member_int @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups1705073143266064639nt_int @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7126_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_o,T: set_nat,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_o_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups3504817904513533571_o_nat @ H
% 5.45/5.79 @ ( collect_o
% 5.45/5.79 @ ^ [X4: $o] :
% 5.45/5.79 ( ( member_o @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7127_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_int,T: set_nat,G: int > nat,H: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_int_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups1707563613775114915nt_nat @ H
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( member_int @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups1707563613775114915nt_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7128_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_Code_integer,T: set_nat,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_951025933927791156er_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups3190895334310489300er_nat @ H
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7129_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_nat,T: set_nat,G: nat > nat,H: nat > nat] :
% 5.45/5.79 ( ( finite_finite_nat @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_nat_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups708209901874060359at_nat @ H
% 5.45/5.79 @ ( collect_nat
% 5.45/5.79 @ ^ [X4: nat] :
% 5.45/5.79 ( ( member_nat @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups708209901874060359at_nat @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7130_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_o,T: set_nat,G: $o > nat,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_o_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups3502327434004483295_o_int @ H
% 5.45/5.79 @ ( collect_o
% 5.45/5.79 @ ^ [X4: $o] :
% 5.45/5.79 ( ( member_o @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7131_prod_Ogroup,axiom,
% 5.45/5.79 ! [S: set_Code_integer,T: set_nat,G: code_integer > nat,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ ( image_951025933927791156er_nat @ G @ S ) @ T )
% 5.45/5.79 => ( ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [Y4: nat] :
% 5.45/5.79 ( groups3188404863801439024er_int @ H
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X4 @ S )
% 5.45/5.79 & ( ( G @ X4 )
% 5.45/5.79 = Y4 ) ) ) )
% 5.45/5.79 @ T )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.group
% 5.45/5.79 thf(fact_7132_subset__eq__atLeast0__atMost__finite,axiom,
% 5.45/5.79 ! [N7: set_nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ N7 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 => ( finite_finite_nat @ N7 ) ) ).
% 5.45/5.79
% 5.45/5.79 % subset_eq_atLeast0_atMost_finite
% 5.45/5.79 thf(fact_7133_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_o,G: $o > code_integer,B3: set_o] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ( groups7694694392188491536nteger @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.79 = ( groups7694694392188491536nteger
% 5.45/5.79 @ ^ [X4: $o] : ( if_Code_integer @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7134_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > code_integer,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( groups3827104343326376752nteger
% 5.45/5.79 @ ^ [X4: int] : ( if_Code_integer @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7135_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > code_integer,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( groups3674199335183972705nteger
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_Code_integer @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_Code_integer )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7136_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_o,G: $o > assn,B3: set_o] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ( groups5301882518646026715o_assn @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.79 = ( groups5301882518646026715o_assn
% 5.45/5.79 @ ^ [X4: $o] : ( if_assn @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7137_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > assn,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( groups7882442080178216443t_assn
% 5.45/5.79 @ ^ [X4: int] : ( if_assn @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7138_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > assn,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( groups1304777262505850412r_assn
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_assn @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_assn )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7139_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_o,G: $o > rat,B3: set_o] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ( groups2869687844427037835_o_rat @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.79 = ( groups2869687844427037835_o_rat
% 5.45/5.79 @ ^ [X4: $o] : ( if_rat @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_rat )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7140_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > rat,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( groups1072433553688619179nt_rat
% 5.45/5.79 @ ^ [X4: int] : ( if_rat @ ( member_int @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_rat )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7141_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > rat,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( groups2555765274223993564er_rat
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_rat @ ( member_Code_integer @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_rat )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7142_prod_Ointer__restrict,axiom,
% 5.45/5.79 ! [A3: set_o,G: $o > nat,B3: set_o] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ( groups3504817904513533571_o_nat @ G @ ( inf_inf_set_o @ A3 @ B3 ) )
% 5.45/5.79 = ( groups3504817904513533571_o_nat
% 5.45/5.79 @ ^ [X4: $o] : ( if_nat @ ( member_o @ X4 @ B3 ) @ ( G @ X4 ) @ one_one_nat )
% 5.45/5.79 @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.inter_restrict
% 5.45/5.79 thf(fact_7143_power__numeral__even,axiom,
% 5.45/5.79 ! [Z: code_integer,W2: num] :
% 5.45/5.79 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W2 ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % power_numeral_even
% 5.45/5.79 thf(fact_7144_power__numeral__even,axiom,
% 5.45/5.79 ! [Z: assn,W2: num] :
% 5.45/5.79 ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.45/5.79 = ( times_times_assn @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % power_numeral_even
% 5.45/5.79 thf(fact_7145_power__numeral__even,axiom,
% 5.45/5.79 ! [Z: rat,W2: num] :
% 5.45/5.79 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % power_numeral_even
% 5.45/5.79 thf(fact_7146_power__numeral__even,axiom,
% 5.45/5.79 ! [Z: nat,W2: num] :
% 5.45/5.79 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % power_numeral_even
% 5.45/5.79 thf(fact_7147_power__numeral__even,axiom,
% 5.45/5.79 ! [Z: int,W2: num] :
% 5.45/5.79 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W2 ) ) )
% 5.45/5.79 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W2 ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % power_numeral_even
% 5.45/5.79 thf(fact_7148_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G
% 5.45/5.79 @ ( minus_minus_set_int @ A3
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_Code_integer ) ) ) )
% 5.45/5.79 = ( groups3827104343326376752nteger @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7149_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G
% 5.45/5.79 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_Code_integer ) ) ) )
% 5.45/5.79 = ( groups3674199335183972705nteger @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7150_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G
% 5.45/5.79 @ ( minus_minus_set_int @ A3
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_assn ) ) ) )
% 5.45/5.79 = ( groups7882442080178216443t_assn @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7151_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G
% 5.45/5.79 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_assn ) ) ) )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7152_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1072433553688619179nt_rat @ G
% 5.45/5.79 @ ( minus_minus_set_int @ A3
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_rat ) ) ) )
% 5.45/5.79 = ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7153_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G
% 5.45/5.79 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_rat ) ) ) )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7154_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1707563613775114915nt_nat @ G
% 5.45/5.79 @ ( minus_minus_set_int @ A3
% 5.45/5.79 @ ( collect_int
% 5.45/5.79 @ ^ [X4: int] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_nat ) ) ) )
% 5.45/5.79 = ( groups1707563613775114915nt_nat @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7155_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G
% 5.45/5.79 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_nat ) ) ) )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7156_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G
% 5.45/5.79 @ ( minus_2355218937544613996nteger @ A3
% 5.45/5.79 @ ( collect_Code_integer
% 5.45/5.79 @ ^ [X4: code_integer] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_int ) ) ) )
% 5.45/5.79 = ( groups3188404863801439024er_int @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7157_prod_Osetdiff__irrelevant,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G
% 5.45/5.79 @ ( minus_minus_set_nat @ A3
% 5.45/5.79 @ ( collect_nat
% 5.45/5.79 @ ^ [X4: nat] :
% 5.45/5.79 ( ( G @ X4 )
% 5.45/5.79 = one_one_Code_integer ) ) ) )
% 5.45/5.79 = ( groups3455450783089532116nteger @ G @ A3 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.setdiff_irrelevant
% 5.45/5.79 thf(fact_7158_finite__abs__int__segment,axiom,
% 5.45/5.79 ! [A: rat] :
% 5.45/5.79 ( finite_finite_rat
% 5.45/5.79 @ ( collect_rat
% 5.45/5.79 @ ^ [K3: rat] :
% 5.45/5.79 ( ( member_rat @ K3 @ ring_1_Ints_rat )
% 5.45/5.79 & ( ord_less_eq_rat @ ( abs_abs_rat @ K3 ) @ A ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % finite_abs_int_segment
% 5.45/5.79 thf(fact_7159_neg__zdiv__mult__2,axiom,
% 5.45/5.79 ! [A: int,B: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.79 => ( ( 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 ) )
% 5.45/5.79 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % neg_zdiv_mult_2
% 5.45/5.79 thf(fact_7160_pos__zdiv__mult__2,axiom,
% 5.45/5.79 ! [A: int,B: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.79 => ( ( 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 ) )
% 5.45/5.79 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % pos_zdiv_mult_2
% 5.45/5.79 thf(fact_7161_pos__zmod__mult__2,axiom,
% 5.45/5.79 ! [A: int,B: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.79 => ( ( 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 ) )
% 5.45/5.79 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % pos_zmod_mult_2
% 5.45/5.79 thf(fact_7162_arith__series__nat,axiom,
% 5.45/5.79 ! [A: nat,D2: nat,N2: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I4 @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % arith_series_nat
% 5.45/5.79 thf(fact_7163_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: assn,B: assn,C: assn,D2: assn] :
% 5.45/5.79 ( ( ord_less_eq_set_assn @ ( set_or7959216805967363635t_assn @ A @ B ) @ ( set_or5523502641901747543n_assn @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_assn @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_assn @ C @ A )
% 5.45/5.79 & ( ord_less_assn @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7164_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: set_int,B: set_int,C: set_int,D2: set_int] :
% 5.45/5.79 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or8585797421378605585et_int @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_set_int @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ C @ A )
% 5.45/5.79 & ( ord_less_set_int @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7165_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.79 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or4029947393144176647an_rat @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.79 & ( ord_less_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7166_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: num,B: num,C: num,D2: num] :
% 5.45/5.79 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or1222409239386451017an_num @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_num @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_num @ C @ A )
% 5.45/5.79 & ( ord_less_num @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7167_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or4665077453230672383an_nat @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_nat @ C @ A )
% 5.45/5.79 & ( ord_less_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7168_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or4662586982721622107an_int @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_eq_int @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_int @ C @ A )
% 5.45/5.79 & ( ord_less_int @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7169_atLeastAtMost__subseteq__atLeastLessThan__iff,axiom,
% 5.45/5.79 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ ( set_or189985376899183464nteger @ A @ B ) @ ( set_or8404916559141939852nteger @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.45/5.79 & ( ord_le6747313008572928689nteger @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastAtMost_subseteq_atLeastLessThan_iff
% 5.45/5.79 thf(fact_7170_atLeastLessThan__subseteq__atLeastAtMost__iff,axiom,
% 5.45/5.79 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.79 ( ( ord_less_eq_set_rat @ ( set_or4029947393144176647an_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D2 ) )
% 5.45/5.79 = ( ( ord_less_rat @ A @ B )
% 5.45/5.79 => ( ( ord_less_eq_rat @ C @ A )
% 5.45/5.79 & ( ord_less_eq_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % atLeastLessThan_subseteq_atLeastAtMost_iff
% 5.45/5.79 thf(fact_7171_ivl__disj__un__two__touch_I2_J,axiom,
% 5.45/5.79 ! [L: rat,M: rat,U: rat] :
% 5.45/5.79 ( ( ord_less_eq_rat @ L @ M )
% 5.45/5.79 => ( ( ord_less_rat @ M @ U )
% 5.45/5.79 => ( ( sup_sup_set_rat @ ( set_or633870826150836451st_rat @ L @ M ) @ ( set_or4029947393144176647an_rat @ M @ U ) )
% 5.45/5.79 = ( set_or4029947393144176647an_rat @ L @ U ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % ivl_disj_un_two_touch(2)
% 5.45/5.79 thf(fact_7172_ivl__disj__un__two__touch_I2_J,axiom,
% 5.45/5.79 ! [L: num,M: num,U: num] :
% 5.45/5.79 ( ( ord_less_eq_num @ L @ M )
% 5.45/5.79 => ( ( ord_less_num @ M @ U )
% 5.45/5.79 => ( ( sup_sup_set_num @ ( set_or7049704709247886629st_num @ L @ M ) @ ( set_or1222409239386451017an_num @ M @ U ) )
% 5.45/5.79 = ( set_or1222409239386451017an_num @ L @ U ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % ivl_disj_un_two_touch(2)
% 5.45/5.79 thf(fact_7173_ivl__disj__un__two__touch_I2_J,axiom,
% 5.45/5.79 ! [L: nat,M: nat,U: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ L @ M )
% 5.45/5.79 => ( ( ord_less_nat @ M @ U )
% 5.45/5.79 => ( ( sup_sup_set_nat @ ( set_or1269000886237332187st_nat @ L @ M ) @ ( set_or4665077453230672383an_nat @ M @ U ) )
% 5.45/5.79 = ( set_or4665077453230672383an_nat @ L @ U ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % ivl_disj_un_two_touch(2)
% 5.45/5.79 thf(fact_7174_ivl__disj__un__two__touch_I2_J,axiom,
% 5.45/5.79 ! [L: int,M: int,U: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ L @ M )
% 5.45/5.79 => ( ( ord_less_int @ M @ U )
% 5.45/5.79 => ( ( sup_sup_set_int @ ( set_or1266510415728281911st_int @ L @ M ) @ ( set_or4662586982721622107an_int @ M @ U ) )
% 5.45/5.79 = ( set_or4662586982721622107an_int @ L @ U ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % ivl_disj_un_two_touch(2)
% 5.45/5.79 thf(fact_7175_ivl__disj__un__two__touch_I2_J,axiom,
% 5.45/5.79 ! [L: code_integer,M: code_integer,U: code_integer] :
% 5.45/5.79 ( ( ord_le3102999989581377725nteger @ L @ M )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ M @ U )
% 5.45/5.79 => ( ( sup_su848401254843788991nteger @ ( set_or189985376899183464nteger @ L @ M ) @ ( set_or8404916559141939852nteger @ M @ U ) )
% 5.45/5.79 = ( set_or8404916559141939852nteger @ L @ U ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % ivl_disj_un_two_touch(2)
% 5.45/5.79 thf(fact_7176_Sum__Icc__nat,axiom,
% 5.45/5.79 ! [M: nat,N2: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [X4: nat] : X4
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % Sum_Icc_nat
% 5.45/5.79 thf(fact_7177_sum_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_p7104986032573967614at_nat @ ( G @ M ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7178_sum_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7179_sum_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7180_sum_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7181_sum_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7182_sum_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7183_sum_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7184_sum_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7185_prod_OatLeast0__lessThan__Suc,axiom,
% 5.45/5.79 ! [G: nat > code_integer,N2: nat] :
% 5.45/5.79 ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast0_lessThan_Suc
% 5.45/5.79 thf(fact_7186_prod_OatLeast0__lessThan__Suc,axiom,
% 5.45/5.79 ! [G: nat > assn,N2: nat] :
% 5.45/5.79 ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast0_lessThan_Suc
% 5.45/5.79 thf(fact_7187_prod_OatLeast0__lessThan__Suc,axiom,
% 5.45/5.79 ! [G: nat > rat,N2: nat] :
% 5.45/5.79 ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast0_lessThan_Suc
% 5.45/5.79 thf(fact_7188_prod_OatLeast0__lessThan__Suc,axiom,
% 5.45/5.79 ! [G: nat > nat,N2: nat] :
% 5.45/5.79 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast0_lessThan_Suc
% 5.45/5.79 thf(fact_7189_prod_OatLeast0__lessThan__Suc,axiom,
% 5.45/5.79 ! [G: nat > int,N2: nat] :
% 5.45/5.79 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.45/5.79 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast0_lessThan_Suc
% 5.45/5.79 thf(fact_7190_prod_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( G @ M ) @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7191_prod_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > assn] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_assn @ ( G @ M ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7192_prod_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_rat @ ( G @ M ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7193_prod_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_nat @ ( G @ M ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7194_prod_OatLeast__Suc__lessThan,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_int @ ( G @ M ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeast_Suc_lessThan
% 5.45/5.79 thf(fact_7195_prod_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7196_prod_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > assn] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7197_prod_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7198_prod_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7199_prod_OatLeastLessThan__Suc,axiom,
% 5.45/5.79 ! [A: nat,B: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_nat @ A @ B )
% 5.45/5.79 => ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ ( suc @ B ) ) )
% 5.45/5.79 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ A @ B ) ) @ ( G @ B ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_Suc
% 5.45/5.79 thf(fact_7200_sum_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_p7104986032573967614at_nat @ ( G @ N2 ) @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.last_plus
% 5.45/5.79 thf(fact_7201_sum_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( G @ N2 ) @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.last_plus
% 5.45/5.79 thf(fact_7202_sum_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_int @ ( G @ N2 ) @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.last_plus
% 5.45/5.79 thf(fact_7203_sum_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_nat @ ( G @ N2 ) @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.last_plus
% 5.45/5.79 thf(fact_7204_prod_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( G @ N2 ) @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.last_plus
% 5.45/5.79 thf(fact_7205_prod_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > assn] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_assn @ ( G @ N2 ) @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.last_plus
% 5.45/5.79 thf(fact_7206_prod_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_rat @ ( G @ N2 ) @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.last_plus
% 5.45/5.79 thf(fact_7207_prod_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_nat @ ( G @ N2 ) @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.last_plus
% 5.45/5.79 thf(fact_7208_prod_Olast__plus,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_int @ ( G @ N2 ) @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.last_plus
% 5.45/5.79 thf(fact_7209_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7210_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_nat,I2: nat,F: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7211_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_int,I2: int,F: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( member_int @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7212_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups879477027807139574nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7213_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7214_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7215_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_int,I2: int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( member_int @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7216_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7217_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7218_sum__pos2,axiom,
% 5.45/5.79 ! [I5: set_int,I2: int,F: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( member_int @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos2
% 5.45/5.79 thf(fact_7219_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups879477027807139574nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7220_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups4406642042086082107nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7221_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_nat,F: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_nat )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7501900531339628137nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7222_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_int,F: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_int )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( groups7873554091576472773nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7223_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups6602215022474089585er_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7224_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups7872700643590313910_o_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7225_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_nat )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7226_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_int )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7227_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( groups7237345082560585321er_nat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7228_sum__pos,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_nat @ zero_zero_nat @ ( groups8507830703676809646_o_nat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_pos
% 5.45/5.79 thf(fact_7229_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7230_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_nat,I2: nat,F: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7231_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_int,I2: int,F: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( member_int @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7232_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7233_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7234_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_nat,I2: nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( member_nat @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7235_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_int,I2: int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( member_int @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7236_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_rat @ one_one_rat @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7237_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_o,I2: $o,F: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( member_o @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7238_less__1__prod2,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,I2: code_integer,F: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( member_Code_integer @ I2 @ I5 )
% 5.45/5.79 => ( ( ord_less_int @ one_one_int @ ( F @ I2 ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_eq_int @ one_one_int @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I5 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod2
% 5.45/5.79 thf(fact_7239_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3674199335183972705nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7240_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups7694694392188491536nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7241_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_nat,F: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_nat )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3455450783089532116nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7242_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_int,F: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_int )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( groups3827104343326376752nteger @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7243_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups2555765274223993564er_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7244_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups2869687844427037835_o_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7245_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_nat )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups73079841787564623at_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7246_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_int )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_rat @ one_one_rat @ ( groups1072433553688619179nt_rat @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7247_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_Code_integer,F: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( groups3188404863801439024er_int @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7248_less__1__prod,axiom,
% 5.45/5.79 ! [I5: set_o,F: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ I5 )
% 5.45/5.79 => ( ( I5 != bot_bot_set_o )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ I5 )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( F @ I3 ) ) )
% 5.45/5.79 => ( ord_less_int @ one_one_int @ ( groups3502327434004483295_o_int @ F @ I5 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % less_1_prod
% 5.45/5.79 thf(fact_7249_binomial__fact__lemma,axiom,
% 5.45/5.79 ! [K: nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.79 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.45/5.79 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % binomial_fact_lemma
% 5.45/5.79 thf(fact_7250_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups4406642042086082107nteger @ G @ A3 )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ B3 ) )
% 5.45/5.79 = ( ( groups4406642042086082107nteger @ G @ C3 )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7251_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups879477027807139574nteger @ G @ A3 )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ B3 ) )
% 5.45/5.79 = ( ( groups879477027807139574nteger @ G @ C3 )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7252_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups7872700643590313910_o_rat @ G @ A3 )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups7872700643590313910_o_rat @ G @ C3 )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7253_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups6602215022474089585er_rat @ G @ A3 )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups6602215022474089585er_rat @ G @ C3 )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7254_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( ( groups8507830703676809646_o_nat @ G @ A3 )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups8507830703676809646_o_nat @ G @ C3 )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7255_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( ( groups7237345082560585321er_nat @ G @ A3 )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups7237345082560585321er_nat @ G @ C3 )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7256_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( ( groups8505340233167759370_o_int @ G @ A3 )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ B3 ) )
% 5.45/5.79 = ( ( groups8505340233167759370_o_int @ G @ C3 )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7257_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( ( groups7234854612051535045er_int @ G @ A3 )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ B3 ) )
% 5.45/5.79 = ( ( groups7234854612051535045er_int @ G @ C3 )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7258_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_nat,A3: set_nat,B3: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: nat] :
% 5.45/5.79 ( ( member_nat @ A4 @ ( minus_minus_set_nat @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups7501900531339628137nteger @ G @ A3 )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ B3 ) )
% 5.45/5.79 = ( ( groups7501900531339628137nteger @ G @ C3 )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7259_sum_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_nat,A3: set_nat,B3: set_nat,G: nat > rat,H: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: nat] :
% 5.45/5.79 ( ( member_nat @ A4 @ ( minus_minus_set_nat @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups2906978787729119204at_rat @ G @ A3 )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups2906978787729119204at_rat @ G @ C3 )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrier
% 5.45/5.79 thf(fact_7260_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups4406642042086082107nteger @ G @ C3 )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ C3 ) )
% 5.45/5.79 => ( ( groups4406642042086082107nteger @ G @ A3 )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7261_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups879477027807139574nteger @ G @ C3 )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ C3 ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ A3 )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7262_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups7872700643590313910_o_rat @ G @ C3 )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups7872700643590313910_o_rat @ G @ A3 )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7263_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups6602215022474089585er_rat @ G @ C3 )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ A3 )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7264_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( ( groups8507830703676809646_o_nat @ G @ C3 )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups8507830703676809646_o_nat @ G @ A3 )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7265_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( ( groups7237345082560585321er_nat @ G @ C3 )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ A3 )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7266_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( ( groups8505340233167759370_o_int @ G @ C3 )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ C3 ) )
% 5.45/5.79 => ( ( groups8505340233167759370_o_int @ G @ A3 )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7267_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( ( groups7234854612051535045er_int @ G @ C3 )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ C3 ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ A3 )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7268_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_nat,A3: set_nat,B3: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: nat] :
% 5.45/5.79 ( ( member_nat @ A4 @ ( minus_minus_set_nat @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( ( groups7501900531339628137nteger @ G @ C3 )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ C3 ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ A3 )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7269_sum_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_nat,A3: set_nat,B3: set_nat,G: nat > rat,H: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: nat] :
% 5.45/5.79 ( ( member_nat @ A4 @ ( minus_minus_set_nat @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( ( groups2906978787729119204at_rat @ G @ C3 )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ A3 )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.same_carrierI
% 5.45/5.79 thf(fact_7270_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ S )
% 5.45/5.79 = ( groups879477027807139574nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7271_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ S )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7272_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ S )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7273_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ S )
% 5.45/5.79 = ( groups7234854612051535045er_int @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7274_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ S )
% 5.45/5.79 = ( groups7501900531339628137nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7275_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ S )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7276_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ S )
% 5.45/5.79 = ( groups3539618377306564664at_int @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7277_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7873554091576472773nteger @ G @ S )
% 5.45/5.79 = ( groups7873554091576472773nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7278_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ S )
% 5.45/5.79 = ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7279_sum_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ S )
% 5.45/5.79 = ( groups4541462559716669496nt_nat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_left
% 5.45/5.79 thf(fact_7280_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ T )
% 5.45/5.79 = ( groups879477027807139574nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7281_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ T )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7282_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ T )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7283_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ T )
% 5.45/5.79 = ( groups7234854612051535045er_int @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7284_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ T )
% 5.45/5.79 = ( groups7501900531339628137nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7285_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ T )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7286_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ T )
% 5.45/5.79 = ( groups3539618377306564664at_int @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7287_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7873554091576472773nteger @ G @ T )
% 5.45/5.79 = ( groups7873554091576472773nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7288_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ T )
% 5.45/5.79 = ( groups3906332499630173760nt_rat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7289_sum_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ T )
% 5.45/5.79 = ( groups4541462559716669496nt_nat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_right
% 5.45/5.79 thf(fact_7290_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups4406642042086082107nteger @ G @ S )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7291_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ S )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7292_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7872700643590313910_o_rat @ G @ S )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7293_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ S )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7294_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8507830703676809646_o_nat @ G @ S )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7295_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ S )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7296_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > int,G: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8505340233167759370_o_int @ G @ S )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7297_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > int,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ S )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7298_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,H: nat > code_integer,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ S )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7299_sum_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,H: nat > rat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ S )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7300_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups4406642042086082107nteger @ G @ T )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7301_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ T )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7302_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7872700643590313910_o_rat @ G @ T )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7303_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ T )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7304_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8507830703676809646_o_nat @ G @ T )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7305_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ T )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7306_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8505340233167759370_o_int @ G @ T )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7307_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ T )
% 5.45/5.79 = ( groups7234854612051535045er_int @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7308_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > code_integer,H: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ T )
% 5.45/5.79 = ( groups7501900531339628137nteger @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7309_sum_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > rat,H: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ T )
% 5.45/5.79 = ( groups2906978787729119204at_rat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7310_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups6602215022474089585er_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7311_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7237345082560585321er_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7312_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7234854612051535045er_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7313_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7314_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7315_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,G: int > rat] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7316_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,G: int > nat] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7317_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > nat] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3542108847815614940at_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7318_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,G: int > int] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7319_sum_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 5.45/5.79 ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( groups342789780944988191at_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) @ ( groups342789780944988191at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.subset_diff
% 5.45/5.79 thf(fact_7320_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7321_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( groups342789780944988191at_rat @ F @ A3 ) @ ( groups342789780944988191at_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7322_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7323_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups975429370522433651at_int @ F @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( groups975429370522433651at_int @ F @ A3 ) @ ( groups975429370522433651at_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7324_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7325_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,F: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7326_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7327_sum__diff,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,F: int > int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff
% 5.45/5.79 thf(fact_7328_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups4406642042086082107nteger @ G @ S )
% 5.45/5.79 = ( groups4406642042086082107nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7329_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > code_integer,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7873554091576472773nteger @ G @ S )
% 5.45/5.79 = ( groups7873554091576472773nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7330_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ S )
% 5.45/5.79 = ( groups879477027807139574nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7331_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7872700643590313910_o_rat @ G @ S )
% 5.45/5.79 = ( groups7872700643590313910_o_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7332_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > rat,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ S )
% 5.45/5.79 = ( groups3906332499630173760nt_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7333_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ S )
% 5.45/5.79 = ( groups6602215022474089585er_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7334_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8507830703676809646_o_nat @ G @ S )
% 5.45/5.79 = ( groups8507830703676809646_o_nat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7335_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > nat,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ S )
% 5.45/5.79 = ( groups4541462559716669496nt_nat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7336_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ S )
% 5.45/5.79 = ( groups7237345082560585321er_nat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7337_sum_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > int,G: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups8505340233167759370_o_int @ G @ S )
% 5.45/5.79 = ( groups8505340233167759370_o_int @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.mono_neutral_cong
% 5.45/5.79 thf(fact_7338_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups3674199335183972705nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7339_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3455450783089532116nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7340_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups1304777262505850412r_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7341_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > assn] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups6906906614972039071t_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7342_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups2555765274223993564er_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7343_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups73079841787564623at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7344_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ A3 )
% 5.45/5.79 = ( times_times_nat @ ( groups3190895334310489300er_nat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups3190895334310489300er_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7345_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ A3 )
% 5.45/5.79 = ( times_times_int @ ( groups3188404863801439024er_int @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups3188404863801439024er_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7346_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups3827104343326376752nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7347_prod_Osubset__diff,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,G: int > assn] :
% 5.45/5.79 ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups7882442080178216443t_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.subset_diff
% 5.45/5.79 thf(fact_7348_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( ( groups7694694392188491536nteger @ G @ A3 )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ B3 ) )
% 5.45/5.79 = ( ( groups7694694392188491536nteger @ G @ C3 )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7349_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( ( groups3674199335183972705nteger @ G @ A3 )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ B3 ) )
% 5.45/5.79 = ( ( groups3674199335183972705nteger @ G @ C3 )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7350_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > assn,H: $o > assn] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( ( groups5301882518646026715o_assn @ G @ A3 )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ B3 ) )
% 5.45/5.79 = ( ( groups5301882518646026715o_assn @ G @ C3 )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7351_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( ( groups1304777262505850412r_assn @ G @ A3 )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ B3 ) )
% 5.45/5.79 = ( ( groups1304777262505850412r_assn @ G @ C3 )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7352_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( ( groups2869687844427037835_o_rat @ G @ A3 )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups2869687844427037835_o_rat @ G @ C3 )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7353_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( ( groups2555765274223993564er_rat @ G @ A3 )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups2555765274223993564er_rat @ G @ C3 )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7354_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( ( groups3504817904513533571_o_nat @ G @ A3 )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups3504817904513533571_o_nat @ G @ C3 )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7355_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( ( groups3190895334310489300er_nat @ G @ A3 )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ B3 ) )
% 5.45/5.79 = ( ( groups3190895334310489300er_nat @ G @ C3 )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7356_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( ( groups3502327434004483295_o_int @ G @ A3 )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ B3 ) )
% 5.45/5.79 = ( ( groups3502327434004483295_o_int @ G @ C3 )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7357_prod_Osame__carrier,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( ( groups3188404863801439024er_int @ G @ A3 )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ B3 ) )
% 5.45/5.79 = ( ( groups3188404863801439024er_int @ G @ C3 )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ C3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrier
% 5.45/5.79 thf(fact_7358_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( ( groups7694694392188491536nteger @ G @ C3 )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ C3 ) )
% 5.45/5.79 => ( ( groups7694694392188491536nteger @ G @ A3 )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7359_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( ( groups3674199335183972705nteger @ G @ C3 )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ C3 ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ A3 )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7360_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > assn,H: $o > assn] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( ( groups5301882518646026715o_assn @ G @ C3 )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ C3 ) )
% 5.45/5.79 => ( ( groups5301882518646026715o_assn @ G @ A3 )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7361_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( ( groups1304777262505850412r_assn @ G @ C3 )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ C3 ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ A3 )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7362_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( ( groups2869687844427037835_o_rat @ G @ C3 )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups2869687844427037835_o_rat @ G @ A3 )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7363_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( ( groups2555765274223993564er_rat @ G @ C3 )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ A3 )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7364_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( ( groups3504817904513533571_o_nat @ G @ C3 )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups3504817904513533571_o_nat @ G @ A3 )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7365_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( ( groups3190895334310489300er_nat @ G @ C3 )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ C3 ) )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ A3 )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7366_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_o,A3: set_o,B3: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: $o] :
% 5.45/5.79 ( ( member_o @ A4 @ ( minus_minus_set_o @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( ( groups3502327434004483295_o_int @ G @ C3 )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ C3 ) )
% 5.45/5.79 => ( ( groups3502327434004483295_o_int @ G @ A3 )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7367_prod_Osame__carrierI,axiom,
% 5.45/5.79 ! [C3: set_Code_integer,A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ C3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ C3 )
% 5.45/5.79 => ( ! [A4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ A4 @ ( minus_2355218937544613996nteger @ C3 @ A3 ) )
% 5.45/5.79 => ( ( G @ A4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ C3 @ B3 ) )
% 5.45/5.79 => ( ( H @ B4 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( ( groups3188404863801439024er_int @ G @ C3 )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ C3 ) )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ A3 )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ B3 ) ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.same_carrierI
% 5.45/5.79 thf(fact_7368_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ S )
% 5.45/5.79 = ( groups3674199335183972705nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7369_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ S )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7370_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ S )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7371_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ S )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7372_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ S )
% 5.45/5.79 = ( groups3188404863801439024er_int @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7373_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ S )
% 5.45/5.79 = ( groups3455450783089532116nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7374_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > assn] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ S )
% 5.45/5.79 = ( groups6906906614972039071t_assn @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7375_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ S )
% 5.45/5.79 = ( groups73079841787564623at_rat @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7376_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ S )
% 5.45/5.79 = ( groups3827104343326376752nteger @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7377_prod_Omono__neutral__left,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ S )
% 5.45/5.79 = ( groups7882442080178216443t_assn @ G @ T ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_left
% 5.45/5.79 thf(fact_7378_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ T )
% 5.45/5.79 = ( groups3674199335183972705nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7379_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ T )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7380_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ T )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7381_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ T )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7382_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ T )
% 5.45/5.79 = ( groups3188404863801439024er_int @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7383_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ T )
% 5.45/5.79 = ( groups3455450783089532116nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7384_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > assn] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ T )
% 5.45/5.79 = ( groups6906906614972039071t_assn @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7385_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_nat,S: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( minus_minus_set_nat @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ T )
% 5.45/5.79 = ( groups73079841787564623at_rat @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7386_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ T )
% 5.45/5.79 = ( groups3827104343326376752nteger @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7387_prod_Omono__neutral__right,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ T )
% 5.45/5.79 = ( groups7882442080178216443t_assn @ G @ S ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_right
% 5.45/5.79 thf(fact_7388_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7694694392188491536nteger @ G @ S )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7389_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ S )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7390_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > assn,G: $o > assn] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups5301882518646026715o_assn @ G @ S )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7391_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > assn,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ S )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7392_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2869687844427037835_o_rat @ G @ S )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7393_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ S )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7394_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3504817904513533571_o_nat @ G @ S )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7395_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ S )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7396_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > int,G: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3502327434004483295_o_int @ G @ S )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7397_prod_Omono__neutral__cong__left,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > int,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ S )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ T ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_left
% 5.45/5.79 thf(fact_7398_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > code_integer,H: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7694694392188491536nteger @ G @ T )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7399_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > code_integer,H: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ T )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7400_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > assn,H: $o > assn] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups5301882518646026715o_assn @ G @ T )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7401_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > assn,H: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ T )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7402_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > rat,H: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2869687844427037835_o_rat @ G @ T )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7403_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > rat,H: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ T )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7404_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > nat,H: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3504817904513533571_o_nat @ G @ T )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7405_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > nat,H: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3190895334310489300er_nat @ G @ T )
% 5.45/5.79 = ( groups3190895334310489300er_nat @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7406_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,G: $o > int,H: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ S @ T )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3502327434004483295_o_int @ G @ T )
% 5.45/5.79 = ( groups3502327434004483295_o_int @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7407_prod_Omono__neutral__cong__right,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,G: code_integer > int,H: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ S )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3188404863801439024er_int @ G @ T )
% 5.45/5.79 = ( groups3188404863801439024er_int @ H @ S ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong_right
% 5.45/5.79 thf(fact_7408_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7409_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A3 ) @ ( groups6602215022474089585er_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7410_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7411_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A3 ) @ ( groups7237345082560585321er_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7412_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A3 ) @ ( groups7234854612051535045er_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7413_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A3 ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7414_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A3 ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7415_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A3 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7416_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A3 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7417_sum_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.79 => ( ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) ) @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ A3 ) @ ( groups342789780944988191at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter
% 5.45/5.79 thf(fact_7418_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > rat,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7419_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > rat,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7420_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > nat,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7421_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > nat,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7422_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > int,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7423_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > rat,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7424_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > int,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7425_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > nat,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7426_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > int,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int @ G @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7427_sum_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( groups342789780944988191at_rat @ G @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.Int_Diff
% 5.45/5.79 thf(fact_7428_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ A3 ) @ ( groups3827104343326376752nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7429_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ A3 ) @ ( groups3674199335183972705nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7430_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups3455450783089532116nteger @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ A3 ) @ ( groups3455450783089532116nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7431_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A3 ) @ ( groups7882442080178216443t_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7432_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A3 ) @ ( groups1304777262505850412r_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7433_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > assn] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A3 ) @ ( groups6906906614972039071t_assn @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7434_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7435_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A3 ) @ ( groups2555765274223993564er_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7436_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A3 ) @ ( groups73079841787564623at_rat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7437_prod_Ounion__inter,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.union_inter
% 5.45/5.79 thf(fact_7438_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > code_integer,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups3827104343326376752nteger @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7439_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > code_integer,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups3674199335183972705nteger @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7440_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > code_integer,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups3455450783089532116nteger @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7441_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > assn,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7442_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > assn,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7443_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > assn,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7444_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > rat,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1072433553688619179nt_rat @ G @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7445_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,G: code_integer > rat,B3: set_Code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7446_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_nat,G: nat > rat,B3: set_nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7447_prod_OInt__Diff,axiom,
% 5.45/5.79 ! [A3: set_int,G: int > nat,B3: set_int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1707563613775114915nt_nat @ G @ A3 )
% 5.45/5.79 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.Int_Diff
% 5.45/5.79 thf(fact_7448_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > code_integer,G: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7694694392188491536nteger @ G @ S )
% 5.45/5.79 = ( groups7694694392188491536nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7449_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > code_integer,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3827104343326376752nteger @ G @ S )
% 5.45/5.79 = ( groups3827104343326376752nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7450_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3674199335183972705nteger @ G @ S )
% 5.45/5.79 = ( groups3674199335183972705nteger @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7451_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > assn,G: $o > assn] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups5301882518646026715o_assn @ G @ S )
% 5.45/5.79 = ( groups5301882518646026715o_assn @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7452_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > assn,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn @ G @ S )
% 5.45/5.79 = ( groups7882442080178216443t_assn @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7453_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > assn,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn @ G @ S )
% 5.45/5.79 = ( groups1304777262505850412r_assn @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7454_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > rat,G: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2869687844427037835_o_rat @ G @ S )
% 5.45/5.79 = ( groups2869687844427037835_o_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7455_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_int,S: set_int,H: int > rat,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ T )
% 5.45/5.79 => ( ( finite_finite_int @ S )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ ( minus_minus_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups1072433553688619179nt_rat @ G @ S )
% 5.45/5.79 = ( groups1072433553688619179nt_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7456_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_Code_integer,S: set_Code_integer,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ T )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ S )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ ( minus_2355218937544613996nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat @ G @ S )
% 5.45/5.79 = ( groups2555765274223993564er_rat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7457_prod_Omono__neutral__cong,axiom,
% 5.45/5.79 ! [T: set_o,S: set_o,H: $o > nat,G: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ T )
% 5.45/5.79 => ( ( finite_finite_o @ S )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ T @ S ) )
% 5.45/5.79 => ( ( H @ I3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ ( minus_minus_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ I3 )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 => ( ! [X3: $o] :
% 5.45/5.79 ( ( member_o @ X3 @ ( inf_inf_set_o @ S @ T ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = ( H @ X3 ) ) )
% 5.45/5.79 => ( ( groups3504817904513533571_o_nat @ G @ S )
% 5.45/5.79 = ( groups3504817904513533571_o_nat @ H @ T ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.mono_neutral_cong
% 5.45/5.79 thf(fact_7458_prod__int__plus__eq,axiom,
% 5.45/5.79 ! [I2: nat,J: nat] :
% 5.45/5.79 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.45/5.79 = ( groups1705073143266064639nt_int
% 5.45/5.79 @ ^ [X4: int] : X4
% 5.45/5.79 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_int_plus_eq
% 5.45/5.79 thf(fact_7459_neg__zmod__mult__2,axiom,
% 5.45/5.79 ! [A: int,B: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.45/5.79 => ( ( 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 ) )
% 5.45/5.79 = ( 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 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % neg_zmod_mult_2
% 5.45/5.79 thf(fact_7460_double__arith__series,axiom,
% 5.45/5.79 ! [A: rat,D2: rat,N2: nat] :
% 5.45/5.79 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.45/5.79 @ ( groups2906978787729119204at_rat
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_arith_series
% 5.45/5.79 thf(fact_7461_double__arith__series,axiom,
% 5.45/5.79 ! [A: code_natural,D2: code_natural,N2: nat] :
% 5.45/5.79 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) )
% 5.45/5.79 @ ( groups6325495683096345652atural
% 5.45/5.79 @ ^ [I4: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_arith_series
% 5.45/5.79 thf(fact_7462_double__arith__series,axiom,
% 5.45/5.79 ! [A: int,D2: int,N2: nat] :
% 5.45/5.79 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.45/5.79 @ ( groups3539618377306564664at_int
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_arith_series
% 5.45/5.79 thf(fact_7463_double__arith__series,axiom,
% 5.45/5.79 ! [A: code_integer,D2: code_integer,N2: nat] :
% 5.45/5.79 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.45/5.79 @ ( groups7501900531339628137nteger
% 5.45/5.79 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_arith_series
% 5.45/5.79 thf(fact_7464_double__arith__series,axiom,
% 5.45/5.79 ! [A: nat,D2: nat,N2: nat] :
% 5.45/5.79 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.45/5.79 @ ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_arith_series
% 5.45/5.79 thf(fact_7465_double__gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum
% 5.45/5.79 thf(fact_7466_double__gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum
% 5.45/5.79 thf(fact_7467_double__gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum
% 5.45/5.79 thf(fact_7468_double__gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum
% 5.45/5.79 thf(fact_7469_double__gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum
% 5.45/5.79 thf(fact_7470_sum__choose__diagonal,axiom,
% 5.45/5.79 ! [M: nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.45/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.79 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_choose_diagonal
% 5.45/5.79 thf(fact_7471_sum__Suc__diff_H,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,F: nat > rat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat
% 5.45/5.79 @ ^ [I4: nat] : ( minus_minus_rat @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Suc_diff'
% 5.45/5.79 thf(fact_7472_sum__Suc__diff_H,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,F: nat > int] :
% 5.45/5.79 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int
% 5.45/5.79 @ ^ [I4: nat] : ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.45/5.79 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Suc_diff'
% 5.45/5.79 thf(fact_7473_sum__diff__nat,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ B3 @ A3 )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff_nat
% 5.45/5.79 thf(fact_7474_sum__diff__nat,axiom,
% 5.45/5.79 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.79 => ( ( ord_le3146513528884898305at_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups977919841031483927at_nat @ F @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( groups977919841031483927at_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff_nat
% 5.45/5.79 thf(fact_7475_sum__diff__nat,axiom,
% 5.45/5.79 ! [B3: set_int,A3: set_int,F: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_int @ B3 @ A3 )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff_nat
% 5.45/5.79 thf(fact_7476_sum__diff__nat,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,F: nat > nat] :
% 5.45/5.79 ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ B3 @ A3 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_diff_nat
% 5.45/5.79 thf(fact_7477_vandermonde,axiom,
% 5.45/5.79 ! [M: nat,N2: nat,R3: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 5.45/5.79 @ ( set_ord_atMost_nat @ R3 ) )
% 5.45/5.79 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R3 ) ) ).
% 5.45/5.79
% 5.45/5.79 % vandermonde
% 5.45/5.79 thf(fact_7478_sum_OatLeastLessThan__rev,axiom,
% 5.45/5.79 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.79 = ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I4 ) ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.atLeastLessThan_rev
% 5.45/5.79 thf(fact_7479_pos__eucl__rel__int__mult__2,axiom,
% 5.45/5.79 ! [B: int,A: int,Q6: int,R3: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.45/5.79 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.79 => ( 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 @ Q6 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % pos_eucl_rel_int_mult_2
% 5.45/5.79 thf(fact_7480_sum_Onested__swap,axiom,
% 5.45/5.79 ! [A: nat > nat > nat,N2: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( A @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [J3: nat] :
% 5.45/5.79 ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.nested_swap
% 5.45/5.79 thf(fact_7481_prod_OatLeastLessThan__rev,axiom,
% 5.45/5.79 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.79 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.79 = ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I4 ) ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_rev
% 5.45/5.79 thf(fact_7482_prod_OatLeastLessThan__rev,axiom,
% 5.45/5.79 ! [G: nat > int,N2: nat,M: nat] :
% 5.45/5.79 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.79 = ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ ( suc @ I4 ) ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ N2 @ M ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.atLeastLessThan_rev
% 5.45/5.79 thf(fact_7483_prod_Onested__swap,axiom,
% 5.45/5.79 ! [A: nat > nat > nat,N2: nat] :
% 5.45/5.79 ( ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [J3: nat] :
% 5.45/5.79 ( groups708209901874060359at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.nested_swap
% 5.45/5.79 thf(fact_7484_prod_Onested__swap,axiom,
% 5.45/5.79 ! [A: nat > nat > int,N2: nat] :
% 5.45/5.79 ( ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A @ I4 ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ I4 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [J3: nat] :
% 5.45/5.79 ( groups705719431365010083at_int
% 5.45/5.79 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.45/5.79 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.nested_swap
% 5.45/5.79 thf(fact_7485_fact__prod__rev,axiom,
% 5.45/5.79 ( semiri1406184849735516958ct_int
% 5.45/5.79 = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % fact_prod_rev
% 5.45/5.79 thf(fact_7486_fact__prod__rev,axiom,
% 5.45/5.79 ( semiri3624122377584611663nteger
% 5.45/5.79 = ( ^ [N: nat] : ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % fact_prod_rev
% 5.45/5.79 thf(fact_7487_fact__prod__rev,axiom,
% 5.45/5.79 ( semiri1408675320244567234ct_nat
% 5.45/5.79 = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ ( minus_minus_nat @ N ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % fact_prod_rev
% 5.45/5.79 thf(fact_7488_gbinomial__sum__nat__pow2,axiom,
% 5.45/5.79 ! [M: nat] :
% 5.45/5.79 ( ( groups2906978787729119204at_rat
% 5.45/5.79 @ ^ [K3: nat] : ( divide_divide_rat @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ K3 ) )
% 5.45/5.79 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.79 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ M ) ) ).
% 5.45/5.79
% 5.45/5.79 % gbinomial_sum_nat_pow2
% 5.45/5.79 thf(fact_7489_divmod__digit__1_I1_J,axiom,
% 5.45/5.79 ! [A: code_integer,B: code_integer] :
% 5.45/5.79 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.45/5.79 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.79 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.45/5.79 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % divmod_digit_1(1)
% 5.45/5.79 thf(fact_7490_divmod__digit__1_I1_J,axiom,
% 5.45/5.79 ! [A: nat,B: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.45/5.79 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.45/5.79 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.79 => ( ( 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 )
% 5.45/5.79 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % divmod_digit_1(1)
% 5.45/5.79 thf(fact_7491_divmod__digit__1_I1_J,axiom,
% 5.45/5.79 ! [A: int,B: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.45/5.79 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.45/5.79 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.45/5.79 => ( ( 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 )
% 5.45/5.79 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % divmod_digit_1(1)
% 5.45/5.79 thf(fact_7492_Sum__Icc__int,axiom,
% 5.45/5.79 ! [M: int,N2: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ M @ N2 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int
% 5.45/5.79 @ ^ [X4: int] : X4
% 5.45/5.79 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.45/5.79 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % Sum_Icc_int
% 5.45/5.79 thf(fact_7493_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > rat,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat
% 5.45/5.79 @ ^ [X4: int] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7494_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7495_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > nat,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat
% 5.45/5.79 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7496_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > nat,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_nat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7497_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > int,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups7234854612051535045er_int
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_int @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups7234854612051535045er_int @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7498_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > rat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat
% 5.45/5.79 @ ^ [X4: nat] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7499_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > int,G: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int
% 5.45/5.79 @ ^ [X4: nat] : ( if_int @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7500_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > nat,G: nat > nat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [X4: nat] : ( if_nat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7501_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > int,G: int > int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int
% 5.45/5.79 @ ^ [X4: int] : ( if_int @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7502_sum_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_list_nat,P: list_nat > $o,H: list_nat > rat,G: list_nat > rat] :
% 5.45/5.79 ( ( finite8100373058378681591st_nat @ A3 )
% 5.45/5.79 => ( ( groups3760926236672600436at_rat
% 5.45/5.79 @ ^ [X4: list_nat] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3760926236672600436at_rat @ H @ ( inf_inf_set_list_nat @ A3 @ ( collect_list_nat @ P ) ) ) @ ( groups3760926236672600436at_rat @ G @ ( inf_inf_set_list_nat @ A3 @ ( uminus3195874150345416415st_nat @ ( collect_list_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.If_cases
% 5.45/5.79 thf(fact_7503_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > code_integer,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups3827104343326376752nteger
% 5.45/5.79 @ ^ [X4: int] : ( if_Code_integer @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7504_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups3674199335183972705nteger
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_Code_integer @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7505_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > code_integer,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups3455450783089532116nteger
% 5.45/5.79 @ ^ [X4: nat] : ( if_Code_integer @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups3455450783089532116nteger @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7506_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > assn,G: int > assn] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups7882442080178216443t_assn
% 5.45/5.79 @ ^ [X4: int] : ( if_assn @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups7882442080178216443t_assn @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7507_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > assn,G: code_integer > assn] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups1304777262505850412r_assn
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_assn @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups1304777262505850412r_assn @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7508_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > assn,G: nat > assn] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn
% 5.45/5.79 @ ^ [X4: nat] : ( if_assn @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7509_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > rat,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1072433553688619179nt_rat
% 5.45/5.79 @ ^ [X4: int] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7510_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,P: code_integer > $o,H: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( groups2555765274223993564er_rat
% 5.45/5.79 @ ^ [X4: code_integer] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups2555765274223993564er_rat @ H @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ ( uminus804700908173204444nteger @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7511_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_nat,P: nat > $o,H: nat > rat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( groups73079841787564623at_rat
% 5.45/5.79 @ ^ [X4: nat] : ( if_rat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ H @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A3 @ ( uminus5710092332889474511et_nat @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7512_prod_OIf__cases,axiom,
% 5.45/5.79 ! [A3: set_int,P: int > $o,H: int > nat,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( groups1707563613775114915nt_nat
% 5.45/5.79 @ ^ [X4: int] : ( if_nat @ ( P @ X4 ) @ ( H @ X4 ) @ ( G @ X4 ) )
% 5.45/5.79 @ A3 )
% 5.45/5.79 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ H @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A3 @ ( uminus1532241313380277803et_int @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.If_cases
% 5.45/5.79 thf(fact_7513_fact__double,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.79 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % fact_double
% 5.45/5.79 thf(fact_7514_binomial__ge__n__over__k__pow__k,axiom,
% 5.45/5.79 ! [K: nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.79 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % binomial_ge_n_over_k_pow_k
% 5.45/5.79 thf(fact_7515_double__gauss__sum__from__Suc__0,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.45/5.79 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum_from_Suc_0
% 5.45/5.79 thf(fact_7516_double__gauss__sum__from__Suc__0,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.45/5.79 = ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum_from_Suc_0
% 5.45/5.79 thf(fact_7517_double__gauss__sum__from__Suc__0,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.45/5.79 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum_from_Suc_0
% 5.45/5.79 thf(fact_7518_double__gauss__sum__from__Suc__0,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum_from_Suc_0
% 5.45/5.79 thf(fact_7519_double__gauss__sum__from__Suc__0,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.45/5.79 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % double_gauss_sum_from_Suc_0
% 5.45/5.79 thf(fact_7520_choose__reduce__nat,axiom,
% 5.45/5.79 ! [N2: nat,K: nat] :
% 5.45/5.79 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.79 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.79 => ( ( binomial @ N2 @ K )
% 5.45/5.79 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % choose_reduce_nat
% 5.45/5.79 thf(fact_7521_arith__series,axiom,
% 5.45/5.79 ! [A: code_natural,D2: code_natural,N2: nat] :
% 5.45/5.79 ( ( groups6325495683096345652atural
% 5.45/5.79 @ ^ [I4: nat] : ( plus_p4538020629002901425atural @ A @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ D2 ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % arith_series
% 5.45/5.79 thf(fact_7522_arith__series,axiom,
% 5.45/5.79 ! [A: int,D2: int,N2: nat] :
% 5.45/5.79 ( ( groups3539618377306564664at_int
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % arith_series
% 5.45/5.79 thf(fact_7523_arith__series,axiom,
% 5.45/5.79 ! [A: code_integer,D2: code_integer,N2: nat] :
% 5.45/5.79 ( ( groups7501900531339628137nteger
% 5.45/5.79 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D2 ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % arith_series
% 5.45/5.79 thf(fact_7524_arith__series,axiom,
% 5.45/5.79 ! [A: nat,D2: nat,N2: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat
% 5.45/5.79 @ ^ [I4: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I4 ) @ D2 ) )
% 5.45/5.79 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D2 ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % arith_series
% 5.45/5.79 thf(fact_7525_gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % gauss_sum
% 5.45/5.79 thf(fact_7526_gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % gauss_sum
% 5.45/5.79 thf(fact_7527_gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % gauss_sum
% 5.45/5.79 thf(fact_7528_gauss__sum,axiom,
% 5.45/5.79 ! [N2: nat] :
% 5.45/5.79 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.45/5.79 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % gauss_sum
% 5.45/5.79 thf(fact_7529_times__binomial__minus1__eq,axiom,
% 5.45/5.79 ! [K: nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.79 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.45/5.79 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % times_binomial_minus1_eq
% 5.45/5.79 thf(fact_7530_sum_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.head_if
% 5.45/5.79 thf(fact_7531_sum_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > multis2468970476368604999at_nat] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = zero_z1048942125864253310at_nat ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups6857163185585827899at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_p7104986032573967614at_nat @ ( groups6857163185585827899at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.head_if
% 5.45/5.79 thf(fact_7532_sum_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.head_if
% 5.45/5.79 thf(fact_7533_sum_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.head_if
% 5.45/5.79 thf(fact_7534_sum_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.head_if
% 5.45/5.79 thf(fact_7535_neg__eucl__rel__int__mult__2,axiom,
% 5.45/5.79 ! [B: int,A: int,Q6: int,R3: int] :
% 5.45/5.79 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.45/5.79 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.79 => ( 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 @ Q6 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % neg_eucl_rel_int_mult_2
% 5.45/5.79 thf(fact_7536_prod_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > code_integer] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = one_one_Code_integer ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups3455450783089532116nteger @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.head_if
% 5.45/5.79 thf(fact_7537_prod_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > assn] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = one_one_assn ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups6906906614972039071t_assn @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.head_if
% 5.45/5.79 thf(fact_7538_prod_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > rat] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = one_one_rat ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.head_if
% 5.45/5.79 thf(fact_7539_prod_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > nat] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = one_one_nat ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.head_if
% 5.45/5.79 thf(fact_7540_prod_Ohead__if,axiom,
% 5.45/5.79 ! [N2: nat,M: nat,G: nat > int] :
% 5.45/5.79 ( ( ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = one_one_int ) )
% 5.45/5.79 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.45/5.79 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.45/5.79 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) @ ( G @ N2 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod.head_if
% 5.45/5.79 thf(fact_7541_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ ( groups3674199335183972705nteger @ F @ A3 ) @ ( groups3674199335183972705nteger @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7542_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_o,F: $o > code_integer,G: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_o )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ ( groups7694694392188491536nteger @ F @ A3 ) @ ( groups7694694392188491536nteger @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7543_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ ( groups3455450783089532116nteger @ F @ A3 ) @ ( groups3455450783089532116nteger @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7544_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_int,F: int > code_integer,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_le6747313008572928689nteger @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_int )
% 5.45/5.79 => ( ord_le6747313008572928689nteger @ ( groups3827104343326376752nteger @ F @ A3 ) @ ( groups3827104343326376752nteger @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7545_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,F: code_integer > rat,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ord_less_rat @ ( groups2555765274223993564er_rat @ F @ A3 ) @ ( groups2555765274223993564er_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7546_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_o,F: $o > rat,G: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_o )
% 5.45/5.79 => ( ord_less_rat @ ( groups2869687844427037835_o_rat @ F @ A3 ) @ ( groups2869687844427037835_o_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7547_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_nat,F: nat > rat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ! [I3: nat] :
% 5.45/5.79 ( ( member_nat @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.79 => ( ord_less_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7548_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_int,F: int > rat,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ! [I3: int] :
% 5.45/5.79 ( ( member_int @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_rat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_int )
% 5.45/5.79 => ( ord_less_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7549_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ! [I3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.79 => ( ord_less_nat @ ( groups3190895334310489300er_nat @ F @ A3 ) @ ( groups3190895334310489300er_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7550_prod__mono__strict,axiom,
% 5.45/5.79 ! [A3: set_o,F: $o > nat,G: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ A3 )
% 5.45/5.79 => ( ! [I3: $o] :
% 5.45/5.79 ( ( member_o @ I3 @ A3 )
% 5.45/5.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I3 ) )
% 5.45/5.79 & ( ord_less_nat @ ( F @ I3 ) @ ( G @ I3 ) ) ) )
% 5.45/5.79 => ( ( A3 != bot_bot_set_o )
% 5.45/5.79 => ( ord_less_nat @ ( groups3504817904513533571_o_nat @ F @ A3 ) @ ( groups3504817904513533571_o_nat @ G @ A3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % prod_mono_strict
% 5.45/5.79 thf(fact_7551_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_o,A3: set_o,F: $o > code_integer] :
% 5.45/5.79 ( ( finite_finite_o @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ ( groups4406642042086082107nteger @ F @ A3 ) @ ( groups4406642042086082107nteger @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7552_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ ( groups879477027807139574nteger @ F @ A3 ) @ ( groups879477027807139574nteger @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7553_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,F: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_le3102999989581377725nteger @ ( groups7501900531339628137nteger @ F @ A3 ) @ ( groups7501900531339628137nteger @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7554_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_o,A3: set_o,F: $o > rat] :
% 5.45/5.79 ( ( finite_finite_o @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7555_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7556_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_nat,A3: set_nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: nat] :
% 5.45/5.79 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7557_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_o,A3: set_o,F: $o > nat] :
% 5.45/5.79 ( ( finite_finite_o @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( groups8507830703676809646_o_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7558_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7559_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_o,A3: set_o,F: $o > int] :
% 5.45/5.79 ( ( finite_finite_o @ B3 )
% 5.45/5.79 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: $o] :
% 5.45/5.79 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_int @ ( groups8505340233167759370_o_int @ F @ A3 ) @ ( groups8505340233167759370_o_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7560_sum__mono2,axiom,
% 5.45/5.79 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.79 => ( ! [B4: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.79 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B4 ) ) )
% 5.45/5.79 => ( ord_less_eq_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ F @ B3 ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_mono2
% 5.45/5.79 thf(fact_7561_binomial__altdef__nat,axiom,
% 5.45/5.79 ! [K: nat,N2: nat] :
% 5.45/5.79 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.79 => ( ( binomial @ N2 @ K )
% 5.45/5.79 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % binomial_altdef_nat
% 5.45/5.79 thf(fact_7562_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > code_integer] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7873554091576472773nteger @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_p5714425477246183910nteger @ ( groups7873554091576472773nteger @ G @ A3 ) @ ( groups7873554091576472773nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7563_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups879477027807139574nteger @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_p5714425477246183910nteger @ ( groups879477027807139574nteger @ G @ A3 ) @ ( groups879477027807139574nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7564_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7565_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A3 ) @ ( groups6602215022474089585er_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7566_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ! [X3: int] :
% 5.45/5.79 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7567_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_nat ) )
% 5.45/5.79 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A3 ) @ ( groups7237345082560585321er_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7568_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ! [X3: code_integer] :
% 5.45/5.79 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A3 ) @ ( groups7234854612051535045er_int @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7569_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > code_integer] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_z3403309356797280102nteger ) )
% 5.45/5.79 => ( ( groups7501900531339628137nteger @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_p5714425477246183910nteger @ ( groups7501900531339628137nteger @ G @ A3 ) @ ( groups7501900531339628137nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7570_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_rat ) )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A3 ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7571_sum_Ounion__inter__neutral,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,G: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ! [X3: nat] :
% 5.45/5.79 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.79 => ( ( G @ X3 )
% 5.45/5.79 = zero_zero_int ) )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A3 ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum.union_inter_neutral
% 5.45/5.79 thf(fact_7572_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,F: int > rat] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ A3 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7573_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( groups6602215022474089585er_rat @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ F @ B3 ) ) @ ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7574_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,F: nat > rat] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( groups2906978787729119204at_rat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) @ ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7575_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > int] :
% 5.45/5.79 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.79 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.79 => ( ( groups7234854612051535045er_int @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ F @ B3 ) ) @ ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7576_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_nat,B3: set_nat,F: nat > int] :
% 5.45/5.79 ( ( finite_finite_nat @ A3 )
% 5.45/5.79 => ( ( finite_finite_nat @ B3 )
% 5.45/5.79 => ( ( groups3539618377306564664at_int @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) @ ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7577_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_int,B3: set_int,F: int > int] :
% 5.45/5.79 ( ( finite_finite_int @ A3 )
% 5.45/5.79 => ( ( finite_finite_int @ B3 )
% 5.45/5.79 => ( ( groups4538972089207619220nt_int @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F @ A3 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) @ ( groups4538972089207619220nt_int @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7578_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 5.45/5.79 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.79 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.79 => ( ( groups342789780944988191at_rat @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.79 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F @ A3 ) @ ( groups342789780944988191at_rat @ F @ B3 ) ) @ ( groups342789780944988191at_rat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.79
% 5.45/5.79 % sum_Un
% 5.45/5.79 thf(fact_7579_sum__Un,axiom,
% 5.45/5.79 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > int] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( ( groups975429370522433651at_int @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_int @ ( plus_plus_int @ ( groups975429370522433651at_int @ F @ A3 ) @ ( groups975429370522433651at_int @ F @ B3 ) ) @ ( groups975429370522433651at_int @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un
% 5.45/5.80 thf(fact_7580_sum__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,F: produc859450856879609959at_nat > rat] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ A3 )
% 5.45/5.80 => ( ( finite4392333629123659920at_nat @ B3 )
% 5.45/5.80 => ( ( groups1265588324298845189at_rat @ F @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_rat @ ( plus_plus_rat @ ( groups1265588324298845189at_rat @ F @ A3 ) @ ( groups1265588324298845189at_rat @ F @ B3 ) ) @ ( groups1265588324298845189at_rat @ F @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un
% 5.45/5.80 thf(fact_7581_sum__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,F: produc859450856879609959at_nat > int] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ A3 )
% 5.45/5.80 => ( ( finite4392333629123659920at_nat @ B3 )
% 5.45/5.80 => ( ( groups1898227913876290649at_int @ F @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_int @ ( plus_plus_int @ ( groups1898227913876290649at_int @ F @ A3 ) @ ( groups1898227913876290649at_int @ F @ B3 ) ) @ ( groups1898227913876290649at_int @ F @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un
% 5.45/5.80 thf(fact_7582_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ A3 ) @ ( groups6602215022474089585er_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7583_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ A3 ) @ ( groups7237345082560585321er_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7584_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ A3 ) @ ( groups7234854612051535045er_int @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7585_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > rat] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups7872700643590313910_o_rat @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( groups7872700643590313910_o_rat @ G @ A3 ) @ ( groups7872700643590313910_o_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7586_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > nat] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups8507830703676809646_o_nat @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( groups8507830703676809646_o_nat @ G @ A3 ) @ ( groups8507830703676809646_o_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7587_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > int] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups8505340233167759370_o_int @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( groups8505340233167759370_o_int @ G @ A3 ) @ ( groups8505340233167759370_o_int @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7588_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_nat )
% 5.45/5.80 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ A3 ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7589_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > int] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_nat )
% 5.45/5.80 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ A3 ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7590_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_int )
% 5.45/5.80 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ A3 ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7591_sum_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_int )
% 5.45/5.80 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ A3 ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_disjoint
% 5.45/5.80 thf(fact_7592_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_Code_integer ) )
% 5.45/5.80 => ( ( groups3827104343326376752nteger @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ A3 ) @ ( groups3827104343326376752nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7593_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_Code_integer ) )
% 5.45/5.80 => ( ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ A3 ) @ ( groups3674199335183972705nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7594_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_Code_integer ) )
% 5.45/5.80 => ( ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ A3 ) @ ( groups3455450783089532116nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7595_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > assn] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_assn ) )
% 5.45/5.80 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A3 ) @ ( groups7882442080178216443t_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7596_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_assn ) )
% 5.45/5.80 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A3 ) @ ( groups1304777262505850412r_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7597_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > assn] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_assn ) )
% 5.45/5.80 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A3 ) @ ( groups6906906614972039071t_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7598_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_rat ) )
% 5.45/5.80 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ A3 ) @ ( groups1072433553688619179nt_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7599_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_rat ) )
% 5.45/5.80 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A3 ) @ ( groups2555765274223993564er_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7600_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_rat ) )
% 5.45/5.80 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ A3 ) @ ( groups73079841787564623at_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7601_prod_Ounion__inter__neutral,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( G @ X3 )
% 5.45/5.80 = one_one_nat ) )
% 5.45/5.80 => ( ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_inter_neutral
% 5.45/5.80 thf(fact_7602_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ A3 ) @ ( groups3674199335183972705nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7603_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > code_integer] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups7694694392188491536nteger @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups7694694392188491536nteger @ G @ A3 ) @ ( groups7694694392188491536nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7604_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_nat )
% 5.45/5.80 => ( ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ A3 ) @ ( groups3455450783089532116nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7605_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_int )
% 5.45/5.80 => ( ( groups3827104343326376752nteger @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ A3 ) @ ( groups3827104343326376752nteger @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7606_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ A3 ) @ ( groups1304777262505850412r_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7607_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > assn] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups5301882518646026715o_assn @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups5301882518646026715o_assn @ G @ A3 ) @ ( groups5301882518646026715o_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7608_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > assn] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_nat @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_nat )
% 5.45/5.80 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ A3 ) @ ( groups6906906614972039071t_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7609_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > assn] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_int @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_int )
% 5.45/5.80 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ A3 ) @ ( groups7882442080178216443t_assn @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7610_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ( inf_in1364745209274528805nteger @ A3 @ B3 )
% 5.45/5.80 = bot_bo3990330152332043303nteger )
% 5.45/5.80 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ A3 ) @ ( groups2555765274223993564er_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7611_prod_Ounion__disjoint,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_o,G: $o > rat] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ( inf_inf_set_o @ A3 @ B3 )
% 5.45/5.80 = bot_bot_set_o )
% 5.45/5.80 => ( ( groups2869687844427037835_o_rat @ G @ ( sup_sup_set_o @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( groups2869687844427037835_o_rat @ G @ A3 ) @ ( groups2869687844427037835_o_rat @ G @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_disjoint
% 5.45/5.80 thf(fact_7612_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups3906332499630173760nt_rat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7613_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups6602215022474089585er_rat @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups6602215022474089585er_rat @ F @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7614_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7615_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups7237345082560585321er_nat @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7237345082560585321er_nat @ F @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7616_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups7234854612051535045er_int @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7234854612051535045er_int @ F @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7617_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups2906978787729119204at_rat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7618_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > int] :
% 5.45/5.80 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups3539618377306564664at_int @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7619_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > nat] :
% 5.45/5.80 ( ( finite_finite_nat @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups3542108847815614940at_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups3542108847815614940at_nat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7620_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > int] :
% 5.45/5.80 ( ( finite_finite_int @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups4538972089207619220nt_int @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups4538972089207619220nt_int @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7621_sum__Un2,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( groups342789780944988191at_rat @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) @ ( groups342789780944988191at_rat @ F @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) ) ) @ ( groups342789780944988191at_rat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un2
% 5.45/5.80 thf(fact_7622_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups3906332499630173760nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups3906332499630173760nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7623_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups6602215022474089585er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups6602215022474089585er_rat @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups6602215022474089585er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7624_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups4541462559716669496nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups4541462559716669496nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7625_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups7237345082560585321er_nat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7237345082560585321er_nat @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups7237345082560585321er_nat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7626_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups7234854612051535045er_int @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups7234854612051535045er_int @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups7234854612051535045er_int @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7627_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups2906978787729119204at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups2906978787729119204at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7628_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > int] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups3539618377306564664at_int @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups3539618377306564664at_int @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7629_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups3542108847815614940at_nat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3542108847815614940at_nat @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups3542108847815614940at_nat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7630_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups4538972089207619220nt_int @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_int @ ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups4538972089207619220nt_int @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7631_sum_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > rat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( ( groups342789780944988191at_rat @ G @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( plus_plus_rat @ ( plus_plus_rat @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) @ ( groups342789780944988191at_rat @ G @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) ) ) @ ( groups342789780944988191at_rat @ G @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.union_diff2
% 5.45/5.80 thf(fact_7632_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups3827104343326376752nteger @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3827104343326376752nteger @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups3827104343326376752nteger @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups3827104343326376752nteger @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7633_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups3674199335183972705nteger @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3674199335183972705nteger @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups3674199335183972705nteger @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups3674199335183972705nteger @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7634_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups3455450783089532116nteger @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups3455450783089532116nteger @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups3455450783089532116nteger @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7635_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > assn] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups7882442080178216443t_assn @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( times_times_assn @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups7882442080178216443t_assn @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups7882442080178216443t_assn @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7636_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > assn] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups1304777262505850412r_assn @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( times_times_assn @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups1304777262505850412r_assn @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups1304777262505850412r_assn @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7637_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > assn] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups6906906614972039071t_assn @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_assn @ ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups6906906614972039071t_assn @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups6906906614972039071t_assn @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7638_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups1072433553688619179nt_rat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups1072433553688619179nt_rat @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups1072433553688619179nt_rat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7639_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,G: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups2555765274223993564er_rat @ G @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( times_times_rat @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( groups2555765274223993564er_rat @ G @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) @ ( groups2555765274223993564er_rat @ G @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7640_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,G: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups73079841787564623at_rat @ G @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( groups73079841787564623at_rat @ G @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) @ ( groups73079841787564623at_rat @ G @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7641_prod_Ounion__diff2,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,G: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups1707563613775114915nt_nat @ G @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( times_times_nat @ ( times_times_nat @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( groups1707563613775114915nt_nat @ G @ ( minus_minus_set_int @ B3 @ A3 ) ) ) @ ( groups1707563613775114915nt_nat @ G @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.union_diff2
% 5.45/5.80 thf(fact_7642_pochhammer__double,axiom,
% 5.45/5.80 ! [Z: rat,N2: nat] :
% 5.45/5.80 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_double
% 5.45/5.80 thf(fact_7643_gauss__sum__from__Suc__0,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( groups6325495683096345652atural @ semiri3763490453095760265atural @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ ( semiri3763490453095760265atural @ N2 ) @ ( plus_p4538020629002901425atural @ ( semiri3763490453095760265atural @ N2 ) @ one_one_Code_natural ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gauss_sum_from_Suc_0
% 5.45/5.80 thf(fact_7644_gauss__sum__from__Suc__0,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.45/5.80 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gauss_sum_from_Suc_0
% 5.45/5.80 thf(fact_7645_gauss__sum__from__Suc__0,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gauss_sum_from_Suc_0
% 5.45/5.80 thf(fact_7646_gauss__sum__from__Suc__0,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.45/5.80 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gauss_sum_from_Suc_0
% 5.45/5.80 thf(fact_7647_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( groups4541462559716669496nt_nat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) @ ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7648_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( groups7237345082560585321er_nat @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ F @ B3 ) ) @ ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7649_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( ( groups977919841031483927at_nat @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups977919841031483927at_nat @ F @ A3 ) @ ( groups977919841031483927at_nat @ F @ B3 ) ) @ ( groups977919841031483927at_nat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7650_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,F: produc859450856879609959at_nat > nat] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ A3 )
% 5.45/5.80 => ( ( finite4392333629123659920at_nat @ B3 )
% 5.45/5.80 => ( ( groups1900718384385340925at_nat @ F @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups1900718384385340925at_nat @ F @ A3 ) @ ( groups1900718384385340925at_nat @ F @ B3 ) ) @ ( groups1900718384385340925at_nat @ F @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7651_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,F: produc4166570645942440679at_nat > nat] :
% 5.45/5.80 ( ( finite1918287321285529104at_nat @ A3 )
% 5.45/5.80 => ( ( finite1918287321285529104at_nat @ B3 )
% 5.45/5.80 => ( ( groups7059897769266147197at_nat @ F @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups7059897769266147197at_nat @ F @ A3 ) @ ( groups7059897769266147197at_nat @ F @ B3 ) ) @ ( groups7059897769266147197at_nat @ F @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7652_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > nat] :
% 5.45/5.80 ( ( finite4343798906461161616at_nat @ A3 )
% 5.45/5.80 => ( ( finite4343798906461161616at_nat @ B3 )
% 5.45/5.80 => ( ( groups3860910324918113789at_nat @ F @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3860910324918113789at_nat @ F @ A3 ) @ ( groups3860910324918113789at_nat @ F @ B3 ) ) @ ( groups3860910324918113789at_nat @ F @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7653_sum__Un__nat,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( groups3542108847815614940at_nat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( minus_minus_nat @ ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) @ ( groups3542108847815614940at_nat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_Un_nat
% 5.45/5.80 thf(fact_7654_sum_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.45/5.80 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.80 ( ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.80 = ( groups3542108847815614940at_nat
% 5.45/5.80 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.80 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum.atLeastLessThan_rev_at_least_Suc_atMost
% 5.45/5.80 thf(fact_7655_binomial,axiom,
% 5.45/5.80 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.80 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups3542108847815614940at_nat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial
% 5.45/5.80 thf(fact_7656_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.45/5.80 ! [G: nat > nat,N2: nat,M: nat] :
% 5.45/5.80 ( ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.80 = ( groups708209901874060359at_nat
% 5.45/5.80 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.80 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 5.45/5.80 thf(fact_7657_prod_OatLeastLessThan__rev__at__least__Suc__atMost,axiom,
% 5.45/5.80 ! [G: nat > int,N2: nat,M: nat] :
% 5.45/5.80 ( ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ N2 @ M ) )
% 5.45/5.80 = ( groups705719431365010083at_int
% 5.45/5.80 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I4 ) )
% 5.45/5.80 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod.atLeastLessThan_rev_at_least_Suc_atMost
% 5.45/5.80 thf(fact_7658_gchoose__row__sum__weighted,axiom,
% 5.45/5.80 ! [R3: rat,M: nat] :
% 5.45/5.80 ( ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.45/5.80 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.45/5.80 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gchoose_row_sum_weighted
% 5.45/5.80 thf(fact_7659_pochhammer__prod,axiom,
% 5.45/5.80 ( comm_s4028243227959126397er_rat
% 5.45/5.80 = ( ^ [A5: rat,N: nat] :
% 5.45/5.80 ( groups73079841787564623at_rat
% 5.45/5.80 @ ^ [I4: nat] : ( plus_plus_rat @ A5 @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_prod
% 5.45/5.80 thf(fact_7660_pochhammer__prod,axiom,
% 5.45/5.80 ( comm_s8582702949713902594nteger
% 5.45/5.80 = ( ^ [A5: code_integer,N: nat] :
% 5.45/5.80 ( groups3455450783089532116nteger
% 5.45/5.80 @ ^ [I4: nat] : ( plus_p5714425477246183910nteger @ A5 @ ( semiri4939895301339042750nteger @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_prod
% 5.45/5.80 thf(fact_7661_pochhammer__prod,axiom,
% 5.45/5.80 ( comm_s4663373288045622133er_nat
% 5.45/5.80 = ( ^ [A5: nat,N: nat] :
% 5.45/5.80 ( groups708209901874060359at_nat
% 5.45/5.80 @ ^ [I4: nat] : ( plus_plus_nat @ A5 @ ( semiri1316708129612266289at_nat @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_prod
% 5.45/5.80 thf(fact_7662_pochhammer__prod,axiom,
% 5.45/5.80 ( comm_s4660882817536571857er_int
% 5.45/5.80 = ( ^ [A5: int,N: nat] :
% 5.45/5.80 ( groups705719431365010083at_int
% 5.45/5.80 @ ^ [I4: nat] : ( plus_plus_int @ A5 @ ( semiri1314217659103216013at_int @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_prod
% 5.45/5.80 thf(fact_7663_binomial__addition__formula,axiom,
% 5.45/5.80 ! [N2: nat,K: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.45/5.80 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_addition_formula
% 5.45/5.80 thf(fact_7664_binomial__fact,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) )
% 5.45/5.80 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_fact
% 5.45/5.80 thf(fact_7665_fact__binomial,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) )
% 5.45/5.80 = ( divide_divide_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % fact_binomial
% 5.45/5.80 thf(fact_7666_fact__split,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( semiri773545260158071498ct_rat @ N2 )
% 5.45/5.80 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K ) @ N2 ) ) ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % fact_split
% 5.45/5.80 thf(fact_7667_fact__split,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.45/5.80 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K ) @ N2 ) ) ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % fact_split
% 5.45/5.80 thf(fact_7668_fact__split,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( semiri3624122377584611663nteger @ N2 )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K ) @ N2 ) ) ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % fact_split
% 5.45/5.80 thf(fact_7669_fact__split,axiom,
% 5.45/5.80 ! [K: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.80 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.45/5.80 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ N2 @ K ) @ N2 ) ) ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % fact_split
% 5.45/5.80 thf(fact_7670_gbinomial__r__part__sum,axiom,
% 5.45/5.80 ! [M: nat] :
% 5.45/5.80 ( ( groups2906978787729119204at_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M ) ) @ one_one_rat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.80 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gbinomial_r_part_sum
% 5.45/5.80 thf(fact_7671_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,B: $o,F: $o > code_integer] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ( member_o @ B @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ B3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_le6747313008572928689nteger @ ( groups4406642042086082107nteger @ F @ A3 ) @ ( groups4406642042086082107nteger @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7672_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,B: code_integer,F: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_le6747313008572928689nteger @ ( groups879477027807139574nteger @ F @ A3 ) @ ( groups879477027807139574nteger @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7673_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_nat,A3: set_nat,B: nat,F: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_le6747313008572928689nteger @ ( groups7501900531339628137nteger @ F @ A3 ) @ ( groups7501900531339628137nteger @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7674_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,B: $o,F: $o > rat] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ( member_o @ B @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_rat @ ( groups7872700643590313910_o_rat @ F @ A3 ) @ ( groups7872700643590313910_o_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7675_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,B: code_integer,F: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_rat @ ( groups6602215022474089585er_rat @ F @ A3 ) @ ( groups6602215022474089585er_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7676_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_nat,A3: set_nat,B: nat,F: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A3 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7677_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,B: $o,F: $o > nat] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ( member_o @ B @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_nat @ ( groups8507830703676809646_o_nat @ F @ A3 ) @ ( groups8507830703676809646_o_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7678_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,B: code_integer,F: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ ( groups7237345082560585321er_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7679_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,B: $o,F: $o > int] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ( member_o @ B @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_int @ ( groups8505340233167759370_o_int @ F @ A3 ) @ ( groups8505340233167759370_o_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7680_sum__strict__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,B: code_integer,F: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ( member_Code_integer @ B @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X3 ) ) )
% 5.45/5.80 => ( ord_less_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ ( groups7234854612051535045er_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % sum_strict_mono2
% 5.45/5.80 thf(fact_7681_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,F: $o > code_integer] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: $o] :
% 5.45/5.80 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: $o] :
% 5.45/5.80 ( ( member_o @ A4 @ A3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ ( groups7694694392188491536nteger @ F @ A3 ) @ ( groups7694694392188491536nteger @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7682_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ ( groups3674199335183972705nteger @ F @ A3 ) @ ( groups3674199335183972705nteger @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7683_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_nat,A3: set_nat,F: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: nat] :
% 5.45/5.80 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: nat] :
% 5.45/5.80 ( ( member_nat @ A4 @ A3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ ( groups3455450783089532116nteger @ F @ A3 ) @ ( groups3455450783089532116nteger @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7684_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,F: $o > rat] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: $o] :
% 5.45/5.80 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: $o] :
% 5.45/5.80 ( ( member_o @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_rat @ ( groups2869687844427037835_o_rat @ F @ A3 ) @ ( groups2869687844427037835_o_rat @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7685_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_rat @ ( groups2555765274223993564er_rat @ F @ A3 ) @ ( groups2555765274223993564er_rat @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7686_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_nat,A3: set_nat,F: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: nat] :
% 5.45/5.80 ( ( member_nat @ B4 @ ( minus_minus_set_nat @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: nat] :
% 5.45/5.80 ( ( member_nat @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7687_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_o,A3: set_o,F: $o > int] :
% 5.45/5.80 ( ( finite_finite_o @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: $o] :
% 5.45/5.80 ( ( member_o @ B4 @ ( minus_minus_set_o @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: $o] :
% 5.45/5.80 ( ( member_o @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_int @ ( groups3502327434004483295_o_int @ F @ A3 ) @ ( groups3502327434004483295_o_int @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7688_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ B4 @ ( minus_2355218937544613996nteger @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_int @ one_one_int @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_int @ zero_zero_int @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_int @ ( groups3188404863801439024er_int @ F @ A3 ) @ ( groups3188404863801439024er_int @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7689_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_int,A3: set_int,F: int > code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: int] :
% 5.45/5.80 ( ( member_int @ B4 @ ( minus_minus_set_int @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: int] :
% 5.45/5.80 ( ( member_int @ A4 @ A3 )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_le3102999989581377725nteger @ ( groups3827104343326376752nteger @ F @ A3 ) @ ( groups3827104343326376752nteger @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7690_prod__mono2,axiom,
% 5.45/5.80 ! [B3: set_int,A3: set_int,F: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.80 => ( ! [B4: int] :
% 5.45/5.80 ( ( member_int @ B4 @ ( minus_minus_set_int @ B3 @ A3 ) )
% 5.45/5.80 => ( ord_less_eq_rat @ one_one_rat @ ( F @ B4 ) ) )
% 5.45/5.80 => ( ! [A4: int] :
% 5.45/5.80 ( ( member_int @ A4 @ A3 )
% 5.45/5.80 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ A4 ) ) )
% 5.45/5.80 => ( ord_less_eq_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ F @ B3 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_mono2
% 5.45/5.80 thf(fact_7691_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > rat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ ( inf_inf_set_int @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups1072433553688619179nt_rat @ F @ ( sup_sup_set_int @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups1072433553688619179nt_rat @ F @ A3 ) @ ( groups1072433553688619179nt_rat @ F @ B3 ) ) @ ( groups1072433553688619179nt_rat @ F @ ( inf_inf_set_int @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7692_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > rat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups2555765274223993564er_rat @ F @ ( sup_su848401254843788991nteger @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups2555765274223993564er_rat @ F @ A3 ) @ ( groups2555765274223993564er_rat @ F @ B3 ) ) @ ( groups2555765274223993564er_rat @ F @ ( inf_in1364745209274528805nteger @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7693_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > rat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.80 ( ( member8440522571783428010at_nat @ X3 @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups3442636767675653108at_rat @ F @ ( sup_su6327502436637775413at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups3442636767675653108at_rat @ F @ A3 ) @ ( groups3442636767675653108at_rat @ F @ B3 ) ) @ ( groups3442636767675653108at_rat @ F @ ( inf_in2572325071724192079at_nat @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7694_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat,F: produc859450856879609959at_nat > rat] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ A3 )
% 5.45/5.80 => ( ( finite4392333629123659920at_nat @ B3 )
% 5.45/5.80 => ( ! [X3: produc859450856879609959at_nat] :
% 5.45/5.80 ( ( member8206827879206165904at_nat @ X3 @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups7136053025338371162at_rat @ F @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups7136053025338371162at_rat @ F @ A3 ) @ ( groups7136053025338371162at_rat @ F @ B3 ) ) @ ( groups7136053025338371162at_rat @ F @ ( inf_in4302113700860409141at_nat @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7695_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat,F: produc4166570645942440679at_nat > rat] :
% 5.45/5.80 ( ( finite1918287321285529104at_nat @ A3 )
% 5.45/5.80 => ( ( finite1918287321285529104at_nat @ B3 )
% 5.45/5.80 => ( ! [X3: produc4166570645942440679at_nat] :
% 5.45/5.80 ( ( member6689249552917799696at_nat @ X3 @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups5938585286922990810at_rat @ F @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups5938585286922990810at_rat @ F @ A3 ) @ ( groups5938585286922990810at_rat @ F @ B3 ) ) @ ( groups5938585286922990810at_rat @ F @ ( inf_in1697001100524423349at_nat @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7696_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat,F: produc3843707927480180839at_nat > rat] :
% 5.45/5.80 ( ( finite4343798906461161616at_nat @ A3 )
% 5.45/5.80 => ( ( finite4343798906461161616at_nat @ B3 )
% 5.45/5.80 => ( ! [X3: produc3843707927480180839at_nat] :
% 5.45/5.80 ( ( member8757157785044589968at_nat @ X3 @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups8874911130973611098at_rat @ F @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups8874911130973611098at_rat @ F @ A3 ) @ ( groups8874911130973611098at_rat @ F @ B3 ) ) @ ( groups8874911130973611098at_rat @ F @ ( inf_in7913087082777306421at_nat @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7697_prod__Un,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > rat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ ( inf_inf_set_nat @ A3 @ B3 ) )
% 5.45/5.80 => ( ( F @ X3 )
% 5.45/5.80 != zero_zero_rat ) )
% 5.45/5.80 => ( ( groups73079841787564623at_rat @ F @ ( sup_sup_set_nat @ A3 @ B3 ) )
% 5.45/5.80 = ( divide_divide_rat @ ( times_times_rat @ ( groups73079841787564623at_rat @ F @ A3 ) @ ( groups73079841787564623at_rat @ F @ B3 ) ) @ ( groups73079841787564623at_rat @ F @ ( inf_inf_set_nat @ A3 @ B3 ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % prod_Un
% 5.45/5.80 thf(fact_7698_gbinomial__partial__row__sum,axiom,
% 5.45/5.80 ! [A: rat,M: nat] :
% 5.45/5.80 ( ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ M ) )
% 5.45/5.80 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ one_one_rat ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ A @ ( plus_plus_nat @ M @ one_one_nat ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gbinomial_partial_row_sum
% 5.45/5.80 thf(fact_7699_binomial__ring,axiom,
% 5.45/5.80 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.80 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_ring
% 5.45/5.80 thf(fact_7700_binomial__ring,axiom,
% 5.45/5.80 ! [A: int,B: int,N2: nat] :
% 5.45/5.80 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups3539618377306564664at_int
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_ring
% 5.45/5.80 thf(fact_7701_binomial__ring,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.80 ( ( power_8256067586552552935nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups7501900531339628137nteger
% 5.45/5.80 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( power_8256067586552552935nteger @ A @ K3 ) ) @ ( power_8256067586552552935nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_ring
% 5.45/5.80 thf(fact_7702_binomial__ring,axiom,
% 5.45/5.80 ! [A: nat,B: nat,N2: nat] :
% 5.45/5.80 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups3542108847815614940at_nat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % binomial_ring
% 5.45/5.80 thf(fact_7703_pochhammer__binomial__sum,axiom,
% 5.45/5.80 ! [A: rat,B: rat,N2: nat] :
% 5.45/5.80 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_binomial_sum
% 5.45/5.80 thf(fact_7704_pochhammer__binomial__sum,axiom,
% 5.45/5.80 ! [A: int,B: int,N2: nat] :
% 5.45/5.80 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups3539618377306564664at_int
% 5.45/5.80 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_binomial_sum
% 5.45/5.80 thf(fact_7705_pochhammer__binomial__sum,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.45/5.80 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ N2 )
% 5.45/5.80 = ( groups7501900531339628137nteger
% 5.45/5.80 @ ^ [K3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ K3 ) ) @ ( comm_s8582702949713902594nteger @ A @ K3 ) ) @ ( comm_s8582702949713902594nteger @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pochhammer_binomial_sum
% 5.45/5.80 thf(fact_7706_gbinomial__altdef__of__nat,axiom,
% 5.45/5.80 ( gbinomial_rat
% 5.45/5.80 = ( ^ [A5: rat,K3: nat] :
% 5.45/5.80 ( groups73079841787564623at_rat
% 5.45/5.80 @ ^ [I4: nat] : ( divide_divide_rat @ ( minus_minus_rat @ A5 @ ( semiri681578069525770553at_rat @ I4 ) ) @ ( semiri681578069525770553at_rat @ ( minus_minus_nat @ K3 @ I4 ) ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gbinomial_altdef_of_nat
% 5.45/5.80 thf(fact_7707_gbinomial__mult__fact_H,axiom,
% 5.45/5.80 ! [A: rat,K: nat] :
% 5.45/5.80 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( semiri773545260158071498ct_rat @ K ) )
% 5.45/5.80 = ( groups73079841787564623at_rat
% 5.45/5.80 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gbinomial_mult_fact'
% 5.45/5.80 thf(fact_7708_gbinomial__mult__fact,axiom,
% 5.45/5.80 ! [K: nat,A: rat] :
% 5.45/5.80 ( ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( gbinomial_rat @ A @ K ) )
% 5.45/5.80 = ( groups73079841787564623at_rat
% 5.45/5.80 @ ^ [I4: nat] : ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ I4 ) )
% 5.45/5.80 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % gbinomial_mult_fact
% 5.45/5.80 thf(fact_7709_half__negative__int__iff,axiom,
% 5.45/5.80 ! [K: int] :
% 5.45/5.80 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.45/5.80 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.45/5.80
% 5.45/5.80 % half_negative_int_iff
% 5.45/5.80 thf(fact_7710_half__nonnegative__int__iff,axiom,
% 5.45/5.80 ! [K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.45/5.80 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % half_nonnegative_int_iff
% 5.45/5.80 thf(fact_7711_divmod__step__eq,axiom,
% 5.45/5.80 ! [L: num,R3: nat,Q6: nat] :
% 5.45/5.80 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.45/5.80 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q6 @ R3 ) )
% 5.45/5.80 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.45/5.80 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.45/5.80 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q6 @ R3 ) )
% 5.45/5.80 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q6 ) @ R3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % divmod_step_eq
% 5.45/5.80 thf(fact_7712_divmod__step__eq,axiom,
% 5.45/5.80 ! [L: num,R3: int,Q6: int] :
% 5.45/5.80 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.45/5.80 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.80 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.45/5.80 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.45/5.80 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.45/5.80 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q6 ) @ R3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % divmod_step_eq
% 5.45/5.80 thf(fact_7713_divmod__step__eq,axiom,
% 5.45/5.80 ! [L: num,R3: code_integer,Q6: code_integer] :
% 5.45/5.80 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.45/5.80 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q6 @ R3 ) )
% 5.45/5.80 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.45/5.80 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.45/5.80 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q6 @ R3 ) )
% 5.45/5.80 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q6 ) @ R3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % divmod_step_eq
% 5.45/5.80 thf(fact_7714_mult__exp__mod__exp__eq,axiom,
% 5.45/5.80 ! [M: nat,N2: nat,A: nat] :
% 5.45/5.80 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.80 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_exp_mod_exp_eq
% 5.45/5.80 thf(fact_7715_mult__exp__mod__exp__eq,axiom,
% 5.45/5.80 ! [M: nat,N2: nat,A: int] :
% 5.45/5.80 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.80 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_exp_mod_exp_eq
% 5.45/5.80 thf(fact_7716_mult__exp__mod__exp__eq,axiom,
% 5.45/5.80 ! [M: nat,N2: nat,A: code_integer] :
% 5.45/5.80 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.80 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_exp_mod_exp_eq
% 5.45/5.80 thf(fact_7717_mult__exp__mod__exp__eq,axiom,
% 5.45/5.80 ! [M: nat,N2: nat,A: code_natural] :
% 5.45/5.80 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.80 => ( ( modulo8411746178871703098atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( times_2397367101498566445atural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_exp_mod_exp_eq
% 5.45/5.80 thf(fact_7718_nat__bit__induct,axiom,
% 5.45/5.80 ! [P: nat > $o,N2: nat] :
% 5.45/5.80 ( ( P @ zero_zero_nat )
% 5.45/5.80 => ( ! [N5: nat] :
% 5.45/5.80 ( ( P @ N5 )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.45/5.80 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 5.45/5.80 => ( ! [N5: nat] :
% 5.45/5.80 ( ( P @ N5 )
% 5.45/5.80 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N5 ) ) ) )
% 5.45/5.80 => ( P @ N2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_bit_induct
% 5.45/5.80 thf(fact_7719_finite__Collect__le__nat,axiom,
% 5.45/5.80 ! [K: nat] :
% 5.45/5.80 ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_le_nat
% 5.45/5.80 thf(fact_7720_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.80 ( ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.80 | ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) )
% 5.45/5.80 => ( finite2998713641127702882nt_int
% 5.45/5.80 @ ( collec213857154873943460nt_int
% 5.45/5.80 @ ^ [X4: product_prod_int_int] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7721_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.80 ( ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.45/5.80 | ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) )
% 5.45/5.80 => ( finite8100373058378681591st_nat
% 5.45/5.80 @ ( collect_list_nat
% 5.45/5.80 @ ^ [X4: list_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7722_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.80 ( ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.45/5.80 | ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) )
% 5.45/5.80 => ( finite1152437895449049373et_nat
% 5.45/5.80 @ ( collect_set_nat
% 5.45/5.80 @ ^ [X4: set_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7723_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.80 ( ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.45/5.80 | ( finite_finite_nat @ ( collect_nat @ Q ) ) )
% 5.45/5.80 => ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [X4: nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7724_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: int > $o,Q: int > $o] :
% 5.45/5.80 ( ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.45/5.80 | ( finite_finite_int @ ( collect_int @ Q ) ) )
% 5.45/5.80 => ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [X4: int] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7725_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: code_integer > $o,Q: code_integer > $o] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.45/5.80 | ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q ) ) )
% 5.45/5.80 => ( finite6017078050557962740nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [X4: code_integer] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7726_finite__Collect__conjI,axiom,
% 5.45/5.80 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.45/5.80 ( ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.45/5.80 | ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) )
% 5.45/5.80 => ( finite6177210948735845034at_nat
% 5.45/5.80 @ ( collec3392354462482085612at_nat
% 5.45/5.80 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 & ( Q @ X4 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_conjI
% 5.45/5.80 thf(fact_7727_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.45/5.80 ( ( finite2998713641127702882nt_int
% 5.45/5.80 @ ( collec213857154873943460nt_int
% 5.45/5.80 @ ^ [X4: product_prod_int_int] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.80 & ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7728_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.45/5.80 ( ( finite8100373058378681591st_nat
% 5.45/5.80 @ ( collect_list_nat
% 5.45/5.80 @ ^ [X4: list_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.45/5.80 & ( finite8100373058378681591st_nat @ ( collect_list_nat @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7729_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.45/5.80 ( ( finite1152437895449049373et_nat
% 5.45/5.80 @ ( collect_set_nat
% 5.45/5.80 @ ^ [X4: set_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.45/5.80 & ( finite1152437895449049373et_nat @ ( collect_set_nat @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7730_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: nat > $o,Q: nat > $o] :
% 5.45/5.80 ( ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [X4: nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.45/5.80 & ( finite_finite_nat @ ( collect_nat @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7731_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: int > $o,Q: int > $o] :
% 5.45/5.80 ( ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [X4: int] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite_finite_int @ ( collect_int @ P ) )
% 5.45/5.80 & ( finite_finite_int @ ( collect_int @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7732_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: code_integer > $o,Q: code_integer > $o] :
% 5.45/5.80 ( ( finite6017078050557962740nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [X4: code_integer] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.45/5.80 & ( finite6017078050557962740nteger @ ( collect_Code_integer @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7733_finite__Collect__disjI,axiom,
% 5.45/5.80 ! [P: product_prod_nat_nat > $o,Q: product_prod_nat_nat > $o] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat
% 5.45/5.80 @ ( collec3392354462482085612at_nat
% 5.45/5.80 @ ^ [X4: product_prod_nat_nat] :
% 5.45/5.80 ( ( P @ X4 )
% 5.45/5.80 | ( Q @ X4 ) ) ) )
% 5.45/5.80 = ( ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.45/5.80 & ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ Q ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_disjI
% 5.45/5.80 thf(fact_7734_finite__interval__int1,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [I4: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ A @ I4 )
% 5.45/5.80 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_interval_int1
% 5.45/5.80 thf(fact_7735_finite__interval__int4,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [I4: int] :
% 5.45/5.80 ( ( ord_less_int @ A @ I4 )
% 5.45/5.80 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_interval_int4
% 5.45/5.80 thf(fact_7736_of__nat__id,axiom,
% 5.45/5.80 ( semiri1316708129612266289at_nat
% 5.45/5.80 = ( ^ [N: nat] : N ) ) ).
% 5.45/5.80
% 5.45/5.80 % of_nat_id
% 5.45/5.80 thf(fact_7737_finite__Int,axiom,
% 5.45/5.80 ! [F4: set_int,G2: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ F4 )
% 5.45/5.80 | ( finite_finite_int @ G2 ) )
% 5.45/5.80 => ( finite_finite_int @ ( inf_inf_set_int @ F4 @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Int
% 5.45/5.80 thf(fact_7738_finite__Int,axiom,
% 5.45/5.80 ! [F4: set_Code_integer,G2: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ F4 )
% 5.45/5.80 | ( finite6017078050557962740nteger @ G2 ) )
% 5.45/5.80 => ( finite6017078050557962740nteger @ ( inf_in1364745209274528805nteger @ F4 @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Int
% 5.45/5.80 thf(fact_7739_finite__Int,axiom,
% 5.45/5.80 ! [F4: set_nat,G2: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ F4 )
% 5.45/5.80 | ( finite_finite_nat @ G2 ) )
% 5.45/5.80 => ( finite_finite_nat @ ( inf_inf_set_nat @ F4 @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Int
% 5.45/5.80 thf(fact_7740_finite__Int,axiom,
% 5.45/5.80 ! [F4: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( ( finite6177210948735845034at_nat @ F4 )
% 5.45/5.80 | ( finite6177210948735845034at_nat @ G2 ) )
% 5.45/5.80 => ( finite6177210948735845034at_nat @ ( inf_in2572325071724192079at_nat @ F4 @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Int
% 5.45/5.80 thf(fact_7741_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_int,G2: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite_finite_int @ F4 )
% 5.45/5.80 & ( finite_finite_int @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7742_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_Code_integer,G2: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite6017078050557962740nteger @ F4 )
% 5.45/5.80 & ( finite6017078050557962740nteger @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7743_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite6177210948735845034at_nat @ F4 )
% 5.45/5.80 & ( finite6177210948735845034at_nat @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7744_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_Pr8693737435421807431at_nat,G2: set_Pr8693737435421807431at_nat] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite4392333629123659920at_nat @ F4 )
% 5.45/5.80 & ( finite4392333629123659920at_nat @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7745_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_Pr8551490117392284871at_nat,G2: set_Pr8551490117392284871at_nat] :
% 5.45/5.80 ( ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite1918287321285529104at_nat @ F4 )
% 5.45/5.80 & ( finite1918287321285529104at_nat @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7746_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_Pr4329608150637261639at_nat,G2: set_Pr4329608150637261639at_nat] :
% 5.45/5.80 ( ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite4343798906461161616at_nat @ F4 )
% 5.45/5.80 & ( finite4343798906461161616at_nat @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7747_finite__Un,axiom,
% 5.45/5.80 ! [F4: set_nat,G2: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G2 ) )
% 5.45/5.80 = ( ( finite_finite_nat @ F4 )
% 5.45/5.80 & ( finite_finite_nat @ G2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Un
% 5.45/5.80 thf(fact_7748_finite__interval__int3,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [I4: int] :
% 5.45/5.80 ( ( ord_less_int @ A @ I4 )
% 5.45/5.80 & ( ord_less_eq_int @ I4 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_interval_int3
% 5.45/5.80 thf(fact_7749_finite__interval__int2,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [I4: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ A @ I4 )
% 5.45/5.80 & ( ord_less_int @ I4 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_interval_int2
% 5.45/5.80 thf(fact_7750_finite__Collect__less__nat,axiom,
% 5.45/5.80 ! [K: nat] :
% 5.45/5.80 ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_less_nat
% 5.45/5.80 thf(fact_7751_finite__Collect__subsets,axiom,
% 5.45/5.80 ! [A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( finite1152437895449049373et_nat
% 5.45/5.80 @ ( collect_set_nat
% 5.45/5.80 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_subsets
% 5.45/5.80 thf(fact_7752_finite__Collect__subsets,axiom,
% 5.45/5.80 ! [A3: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( finite6931041176100689706nteger
% 5.45/5.80 @ ( collec574505750873337192nteger
% 5.45/5.80 @ ^ [B6: set_Code_integer] : ( ord_le7084787975880047091nteger @ B6 @ A3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_subsets
% 5.45/5.80 thf(fact_7753_finite__Collect__subsets,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( finite9047747110432174090at_nat
% 5.45/5.80 @ ( collec5514110066124741708at_nat
% 5.45/5.80 @ ^ [B6: set_Pr1261947904930325089at_nat] : ( ord_le3146513528884898305at_nat @ B6 @ A3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_subsets
% 5.45/5.80 thf(fact_7754_finite__Collect__subsets,axiom,
% 5.45/5.80 ! [A3: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( finite6197958912794628473et_int
% 5.45/5.80 @ ( collect_set_int
% 5.45/5.80 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_Collect_subsets
% 5.45/5.80 thf(fact_7755_finite__maxlen,axiom,
% 5.45/5.80 ! [M6: set_list_nat] :
% 5.45/5.80 ( ( finite8100373058378681591st_nat @ M6 )
% 5.45/5.80 => ? [N5: nat] :
% 5.45/5.80 ! [X7: list_nat] :
% 5.45/5.80 ( ( member_list_nat @ X7 @ M6 )
% 5.45/5.80 => ( ord_less_nat @ ( size_size_list_nat @ X7 ) @ N5 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_maxlen
% 5.45/5.80 thf(fact_7756_finite__maxlen,axiom,
% 5.45/5.80 ! [M6: set_list_o] :
% 5.45/5.80 ( ( finite_finite_list_o @ M6 )
% 5.45/5.80 => ? [N5: nat] :
% 5.45/5.80 ! [X7: list_o] :
% 5.45/5.80 ( ( member_list_o @ X7 @ M6 )
% 5.45/5.80 => ( ord_less_nat @ ( size_size_list_o @ X7 ) @ N5 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_maxlen
% 5.45/5.80 thf(fact_7757_image__add__int__atLeastLessThan,axiom,
% 5.45/5.80 ! [L: int,U: int] :
% 5.45/5.80 ( ( image_int_int
% 5.45/5.80 @ ^ [X4: int] : ( plus_plus_int @ X4 @ L )
% 5.45/5.80 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.45/5.80 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.45/5.80
% 5.45/5.80 % image_add_int_atLeastLessThan
% 5.45/5.80 thf(fact_7758_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: product_prod_int_int > $o] :
% 5.45/5.80 ( ~ ( finite2998713641127702882nt_int @ ( collec213857154873943460nt_int @ P ) )
% 5.45/5.80 => ? [X_1: product_prod_int_int] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7759_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: list_nat > $o] :
% 5.45/5.80 ( ~ ( finite8100373058378681591st_nat @ ( collect_list_nat @ P ) )
% 5.45/5.80 => ? [X_1: list_nat] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7760_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: set_nat > $o] :
% 5.45/5.80 ( ~ ( finite1152437895449049373et_nat @ ( collect_set_nat @ P ) )
% 5.45/5.80 => ? [X_1: set_nat] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7761_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: nat > $o] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ ( collect_nat @ P ) )
% 5.45/5.80 => ? [X_1: nat] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7762_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: int > $o] :
% 5.45/5.80 ( ~ ( finite_finite_int @ ( collect_int @ P ) )
% 5.45/5.80 => ? [X_1: int] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7763_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: code_integer > $o] :
% 5.45/5.80 ( ~ ( finite6017078050557962740nteger @ ( collect_Code_integer @ P ) )
% 5.45/5.80 => ? [X_1: code_integer] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7764_not__finite__existsD,axiom,
% 5.45/5.80 ! [P: product_prod_nat_nat > $o] :
% 5.45/5.80 ( ~ ( finite6177210948735845034at_nat @ ( collec3392354462482085612at_nat @ P ) )
% 5.45/5.80 => ? [X_1: product_prod_nat_nat] : ( P @ X_1 ) ) ).
% 5.45/5.80
% 5.45/5.80 % not_finite_existsD
% 5.45/5.80 thf(fact_7765_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_nat,R: $o > nat > $o] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7766_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_int,R: $o > int > $o] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7767_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_o,B3: set_Code_integer,R: $o > code_integer > $o] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7768_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,R: nat > nat > $o] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7769_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_int,R: nat > int > $o] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7770_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_Code_integer,R: nat > code_integer > $o] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7771_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_nat,R: int > nat > $o] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7772_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,R: int > int > $o] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7773_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_Code_integer,R: int > code_integer > $o] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ! [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7774_pigeonhole__infinite__rel,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_nat,R: code_integer > nat > $o] :
% 5.45/5.80 ( ~ ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ! [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 => ? [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ B3 )
% 5.45/5.80 & ( R @ X3 @ Xa2 ) ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ B3 )
% 5.45/5.80 & ~ ( finite6017078050557962740nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [A5: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ A5 @ A3 )
% 5.45/5.80 & ( R @ A5 @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite_rel
% 5.45/5.80 thf(fact_7775_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_o,A: $o] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( member_o @ A @ A3 )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_o @ A @ X3 )
% 5.45/5.80 & ! [Xa2: $o] :
% 5.45/5.80 ( ( member_o @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_o @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7776_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_set_nat,A: set_nat] :
% 5.45/5.80 ( ( finite1152437895449049373et_nat @ A3 )
% 5.45/5.80 => ( ( member_set_nat @ A @ A3 )
% 5.45/5.80 => ? [X3: set_nat] :
% 5.45/5.80 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ A @ X3 )
% 5.45/5.80 & ! [Xa2: set_nat] :
% 5.45/5.80 ( ( member_set_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7777_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,A: code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( member_Code_integer @ A @ A3 )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 & ( ord_le3102999989581377725nteger @ A @ X3 )
% 5.45/5.80 & ! [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7778_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_set_int,A: set_int] :
% 5.45/5.80 ( ( finite6197958912794628473et_int @ A3 )
% 5.45/5.80 => ( ( member_set_int @ A @ A3 )
% 5.45/5.80 => ? [X3: set_int] :
% 5.45/5.80 ( ( member_set_int @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_set_int @ A @ X3 )
% 5.45/5.80 & ! [Xa2: set_int] :
% 5.45/5.80 ( ( member_set_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7779_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_rat,A: rat] :
% 5.45/5.80 ( ( finite_finite_rat @ A3 )
% 5.45/5.80 => ( ( member_rat @ A @ A3 )
% 5.45/5.80 => ? [X3: rat] :
% 5.45/5.80 ( ( member_rat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_rat @ A @ X3 )
% 5.45/5.80 & ! [Xa2: rat] :
% 5.45/5.80 ( ( member_rat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_rat @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7780_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_num,A: num] :
% 5.45/5.80 ( ( finite_finite_num @ A3 )
% 5.45/5.80 => ( ( member_num @ A @ A3 )
% 5.45/5.80 => ? [X3: num] :
% 5.45/5.80 ( ( member_num @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_num @ A @ X3 )
% 5.45/5.80 & ! [Xa2: num] :
% 5.45/5.80 ( ( member_num @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_num @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7781_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_nat,A: nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( member_nat @ A @ A3 )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_nat @ A @ X3 )
% 5.45/5.80 & ! [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_nat @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7782_finite__has__maximal2,axiom,
% 5.45/5.80 ! [A3: set_int,A: int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( member_int @ A @ A3 )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_int @ A @ X3 )
% 5.45/5.80 & ! [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_int @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal2
% 5.45/5.80 thf(fact_7783_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_o,A: $o] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( member_o @ A @ A3 )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_o @ X3 @ A )
% 5.45/5.80 & ! [Xa2: $o] :
% 5.45/5.80 ( ( member_o @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_o @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7784_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_set_nat,A: set_nat] :
% 5.45/5.80 ( ( finite1152437895449049373et_nat @ A3 )
% 5.45/5.80 => ( ( member_set_nat @ A @ A3 )
% 5.45/5.80 => ? [X3: set_nat] :
% 5.45/5.80 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ X3 @ A )
% 5.45/5.80 & ! [Xa2: set_nat] :
% 5.45/5.80 ( ( member_set_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7785_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,A: code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( member_Code_integer @ A @ A3 )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 & ( ord_le3102999989581377725nteger @ X3 @ A )
% 5.45/5.80 & ! [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_le3102999989581377725nteger @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7786_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_set_int,A: set_int] :
% 5.45/5.80 ( ( finite6197958912794628473et_int @ A3 )
% 5.45/5.80 => ( ( member_set_int @ A @ A3 )
% 5.45/5.80 => ? [X3: set_int] :
% 5.45/5.80 ( ( member_set_int @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_set_int @ X3 @ A )
% 5.45/5.80 & ! [Xa2: set_int] :
% 5.45/5.80 ( ( member_set_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7787_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_rat,A: rat] :
% 5.45/5.80 ( ( finite_finite_rat @ A3 )
% 5.45/5.80 => ( ( member_rat @ A @ A3 )
% 5.45/5.80 => ? [X3: rat] :
% 5.45/5.80 ( ( member_rat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_rat @ X3 @ A )
% 5.45/5.80 & ! [Xa2: rat] :
% 5.45/5.80 ( ( member_rat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_rat @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7788_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_num,A: num] :
% 5.45/5.80 ( ( finite_finite_num @ A3 )
% 5.45/5.80 => ( ( member_num @ A @ A3 )
% 5.45/5.80 => ? [X3: num] :
% 5.45/5.80 ( ( member_num @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_num @ X3 @ A )
% 5.45/5.80 & ! [Xa2: num] :
% 5.45/5.80 ( ( member_num @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_num @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7789_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_nat,A: nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( member_nat @ A @ A3 )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_nat @ X3 @ A )
% 5.45/5.80 & ! [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7790_finite__has__minimal2,axiom,
% 5.45/5.80 ! [A3: set_int,A: int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( member_int @ A @ A3 )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ( ord_less_eq_int @ X3 @ A )
% 5.45/5.80 & ! [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_int @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal2
% 5.45/5.80 thf(fact_7791_finite_OemptyI,axiom,
% 5.45/5.80 finite6017078050557962740nteger @ bot_bo3990330152332043303nteger ).
% 5.45/5.80
% 5.45/5.80 % finite.emptyI
% 5.45/5.80 thf(fact_7792_finite_OemptyI,axiom,
% 5.45/5.80 finite6177210948735845034at_nat @ bot_bo2099793752762293965at_nat ).
% 5.45/5.80
% 5.45/5.80 % finite.emptyI
% 5.45/5.80 thf(fact_7793_finite_OemptyI,axiom,
% 5.45/5.80 finite_finite_o @ bot_bot_set_o ).
% 5.45/5.80
% 5.45/5.80 % finite.emptyI
% 5.45/5.80 thf(fact_7794_finite_OemptyI,axiom,
% 5.45/5.80 finite_finite_nat @ bot_bot_set_nat ).
% 5.45/5.80
% 5.45/5.80 % finite.emptyI
% 5.45/5.80 thf(fact_7795_finite_OemptyI,axiom,
% 5.45/5.80 finite_finite_int @ bot_bot_set_int ).
% 5.45/5.80
% 5.45/5.80 % finite.emptyI
% 5.45/5.80 thf(fact_7796_infinite__imp__nonempty,axiom,
% 5.45/5.80 ! [S: set_Code_integer] :
% 5.45/5.80 ( ~ ( finite6017078050557962740nteger @ S )
% 5.45/5.80 => ( S != bot_bo3990330152332043303nteger ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_imp_nonempty
% 5.45/5.80 thf(fact_7797_infinite__imp__nonempty,axiom,
% 5.45/5.80 ! [S: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ~ ( finite6177210948735845034at_nat @ S )
% 5.45/5.80 => ( S != bot_bo2099793752762293965at_nat ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_imp_nonempty
% 5.45/5.80 thf(fact_7798_infinite__imp__nonempty,axiom,
% 5.45/5.80 ! [S: set_o] :
% 5.45/5.80 ( ~ ( finite_finite_o @ S )
% 5.45/5.80 => ( S != bot_bot_set_o ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_imp_nonempty
% 5.45/5.80 thf(fact_7799_infinite__imp__nonempty,axiom,
% 5.45/5.80 ! [S: set_nat] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ S )
% 5.45/5.80 => ( S != bot_bot_set_nat ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_imp_nonempty
% 5.45/5.80 thf(fact_7800_infinite__imp__nonempty,axiom,
% 5.45/5.80 ! [S: set_int] :
% 5.45/5.80 ( ~ ( finite_finite_int @ S )
% 5.45/5.80 => ( S != bot_bot_set_int ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_imp_nonempty
% 5.45/5.80 thf(fact_7801_all__subset__image,axiom,
% 5.45/5.80 ! [F: nat > set_nat,A3: set_nat,P: set_set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_set_nat] :
% 5.45/5.80 ( ( ord_le6893508408891458716et_nat @ B6 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 => ( P @ ( image_nat_set_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_subset_image
% 5.45/5.80 thf(fact_7802_all__subset__image,axiom,
% 5.45/5.80 ! [F: nat > nat,A3: set_nat,P: set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 => ( P @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_subset_image
% 5.45/5.80 thf(fact_7803_all__subset__image,axiom,
% 5.45/5.80 ! [F: int > nat,A3: set_int,P: set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ B6 @ A3 )
% 5.45/5.80 => ( P @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_subset_image
% 5.45/5.80 thf(fact_7804_all__subset__image,axiom,
% 5.45/5.80 ! [F: nat > int,A3: set_nat,P: set_int > $o] :
% 5.45/5.80 ( ( ! [B6: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 => ( P @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_subset_image
% 5.45/5.80 thf(fact_7805_all__subset__image,axiom,
% 5.45/5.80 ! [F: int > int,A3: set_int,P: set_int > $o] :
% 5.45/5.80 ( ( ! [B6: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ B6 @ A3 )
% 5.45/5.80 => ( P @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_subset_image
% 5.45/5.80 thf(fact_7806_finite__subset,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( finite_finite_nat @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset
% 5.45/5.80 thf(fact_7807_finite__subset,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( finite6017078050557962740nteger @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset
% 5.45/5.80 thf(fact_7808_finite__subset,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset
% 5.45/5.80 thf(fact_7809_finite__subset,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.80 => ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( finite_finite_int @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset
% 5.45/5.80 thf(fact_7810_infinite__super,axiom,
% 5.45/5.80 ! [S: set_nat,T: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ S @ T )
% 5.45/5.80 => ( ~ ( finite_finite_nat @ S )
% 5.45/5.80 => ~ ( finite_finite_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_super
% 5.45/5.80 thf(fact_7811_infinite__super,axiom,
% 5.45/5.80 ! [S: set_Code_integer,T: set_Code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger @ S @ T )
% 5.45/5.80 => ( ~ ( finite6017078050557962740nteger @ S )
% 5.45/5.80 => ~ ( finite6017078050557962740nteger @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_super
% 5.45/5.80 thf(fact_7812_infinite__super,axiom,
% 5.45/5.80 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( ord_le3146513528884898305at_nat @ S @ T )
% 5.45/5.80 => ( ~ ( finite6177210948735845034at_nat @ S )
% 5.45/5.80 => ~ ( finite6177210948735845034at_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_super
% 5.45/5.80 thf(fact_7813_infinite__super,axiom,
% 5.45/5.80 ! [S: set_int,T: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ S @ T )
% 5.45/5.80 => ( ~ ( finite_finite_int @ S )
% 5.45/5.80 => ~ ( finite_finite_int @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_super
% 5.45/5.80 thf(fact_7814_rev__finite__subset,axiom,
% 5.45/5.80 ! [B3: set_nat,A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.80 => ( finite_finite_nat @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % rev_finite_subset
% 5.45/5.80 thf(fact_7815_rev__finite__subset,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,A3: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.80 => ( finite6017078050557962740nteger @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % rev_finite_subset
% 5.45/5.80 thf(fact_7816_rev__finite__subset,axiom,
% 5.45/5.80 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.80 => ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.80 => ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % rev_finite_subset
% 5.45/5.80 thf(fact_7817_rev__finite__subset,axiom,
% 5.45/5.80 ! [B3: set_int,A3: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.80 => ( finite_finite_int @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % rev_finite_subset
% 5.45/5.80 thf(fact_7818_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_int,G2: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ F4 )
% 5.45/5.80 => ( ( finite_finite_int @ G2 )
% 5.45/5.80 => ( finite_finite_int @ ( sup_sup_set_int @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7819_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_Code_integer,G2: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ F4 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ G2 )
% 5.45/5.80 => ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7820_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_Pr1261947904930325089at_nat,G2: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ F4 )
% 5.45/5.80 => ( ( finite6177210948735845034at_nat @ G2 )
% 5.45/5.80 => ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7821_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_Pr8693737435421807431at_nat,G2: set_Pr8693737435421807431at_nat] :
% 5.45/5.80 ( ( finite4392333629123659920at_nat @ F4 )
% 5.45/5.80 => ( ( finite4392333629123659920at_nat @ G2 )
% 5.45/5.80 => ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7822_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_Pr8551490117392284871at_nat,G2: set_Pr8551490117392284871at_nat] :
% 5.45/5.80 ( ( finite1918287321285529104at_nat @ F4 )
% 5.45/5.80 => ( ( finite1918287321285529104at_nat @ G2 )
% 5.45/5.80 => ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7823_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_Pr4329608150637261639at_nat,G2: set_Pr4329608150637261639at_nat] :
% 5.45/5.80 ( ( finite4343798906461161616at_nat @ F4 )
% 5.45/5.80 => ( ( finite4343798906461161616at_nat @ G2 )
% 5.45/5.80 => ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7824_finite__UnI,axiom,
% 5.45/5.80 ! [F4: set_nat,G2: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ F4 )
% 5.45/5.80 => ( ( finite_finite_nat @ G2 )
% 5.45/5.80 => ( finite_finite_nat @ ( sup_sup_set_nat @ F4 @ G2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_UnI
% 5.45/5.80 thf(fact_7825_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_int,T: set_int] :
% 5.45/5.80 ( ~ ( finite_finite_int @ S )
% 5.45/5.80 => ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7826_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_Code_integer,T: set_Code_integer] :
% 5.45/5.80 ( ~ ( finite6017078050557962740nteger @ S )
% 5.45/5.80 => ~ ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7827_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ~ ( finite6177210948735845034at_nat @ S )
% 5.45/5.80 => ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7828_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.80 ( ~ ( finite4392333629123659920at_nat @ S )
% 5.45/5.80 => ~ ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7829_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.80 ( ~ ( finite1918287321285529104at_nat @ S )
% 5.45/5.80 => ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7830_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.80 ( ~ ( finite4343798906461161616at_nat @ S )
% 5.45/5.80 => ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7831_Un__infinite,axiom,
% 5.45/5.80 ! [S: set_nat,T: set_nat] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ S )
% 5.45/5.80 => ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % Un_infinite
% 5.45/5.80 thf(fact_7832_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_int,T: set_int] :
% 5.45/5.80 ( ( ~ ( finite_finite_int @ ( sup_sup_set_int @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite_finite_int @ S )
% 5.45/5.80 | ~ ( finite_finite_int @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7833_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_Code_integer,T: set_Code_integer] :
% 5.45/5.80 ( ( ~ ( finite6017078050557962740nteger @ ( sup_su848401254843788991nteger @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite6017078050557962740nteger @ S )
% 5.45/5.80 | ~ ( finite6017078050557962740nteger @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7834_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_Pr1261947904930325089at_nat,T: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( ~ ( finite6177210948735845034at_nat @ ( sup_su6327502436637775413at_nat @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite6177210948735845034at_nat @ S )
% 5.45/5.80 | ~ ( finite6177210948735845034at_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7835_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_Pr8693737435421807431at_nat,T: set_Pr8693737435421807431at_nat] :
% 5.45/5.80 ( ( ~ ( finite4392333629123659920at_nat @ ( sup_su718114333110466843at_nat @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite4392333629123659920at_nat @ S )
% 5.45/5.80 | ~ ( finite4392333629123659920at_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7836_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_Pr8551490117392284871at_nat,T: set_Pr8551490117392284871at_nat] :
% 5.45/5.80 ( ( ~ ( finite1918287321285529104at_nat @ ( sup_su3035147773818789531at_nat @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite1918287321285529104at_nat @ S )
% 5.45/5.80 | ~ ( finite1918287321285529104at_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7837_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_Pr4329608150637261639at_nat,T: set_Pr4329608150637261639at_nat] :
% 5.45/5.80 ( ( ~ ( finite4343798906461161616at_nat @ ( sup_su5525570899277871387at_nat @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite4343798906461161616at_nat @ S )
% 5.45/5.80 | ~ ( finite4343798906461161616at_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7838_infinite__Un,axiom,
% 5.45/5.80 ! [S: set_nat,T: set_nat] :
% 5.45/5.80 ( ( ~ ( finite_finite_nat @ ( sup_sup_set_nat @ S @ T ) ) )
% 5.45/5.80 = ( ~ ( finite_finite_nat @ S )
% 5.45/5.80 | ~ ( finite_finite_nat @ T ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % infinite_Un
% 5.45/5.80 thf(fact_7839_finite__psubset__induct,axiom,
% 5.45/5.80 ! [A3: set_nat,P: set_nat > $o] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ! [A8: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A8 )
% 5.45/5.80 => ( ! [B8: set_nat] :
% 5.45/5.80 ( ( ord_less_set_nat @ B8 @ A8 )
% 5.45/5.80 => ( P @ B8 ) )
% 5.45/5.80 => ( P @ A8 ) ) )
% 5.45/5.80 => ( P @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_psubset_induct
% 5.45/5.80 thf(fact_7840_finite__psubset__induct,axiom,
% 5.45/5.80 ! [A3: set_int,P: set_int > $o] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ! [A8: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ A8 )
% 5.45/5.80 => ( ! [B8: set_int] :
% 5.45/5.80 ( ( ord_less_set_int @ B8 @ A8 )
% 5.45/5.80 => ( P @ B8 ) )
% 5.45/5.80 => ( P @ A8 ) ) )
% 5.45/5.80 => ( P @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_psubset_induct
% 5.45/5.80 thf(fact_7841_finite__psubset__induct,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ! [A8: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A8 )
% 5.45/5.80 => ( ! [B8: set_Code_integer] :
% 5.45/5.80 ( ( ord_le1307284697595431911nteger @ B8 @ A8 )
% 5.45/5.80 => ( P @ B8 ) )
% 5.45/5.80 => ( P @ A8 ) ) )
% 5.45/5.80 => ( P @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_psubset_induct
% 5.45/5.80 thf(fact_7842_finite__psubset__induct,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,P: set_Pr1261947904930325089at_nat > $o] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.80 => ( ! [A8: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( finite6177210948735845034at_nat @ A8 )
% 5.45/5.80 => ( ! [B8: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ( ( ord_le7866589430770878221at_nat @ B8 @ A8 )
% 5.45/5.80 => ( P @ B8 ) )
% 5.45/5.80 => ( P @ A8 ) ) )
% 5.45/5.80 => ( P @ A3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_psubset_induct
% 5.45/5.80 thf(fact_7843_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_o,F: $o > nat] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ ( image_o_nat @ F @ A3 ) )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7844_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_o,F: $o > int] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ ( image_o_int @ F @ A3 ) )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7845_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_o,F: $o > code_integer] :
% 5.45/5.80 ( ~ ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ ( image_o_Code_integer @ F @ A3 ) )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_o
% 5.45/5.80 @ ( collect_o
% 5.45/5.80 @ ^ [A5: $o] :
% 5.45/5.80 ( ( member_o @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7846_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_nat,F: nat > nat] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7847_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_nat,F: nat > int] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7848_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_nat,F: nat > code_integer] :
% 5.45/5.80 ( ~ ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ ( image_1215581382706833972nteger @ F @ A3 ) )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [A5: nat] :
% 5.45/5.80 ( ( member_nat @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7849_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_int,F: int > nat] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7850_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_int,F: int > int] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite_finite_int @ ( image_int_int @ F @ A3 ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7851_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_int,F: int > code_integer] :
% 5.45/5.80 ( ~ ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( finite6017078050557962740nteger @ ( image_1587234942943678608nteger @ F @ A3 ) )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite_finite_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [A5: int] :
% 5.45/5.80 ( ( member_int @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7852_pigeonhole__infinite,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.80 ( ~ ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( finite_finite_nat @ ( image_951025933927791156er_nat @ F @ A3 ) )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 & ~ ( finite6017078050557962740nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [A5: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ A5 @ A3 )
% 5.45/5.80 & ( ( F @ A5 )
% 5.45/5.80 = ( F @ X3 ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pigeonhole_infinite
% 5.45/5.80 thf(fact_7853_nat__seg__image__imp__finite,axiom,
% 5.45/5.80 ! [A3: set_set_nat,F: nat > set_nat,N2: nat] :
% 5.45/5.80 ( ( A3
% 5.45/5.80 = ( image_nat_set_nat @ F
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) ) )
% 5.45/5.80 => ( finite1152437895449049373et_nat @ A3 ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_seg_image_imp_finite
% 5.45/5.80 thf(fact_7854_nat__seg__image__imp__finite,axiom,
% 5.45/5.80 ! [A3: set_nat,F: nat > nat,N2: nat] :
% 5.45/5.80 ( ( A3
% 5.45/5.80 = ( image_nat_nat @ F
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) ) )
% 5.45/5.80 => ( finite_finite_nat @ A3 ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_seg_image_imp_finite
% 5.45/5.80 thf(fact_7855_nat__seg__image__imp__finite,axiom,
% 5.45/5.80 ! [A3: set_int,F: nat > int,N2: nat] :
% 5.45/5.80 ( ( A3
% 5.45/5.80 = ( image_nat_int @ F
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) ) )
% 5.45/5.80 => ( finite_finite_int @ A3 ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_seg_image_imp_finite
% 5.45/5.80 thf(fact_7856_nat__seg__image__imp__finite,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,F: nat > code_integer,N2: nat] :
% 5.45/5.80 ( ( A3
% 5.45/5.80 = ( image_1215581382706833972nteger @ F
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) ) )
% 5.45/5.80 => ( finite6017078050557962740nteger @ A3 ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_seg_image_imp_finite
% 5.45/5.80 thf(fact_7857_nat__seg__image__imp__finite,axiom,
% 5.45/5.80 ! [A3: set_Pr1261947904930325089at_nat,F: nat > product_prod_nat_nat,N2: nat] :
% 5.45/5.80 ( ( A3
% 5.45/5.80 = ( image_5846123807819985514at_nat @ F
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) ) )
% 5.45/5.80 => ( finite6177210948735845034at_nat @ A3 ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_seg_image_imp_finite
% 5.45/5.80 thf(fact_7858_finite__conv__nat__seg__image,axiom,
% 5.45/5.80 ( finite1152437895449049373et_nat
% 5.45/5.80 = ( ^ [A6: set_set_nat] :
% 5.45/5.80 ? [N: nat,F3: nat > set_nat] :
% 5.45/5.80 ( A6
% 5.45/5.80 = ( image_nat_set_nat @ F3
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_conv_nat_seg_image
% 5.45/5.80 thf(fact_7859_finite__conv__nat__seg__image,axiom,
% 5.45/5.80 ( finite_finite_nat
% 5.45/5.80 = ( ^ [A6: set_nat] :
% 5.45/5.80 ? [N: nat,F3: nat > nat] :
% 5.45/5.80 ( A6
% 5.45/5.80 = ( image_nat_nat @ F3
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_conv_nat_seg_image
% 5.45/5.80 thf(fact_7860_finite__conv__nat__seg__image,axiom,
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 = ( ^ [A6: set_int] :
% 5.45/5.80 ? [N: nat,F3: nat > int] :
% 5.45/5.80 ( A6
% 5.45/5.80 = ( image_nat_int @ F3
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_conv_nat_seg_image
% 5.45/5.80 thf(fact_7861_finite__conv__nat__seg__image,axiom,
% 5.45/5.80 ( finite6017078050557962740nteger
% 5.45/5.80 = ( ^ [A6: set_Code_integer] :
% 5.45/5.80 ? [N: nat,F3: nat > code_integer] :
% 5.45/5.80 ( A6
% 5.45/5.80 = ( image_1215581382706833972nteger @ F3
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_conv_nat_seg_image
% 5.45/5.80 thf(fact_7862_finite__conv__nat__seg__image,axiom,
% 5.45/5.80 ( finite6177210948735845034at_nat
% 5.45/5.80 = ( ^ [A6: set_Pr1261947904930325089at_nat] :
% 5.45/5.80 ? [N: nat,F3: nat > product_prod_nat_nat] :
% 5.45/5.80 ( A6
% 5.45/5.80 = ( image_5846123807819985514at_nat @ F3
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_conv_nat_seg_image
% 5.45/5.80 thf(fact_7863_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_le3102999989581377725nteger @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7864_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_o] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_o )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: $o] :
% 5.45/5.80 ( ( member_o @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_o @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7865_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_set_int] :
% 5.45/5.80 ( ( finite6197958912794628473et_int @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_set_int )
% 5.45/5.80 => ? [X3: set_int] :
% 5.45/5.80 ( ( member_set_int @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: set_int] :
% 5.45/5.80 ( ( member_set_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7866_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_rat] :
% 5.45/5.80 ( ( finite_finite_rat @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_rat )
% 5.45/5.80 => ? [X3: rat] :
% 5.45/5.80 ( ( member_rat @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: rat] :
% 5.45/5.80 ( ( member_rat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_rat @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7867_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_num] :
% 5.45/5.80 ( ( finite_finite_num @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_num )
% 5.45/5.80 => ? [X3: num] :
% 5.45/5.80 ( ( member_num @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: num] :
% 5.45/5.80 ( ( member_num @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_num @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7868_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_nat @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7869_finite__has__minimal,axiom,
% 5.45/5.80 ! [A3: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_int )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_int @ Xa2 @ X3 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_minimal
% 5.45/5.80 thf(fact_7870_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bo3990330152332043303nteger )
% 5.45/5.80 => ? [X3: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: code_integer] :
% 5.45/5.80 ( ( member_Code_integer @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_le3102999989581377725nteger @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7871_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_o] :
% 5.45/5.80 ( ( finite_finite_o @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_o )
% 5.45/5.80 => ? [X3: $o] :
% 5.45/5.80 ( ( member_o @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: $o] :
% 5.45/5.80 ( ( member_o @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_o @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7872_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_set_int] :
% 5.45/5.80 ( ( finite6197958912794628473et_int @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_set_int )
% 5.45/5.80 => ? [X3: set_int] :
% 5.45/5.80 ( ( member_set_int @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: set_int] :
% 5.45/5.80 ( ( member_set_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7873_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_rat] :
% 5.45/5.80 ( ( finite_finite_rat @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_rat )
% 5.45/5.80 => ? [X3: rat] :
% 5.45/5.80 ( ( member_rat @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: rat] :
% 5.45/5.80 ( ( member_rat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_rat @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7874_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_num] :
% 5.45/5.80 ( ( finite_finite_num @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_num )
% 5.45/5.80 => ? [X3: num] :
% 5.45/5.80 ( ( member_num @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: num] :
% 5.45/5.80 ( ( member_num @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_num @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7875_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_nat )
% 5.45/5.80 => ? [X3: nat] :
% 5.45/5.80 ( ( member_nat @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: nat] :
% 5.45/5.80 ( ( member_nat @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_nat @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7876_finite__has__maximal,axiom,
% 5.45/5.80 ! [A3: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( A3 != bot_bot_set_int )
% 5.45/5.80 => ? [X3: int] :
% 5.45/5.80 ( ( member_int @ X3 @ A3 )
% 5.45/5.80 & ! [Xa2: int] :
% 5.45/5.80 ( ( member_int @ Xa2 @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_int @ X3 @ Xa2 )
% 5.45/5.80 => ( X3 = Xa2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_has_maximal
% 5.45/5.80 thf(fact_7877_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_nat,F: nat > nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_nat @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7878_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_Code_integer,F: nat > code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_1215581382706833972nteger @ F @ A3 ) )
% 5.45/5.80 => ( finite6017078050557962740nteger @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7879_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_nat,F: int > nat] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_nat @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7880_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_Code_integer,F: int > code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_1587234942943678608nteger @ F @ A3 ) )
% 5.45/5.80 => ( finite6017078050557962740nteger @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7881_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_nat,F: code_integer > nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_951025933927791156er_nat @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_nat @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7882_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_4470545334726330049nteger @ F @ A3 ) )
% 5.45/5.80 => ( finite6017078050557962740nteger @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7883_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_int,F: nat > int] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_int @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7884_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_int,B3: set_int,F: int > int] :
% 5.45/5.80 ( ( finite_finite_int @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_int @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7885_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_Code_integer,B3: set_int,F: code_integer > int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_948535463418740880er_int @ F @ A3 ) )
% 5.45/5.80 => ( finite_finite_int @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7886_finite__surj,axiom,
% 5.45/5.80 ! [A3: set_nat,B3: set_set_nat,F: nat > set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ A3 )
% 5.45/5.80 => ( ( ord_le6893508408891458716et_nat @ B3 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.80 => ( finite1152437895449049373et_nat @ B3 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_surj
% 5.45/5.80 thf(fact_7887_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_nat,F: nat > nat,A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_nat @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_nat_nat @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7888_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_nat,F: code_integer > nat,A3: set_Code_integer] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_951025933927791156er_nat @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_Code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger @ C5 @ A3 )
% 5.45/5.80 & ( finite6017078050557962740nteger @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_951025933927791156er_nat @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7889_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,F: nat > code_integer,A3: set_nat] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_1215581382706833972nteger @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_nat @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_1215581382706833972nteger @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7890_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,F: code_integer > code_integer,A3: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_4470545334726330049nteger @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_Code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger @ C5 @ A3 )
% 5.45/5.80 & ( finite6017078050557962740nteger @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_4470545334726330049nteger @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7891_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_nat,F: int > nat,A3: set_int] :
% 5.45/5.80 ( ( finite_finite_nat @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_nat @ B3 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_int @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_int_nat @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7892_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_Code_integer,F: int > code_integer,A3: set_int] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.80 => ( ( ord_le7084787975880047091nteger @ B3 @ ( image_1587234942943678608nteger @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_int @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_1587234942943678608nteger @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7893_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_int,F: nat > int,A3: set_nat] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_nat @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_nat_int @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7894_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_int,F: code_integer > int,A3: set_Code_integer] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_948535463418740880er_int @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_Code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger @ C5 @ A3 )
% 5.45/5.80 & ( finite6017078050557962740nteger @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_948535463418740880er_int @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7895_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_int,F: int > int,A3: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B3 )
% 5.45/5.80 => ( ( ord_less_eq_set_int @ B3 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_int] :
% 5.45/5.80 ( ( ord_less_eq_set_int @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_int @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_int_int @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7896_finite__subset__image,axiom,
% 5.45/5.80 ! [B3: set_set_nat,F: nat > set_nat,A3: set_nat] :
% 5.45/5.80 ( ( finite1152437895449049373et_nat @ B3 )
% 5.45/5.80 => ( ( ord_le6893508408891458716et_nat @ B3 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.80 => ? [C5: set_nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat @ C5 @ A3 )
% 5.45/5.80 & ( finite_finite_nat @ C5 )
% 5.45/5.80 & ( B3
% 5.45/5.80 = ( image_nat_set_nat @ F @ C5 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_subset_image
% 5.45/5.80 thf(fact_7897_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > nat,A3: set_nat,P: set_nat > $o] :
% 5.45/5.80 ( ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7898_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > nat,A3: set_Code_integer,P: set_nat > $o] :
% 5.45/5.80 ( ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7899_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > code_integer,A3: set_nat,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7900_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > code_integer,A3: set_Code_integer,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7901_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > nat,A3: set_int,P: set_nat > $o] :
% 5.45/5.80 ( ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7902_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > code_integer,A3: set_int,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1587234942943678608nteger @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_1587234942943678608nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7903_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > int,A3: set_nat,P: set_int > $o] :
% 5.45/5.80 ( ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7904_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > int,A3: set_Code_integer,P: set_int > $o] :
% 5.45/5.80 ( ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_948535463418740880er_int @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_Code_integer] :
% 5.45/5.80 ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_948535463418740880er_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7905_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > int,A3: set_int,P: set_int > $o] :
% 5.45/5.80 ( ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_int] :
% 5.45/5.80 ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7906_ex__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > set_nat,A3: set_nat,P: set_set_nat > $o] :
% 5.45/5.80 ( ( ? [B6: set_set_nat] :
% 5.45/5.80 ( ( finite1152437895449049373et_nat @ B6 )
% 5.45/5.80 & ( ord_le6893508408891458716et_nat @ B6 @ ( image_nat_set_nat @ F @ A3 ) )
% 5.45/5.80 & ( P @ B6 ) ) )
% 5.45/5.80 = ( ? [B6: set_nat] :
% 5.45/5.80 ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.45/5.80 & ( P @ ( image_nat_set_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % ex_finite_subset_image
% 5.45/5.80 thf(fact_7907_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > nat,A3: set_nat,P: set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_nat_nat @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_nat_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7908_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > nat,A3: set_Code_integer,P: set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_951025933927791156er_nat @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_951025933927791156er_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7909_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > code_integer,A3: set_nat,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1215581382706833972nteger @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_1215581382706833972nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7910_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > code_integer,A3: set_Code_integer,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_4470545334726330049nteger @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_4470545334726330049nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7911_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > nat,A3: set_int,P: set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ ( image_int_nat @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_int_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7912_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > code_integer,A3: set_int,P: set_Code_integer > $o] :
% 5.45/5.80 ( ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ ( image_1587234942943678608nteger @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_1587234942943678608nteger @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7913_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > int,A3: set_nat,P: set_int > $o] :
% 5.45/5.80 ( ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_nat_int @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_nat_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7914_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: code_integer > int,A3: set_Code_integer,P: set_int > $o] :
% 5.45/5.80 ( ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_948535463418740880er_int @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_Code_integer] :
% 5.45/5.80 ( ( ( finite6017078050557962740nteger @ B6 )
% 5.45/5.80 & ( ord_le7084787975880047091nteger @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_948535463418740880er_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7915_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: int > int,A3: set_int,P: set_int > $o] :
% 5.45/5.80 ( ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ ( image_int_int @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_int] :
% 5.45/5.80 ( ( ( finite_finite_int @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_int @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_int_int @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7916_all__finite__subset__image,axiom,
% 5.45/5.80 ! [F: nat > set_nat,A3: set_nat,P: set_set_nat > $o] :
% 5.45/5.80 ( ( ! [B6: set_set_nat] :
% 5.45/5.80 ( ( ( finite1152437895449049373et_nat @ B6 )
% 5.45/5.80 & ( ord_le6893508408891458716et_nat @ B6 @ ( image_nat_set_nat @ F @ A3 ) ) )
% 5.45/5.80 => ( P @ B6 ) ) )
% 5.45/5.80 = ( ! [B6: set_nat] :
% 5.45/5.80 ( ( ( finite_finite_nat @ B6 )
% 5.45/5.80 & ( ord_less_eq_set_nat @ B6 @ A3 ) )
% 5.45/5.80 => ( P @ ( image_nat_set_nat @ F @ B6 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % all_finite_subset_image
% 5.45/5.80 thf(fact_7917_not__exp__less__eq__0__int,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 5.45/5.80
% 5.45/5.80 % not_exp_less_eq_0_int
% 5.45/5.80 thf(fact_7918_set__bit__0,axiom,
% 5.45/5.80 ! [A: nat] :
% 5.45/5.80 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.45/5.80 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_0
% 5.45/5.80 thf(fact_7919_set__bit__0,axiom,
% 5.45/5.80 ! [A: code_integer] :
% 5.45/5.80 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_0
% 5.45/5.80 thf(fact_7920_set__bit__0,axiom,
% 5.45/5.80 ! [A: code_natural] :
% 5.45/5.80 ( ( bit_se1617098188084679374atural @ zero_zero_nat @ A )
% 5.45/5.80 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_0
% 5.45/5.80 thf(fact_7921_set__bit__0,axiom,
% 5.45/5.80 ! [A: int] :
% 5.45/5.80 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.45/5.80 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_0
% 5.45/5.80 thf(fact_7922_unset__bit__0,axiom,
% 5.45/5.80 ! [A: nat] :
% 5.45/5.80 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.45/5.80 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_0
% 5.45/5.80 thf(fact_7923_unset__bit__0,axiom,
% 5.45/5.80 ! [A: code_integer] :
% 5.45/5.80 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_0
% 5.45/5.80 thf(fact_7924_unset__bit__0,axiom,
% 5.45/5.80 ! [A: code_natural] :
% 5.45/5.80 ( ( bit_se7083795435491715335atural @ zero_zero_nat @ A )
% 5.45/5.80 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_0
% 5.45/5.80 thf(fact_7925_unset__bit__0,axiom,
% 5.45/5.80 ! [A: int] :
% 5.45/5.80 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.45/5.80 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_0
% 5.45/5.80 thf(fact_7926_set__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: nat] :
% 5.45/5.80 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_Suc
% 5.45/5.80 thf(fact_7927_set__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_integer] :
% 5.45/5.80 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_Suc
% 5.45/5.80 thf(fact_7928_set__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_natural] :
% 5.45/5.80 ( ( bit_se1617098188084679374atural @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se1617098188084679374atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_Suc
% 5.45/5.80 thf(fact_7929_set__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: int] :
% 5.45/5.80 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_Suc
% 5.45/5.80 thf(fact_7930_flip__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: nat] :
% 5.45/5.80 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_Suc
% 5.45/5.80 thf(fact_7931_flip__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_integer] :
% 5.45/5.80 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_Suc
% 5.45/5.80 thf(fact_7932_flip__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_natural] :
% 5.45/5.80 ( ( bit_se168947363167071951atural @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se168947363167071951atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_Suc
% 5.45/5.80 thf(fact_7933_flip__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: int] :
% 5.45/5.80 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_Suc
% 5.45/5.80 thf(fact_7934_unset__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: nat] :
% 5.45/5.80 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_Suc
% 5.45/5.80 thf(fact_7935_unset__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_integer] :
% 5.45/5.80 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_Suc
% 5.45/5.80 thf(fact_7936_unset__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_natural] :
% 5.45/5.80 ( ( bit_se7083795435491715335atural @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p4538020629002901425atural @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se7083795435491715335atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_Suc
% 5.45/5.80 thf(fact_7937_unset__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: int] :
% 5.45/5.80 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_Suc
% 5.45/5.80 thf(fact_7938_signed__take__bit__rec,axiom,
% 5.45/5.80 ( bit_ri6519982836138164636nteger
% 5.45/5.80 = ( ^ [N: nat,A5: code_integer] : ( if_Code_integer @ ( N = 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 @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_rec
% 5.45/5.80 thf(fact_7939_signed__take__bit__rec,axiom,
% 5.45/5.80 ( bit_ri631733984087533419it_int
% 5.45/5.80 = ( ^ [N: nat,A5: int] : ( if_int @ ( N = 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 @ N @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_rec
% 5.45/5.80 thf(fact_7940_unset__bit__nonnegative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 5.45/5.80 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_nonnegative_int_iff
% 5.45/5.80 thf(fact_7941_set__bit__nonnegative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 5.45/5.80 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_nonnegative_int_iff
% 5.45/5.80 thf(fact_7942_flip__bit__nonnegative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 5.45/5.80 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_nonnegative_int_iff
% 5.45/5.80 thf(fact_7943_unset__bit__negative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 5.45/5.80 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_negative_int_iff
% 5.45/5.80 thf(fact_7944_set__bit__negative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 5.45/5.80 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_negative_int_iff
% 5.45/5.80 thf(fact_7945_flip__bit__negative__int__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 5.45/5.80 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.45/5.80
% 5.45/5.80 % flip_bit_negative_int_iff
% 5.45/5.80 thf(fact_7946_unset__bit__less__eq,axiom,
% 5.45/5.80 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 5.45/5.80
% 5.45/5.80 % unset_bit_less_eq
% 5.45/5.80 thf(fact_7947_set__bit__greater__eq,axiom,
% 5.45/5.80 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % set_bit_greater_eq
% 5.45/5.80 thf(fact_7948_signed__take__bit__int__less__exp,axiom,
% 5.45/5.80 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_less_exp
% 5.45/5.80 thf(fact_7949_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.45/5.80 ! [K: int,N2: nat] :
% 5.45/5.80 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.45/5.80 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_greater_eq_self_iff
% 5.45/5.80 thf(fact_7950_signed__take__bit__int__less__self__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.45/5.80 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_less_self_iff
% 5.45/5.80 thf(fact_7951_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.45/5.80 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_greater_eq_minus_exp
% 5.45/5.80 thf(fact_7952_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.45/5.80 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_less_eq_self_iff
% 5.45/5.80 thf(fact_7953_signed__take__bit__int__greater__self__iff,axiom,
% 5.45/5.80 ! [K: int,N2: nat] :
% 5.45/5.80 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.45/5.80 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_greater_self_iff
% 5.45/5.80 thf(fact_7954_signed__take__bit__int__less__eq,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.45/5.80 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_less_eq
% 5.45/5.80 thf(fact_7955_signed__take__bit__int__eq__self,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.45/5.80 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.45/5.80 = K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_eq_self
% 5.45/5.80 thf(fact_7956_signed__take__bit__int__eq__self__iff,axiom,
% 5.45/5.80 ! [N2: nat,K: int] :
% 5.45/5.80 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.45/5.80 = K )
% 5.45/5.80 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.45/5.80 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_eq_self_iff
% 5.45/5.80 thf(fact_7957_signed__take__bit__int__greater__eq,axiom,
% 5.45/5.80 ! [K: int,N2: nat] :
% 5.45/5.80 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.80 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_int_greater_eq
% 5.45/5.80 thf(fact_7958_signed__take__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: code_integer] :
% 5.45/5.80 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_Suc
% 5.45/5.80 thf(fact_7959_signed__take__bit__Suc,axiom,
% 5.45/5.80 ! [N2: nat,A: int] :
% 5.45/5.80 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 5.45/5.80 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % signed_take_bit_Suc
% 5.45/5.80 thf(fact_7960_round__unique,axiom,
% 5.45/5.80 ! [X: rat,Y: int] :
% 5.45/5.80 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.45/5.80 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.45/5.80 => ( ( archim7778729529865785530nd_rat @ X )
% 5.45/5.80 = Y ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % round_unique
% 5.45/5.80 thf(fact_7961_finite__int__iff__bounded__le,axiom,
% 5.45/5.80 ( finite_finite_int
% 5.45/5.80 = ( ^ [S5: set_int] :
% 5.45/5.80 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_int_iff_bounded_le
% 5.45/5.80 thf(fact_7962_choose__odd__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [I4: nat] :
% 5.45/5.80 ( if_rat
% 5.45/5.80 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.45/5.80 @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I4 ) )
% 5.45/5.80 @ zero_zero_rat )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_odd_sum
% 5.45/5.80 thf(fact_7963_choose__odd__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups3539618377306564664at_int
% 5.45/5.80 @ ^ [I4: nat] :
% 5.45/5.80 ( if_int
% 5.45/5.80 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.45/5.80 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I4 ) )
% 5.45/5.80 @ zero_zero_int )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_odd_sum
% 5.45/5.80 thf(fact_7964_choose__odd__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups7501900531339628137nteger
% 5.45/5.80 @ ^ [I4: nat] :
% 5.45/5.80 ( if_Code_integer
% 5.45/5.80 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 )
% 5.45/5.80 @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I4 ) )
% 5.45/5.80 @ zero_z3403309356797280102nteger )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_odd_sum
% 5.45/5.80 thf(fact_7965_choose__even__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups2906978787729119204at_rat
% 5.45/5.80 @ ^ [I4: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I4 ) ) @ zero_zero_rat )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_even_sum
% 5.45/5.80 thf(fact_7966_choose__even__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups3539618377306564664at_int
% 5.45/5.80 @ ^ [I4: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I4 ) ) @ zero_zero_int )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_even_sum
% 5.45/5.80 thf(fact_7967_choose__even__sum,axiom,
% 5.45/5.80 ! [N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) )
% 5.45/5.80 @ ( groups7501900531339628137nteger
% 5.45/5.80 @ ^ [I4: nat] : ( if_Code_integer @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I4 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I4 ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.80 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.45/5.80 = ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % choose_even_sum
% 5.45/5.80 thf(fact_7968_round__altdef,axiom,
% 5.45/5.80 ( archim7778729529865785530nd_rat
% 5.45/5.80 = ( ^ [X4: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X4 ) ) @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim3151403230148437115or_rat @ X4 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % round_altdef
% 5.45/5.80 thf(fact_7969_finite__nat__iff__bounded__le,axiom,
% 5.45/5.80 ( finite_finite_nat
% 5.45/5.80 = ( ^ [S5: set_nat] :
% 5.45/5.80 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % finite_nat_iff_bounded_le
% 5.45/5.80 thf(fact_7970_nat__dvd__1__iff__1,axiom,
% 5.45/5.80 ! [M: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.45/5.80 = ( M = one_one_nat ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_dvd_1_iff_1
% 5.45/5.80 thf(fact_7971_dvd__mult__cancel__left,axiom,
% 5.45/5.80 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.80 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.80 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_left
% 5.45/5.80 thf(fact_7972_dvd__mult__cancel__left,axiom,
% 5.45/5.80 ! [C: rat,A: rat,B: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.45/5.80 = ( ( C = zero_zero_rat )
% 5.45/5.80 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_left
% 5.45/5.80 thf(fact_7973_dvd__mult__cancel__left,axiom,
% 5.45/5.80 ! [C: int,A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.45/5.80 = ( ( C = zero_zero_int )
% 5.45/5.80 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_left
% 5.45/5.80 thf(fact_7974_dvd__mult__cancel__right,axiom,
% 5.45/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.80 = ( ( C = zero_z3403309356797280102nteger )
% 5.45/5.80 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_right
% 5.45/5.80 thf(fact_7975_dvd__mult__cancel__right,axiom,
% 5.45/5.80 ! [A: rat,C: rat,B: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.45/5.80 = ( ( C = zero_zero_rat )
% 5.45/5.80 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_right
% 5.45/5.80 thf(fact_7976_dvd__mult__cancel__right,axiom,
% 5.45/5.80 ! [A: int,C: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.45/5.80 = ( ( C = zero_zero_int )
% 5.45/5.80 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_cancel_right
% 5.45/5.80 thf(fact_7977_dvd__times__left__cancel__iff,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_left_cancel_iff
% 5.45/5.80 thf(fact_7978_dvd__times__left__cancel__iff,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( A != zero_zero_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.45/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_left_cancel_iff
% 5.45/5.80 thf(fact_7979_dvd__times__left__cancel__iff,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( A != zero_zero_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.45/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_left_cancel_iff
% 5.45/5.80 thf(fact_7980_dvd__times__right__cancel__iff,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_right_cancel_iff
% 5.45/5.80 thf(fact_7981_dvd__times__right__cancel__iff,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( A != zero_zero_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.45/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_right_cancel_iff
% 5.45/5.80 thf(fact_7982_dvd__times__right__cancel__iff,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( A != zero_zero_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.45/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_times_right_cancel_iff
% 5.45/5.80 thf(fact_7983_dvd__add__times__triv__right__iff,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_right_iff
% 5.45/5.80 thf(fact_7984_dvd__add__times__triv__right__iff,axiom,
% 5.45/5.80 ! [A: rat,B: rat,C: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.45/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_right_iff
% 5.45/5.80 thf(fact_7985_dvd__add__times__triv__right__iff,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_right_iff
% 5.45/5.80 thf(fact_7986_dvd__add__times__triv__right__iff,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_right_iff
% 5.45/5.80 thf(fact_7987_dvd__add__times__triv__left__iff,axiom,
% 5.45/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_left_iff
% 5.45/5.80 thf(fact_7988_dvd__add__times__triv__left__iff,axiom,
% 5.45/5.80 ! [A: rat,C: rat,B: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.45/5.80 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_left_iff
% 5.45/5.80 thf(fact_7989_dvd__add__times__triv__left__iff,axiom,
% 5.45/5.80 ! [A: nat,C: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_left_iff
% 5.45/5.80 thf(fact_7990_dvd__add__times__triv__left__iff,axiom,
% 5.45/5.80 ! [A: int,C: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_add_times_triv_left_iff
% 5.45/5.80 thf(fact_7991_unit__prod,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_prod
% 5.45/5.80 thf(fact_7992_unit__prod,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.80 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_prod
% 5.45/5.80 thf(fact_7993_unit__prod,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.80 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_prod
% 5.45/5.80 thf(fact_7994_dvd__mult__div__cancel,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_div_cancel
% 5.45/5.80 thf(fact_7995_dvd__mult__div__cancel,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.45/5.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_div_cancel
% 5.45/5.80 thf(fact_7996_dvd__mult__div__cancel,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_div_cancel
% 5.45/5.80 thf(fact_7997_dvd__mult__div__cancel,axiom,
% 5.45/5.80 ! [A: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ A @ B )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ A ) )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_div_cancel
% 5.45/5.80 thf(fact_7998_dvd__div__mult__self,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult_self
% 5.45/5.80 thf(fact_7999_dvd__div__mult__self,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.45/5.80 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult_self
% 5.45/5.80 thf(fact_8000_dvd__div__mult__self,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult_self
% 5.45/5.80 thf(fact_8001_dvd__div__mult__self,axiom,
% 5.45/5.80 ! [A: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ A @ B )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult_self
% 5.45/5.80 thf(fact_8002_dvd__1__iff__1,axiom,
% 5.45/5.80 ! [M: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.45/5.80 = ( M
% 5.45/5.80 = ( suc @ zero_zero_nat ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_1_iff_1
% 5.45/5.80 thf(fact_8003_dvd__1__left,axiom,
% 5.45/5.80 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_1_left
% 5.45/5.80 thf(fact_8004_unit__div__mult__self,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_div_mult_self
% 5.45/5.80 thf(fact_8005_unit__div__mult__self,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_div_mult_self
% 5.45/5.80 thf(fact_8006_unit__div__mult__self,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_div_mult_self
% 5.45/5.80 thf(fact_8007_unit__div__mult__self,axiom,
% 5.45/5.80 ! [A: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ A ) @ A )
% 5.45/5.80 = B ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_div_mult_self
% 5.45/5.80 thf(fact_8008_unit__mult__div__div,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.45/5.80 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_div_div
% 5.45/5.80 thf(fact_8009_unit__mult__div__div,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.45/5.80 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_div_div
% 5.45/5.80 thf(fact_8010_unit__mult__div__div,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_div_div
% 5.45/5.80 thf(fact_8011_unit__mult__div__div,axiom,
% 5.45/5.80 ! [A: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ B @ ( divide5121882707175180666atural @ one_one_Code_natural @ A ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_div_div
% 5.45/5.80 thf(fact_8012_pow__divides__pow__iff,axiom,
% 5.45/5.80 ! [N2: nat,A: nat,B: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pow_divides_pow_iff
% 5.45/5.80 thf(fact_8013_pow__divides__pow__iff,axiom,
% 5.45/5.80 ! [N2: nat,A: int,B: int] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pow_divides_pow_iff
% 5.45/5.80 thf(fact_8014_even__mult__iff,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_mult_iff
% 5.45/5.80 thf(fact_8015_even__mult__iff,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.45/5.80 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_mult_iff
% 5.45/5.80 thf(fact_8016_even__mult__iff,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.80 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_mult_iff
% 5.45/5.80 thf(fact_8017_even__mult__iff,axiom,
% 5.45/5.80 ! [A: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( times_2397367101498566445atural @ A @ B ) )
% 5.45/5.80 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 | ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_mult_iff
% 5.45/5.80 thf(fact_8018_even__power,axiom,
% 5.45/5.80 ! [A: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_power
% 5.45/5.80 thf(fact_8019_even__power,axiom,
% 5.45/5.80 ! [A: int,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 5.45/5.80 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_power
% 5.45/5.80 thf(fact_8020_even__power,axiom,
% 5.45/5.80 ! [A: code_integer,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.80 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_power
% 5.45/5.80 thf(fact_8021_even__power,axiom,
% 5.45/5.80 ! [A: code_natural,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( power_7079662738309270450atural @ A @ N2 ) )
% 5.45/5.80 = ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_power
% 5.45/5.80 thf(fact_8022_zero__le__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: code_integer,W2: num] :
% 5.45/5.80 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_le_power_eq_numeral
% 5.45/5.80 thf(fact_8023_zero__le__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: rat,W2: num] :
% 5.45/5.80 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_le_power_eq_numeral
% 5.45/5.80 thf(fact_8024_zero__le__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: int,W2: num] :
% 5.45/5.80 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_le_power_eq_numeral
% 5.45/5.80 thf(fact_8025_power__less__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: code_integer,W2: num] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq_numeral
% 5.45/5.80 thf(fact_8026_power__less__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: rat,W2: num] :
% 5.45/5.80 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq_numeral
% 5.45/5.80 thf(fact_8027_power__less__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: int,W2: num] :
% 5.45/5.80 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq_numeral
% 5.45/5.80 thf(fact_8028_power__less__zero__eq,axiom,
% 5.45/5.80 ! [A: code_integer,N2: nat] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ zero_z3403309356797280102nteger )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.80 & ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq
% 5.45/5.80 thf(fact_8029_power__less__zero__eq,axiom,
% 5.45/5.80 ! [A: rat,N2: nat] :
% 5.45/5.80 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.80 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq
% 5.45/5.80 thf(fact_8030_power__less__zero__eq,axiom,
% 5.45/5.80 ! [A: int,N2: nat] :
% 5.45/5.80 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.80 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_less_zero_eq
% 5.45/5.80 thf(fact_8031_even__diff__nat,axiom,
% 5.45/5.80 ! [M: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.80 = ( ( ord_less_nat @ M @ N2 )
% 5.45/5.80 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_diff_nat
% 5.45/5.80 thf(fact_8032_odd__two__times__div__two__succ,axiom,
% 5.45/5.80 ! [A: nat] :
% 5.45/5.80 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.45/5.80 = A ) ) ).
% 5.45/5.80
% 5.45/5.80 % odd_two_times_div_two_succ
% 5.45/5.80 thf(fact_8033_odd__two__times__div__two__succ,axiom,
% 5.45/5.80 ! [A: int] :
% 5.45/5.80 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.45/5.80 = A ) ) ).
% 5.45/5.80
% 5.45/5.80 % odd_two_times_div_two_succ
% 5.45/5.80 thf(fact_8034_odd__two__times__div__two__succ,axiom,
% 5.45/5.80 ! [A: code_integer] :
% 5.45/5.80 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.45/5.80 = A ) ) ).
% 5.45/5.80
% 5.45/5.80 % odd_two_times_div_two_succ
% 5.45/5.80 thf(fact_8035_odd__two__times__div__two__succ,axiom,
% 5.45/5.80 ! [A: code_natural] :
% 5.45/5.80 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ one_one_Code_natural )
% 5.45/5.80 = A ) ) ).
% 5.45/5.80
% 5.45/5.80 % odd_two_times_div_two_succ
% 5.45/5.80 thf(fact_8036_zero__less__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: code_integer,W2: num] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( ( numeral_numeral_nat @ W2 )
% 5.45/5.80 = zero_zero_nat )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A != zero_z3403309356797280102nteger ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_less_power_eq_numeral
% 5.45/5.80 thf(fact_8037_zero__less__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: rat,W2: num] :
% 5.45/5.80 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( ( numeral_numeral_nat @ W2 )
% 5.45/5.80 = zero_zero_nat )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A != zero_zero_rat ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_less_power_eq_numeral
% 5.45/5.80 thf(fact_8038_zero__less__power__eq__numeral,axiom,
% 5.45/5.80 ! [A: int,W2: num] :
% 5.45/5.80 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) )
% 5.45/5.80 = ( ( ( numeral_numeral_nat @ W2 )
% 5.45/5.80 = zero_zero_nat )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A != zero_zero_int ) )
% 5.45/5.80 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % zero_less_power_eq_numeral
% 5.45/5.80 thf(fact_8039_power__le__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: code_integer,W2: num] :
% 5.45/5.80 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_z3403309356797280102nteger )
% 5.45/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_le_zero_eq_numeral
% 5.45/5.80 thf(fact_8040_power__le__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: rat,W2: num] :
% 5.45/5.80 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_rat )
% 5.45/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_le_zero_eq_numeral
% 5.45/5.80 thf(fact_8041_power__le__zero__eq__numeral,axiom,
% 5.45/5.80 ! [A: int,W2: num] :
% 5.45/5.80 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W2 ) ) @ zero_zero_int )
% 5.45/5.80 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.45/5.80 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W2 ) )
% 5.45/5.80 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % power_le_zero_eq_numeral
% 5.45/5.80 thf(fact_8042_even__succ__div__exp,axiom,
% 5.45/5.80 ! [A: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_div_exp
% 5.45/5.80 thf(fact_8043_even__succ__div__exp,axiom,
% 5.45/5.80 ! [A: int,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_div_exp
% 5.45/5.80 thf(fact_8044_even__succ__div__exp,axiom,
% 5.45/5.80 ! [A: code_integer,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_div_exp
% 5.45/5.80 thf(fact_8045_even__succ__div__exp,axiom,
% 5.45/5.80 ! [A: code_natural,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_div_exp
% 5.45/5.80 thf(fact_8046_even__succ__mod__exp,axiom,
% 5.45/5.80 ! [A: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_mod_exp
% 5.45/5.80 thf(fact_8047_even__succ__mod__exp,axiom,
% 5.45/5.80 ! [A: int,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_mod_exp
% 5.45/5.80 thf(fact_8048_even__succ__mod__exp,axiom,
% 5.45/5.80 ! [A: code_integer,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_mod_exp
% 5.45/5.80 thf(fact_8049_even__succ__mod__exp,axiom,
% 5.45/5.80 ! [A: code_natural,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.80 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( modulo8411746178871703098atural @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ A ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.80 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( modulo8411746178871703098atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % even_succ_mod_exp
% 5.45/5.80 thf(fact_8050_dvd__antisym,axiom,
% 5.45/5.80 ! [M: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ M @ N2 )
% 5.45/5.80 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.45/5.80 => ( M = N2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_antisym
% 5.45/5.80 thf(fact_8051_division__decomp,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.80 => ? [B9: nat,C6: nat] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_nat @ B9 @ C6 ) )
% 5.45/5.80 & ( dvd_dvd_nat @ B9 @ B )
% 5.45/5.80 & ( dvd_dvd_nat @ C6 @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % division_decomp
% 5.45/5.80 thf(fact_8052_division__decomp,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.80 => ? [B9: int,C6: int] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_int @ B9 @ C6 ) )
% 5.45/5.80 & ( dvd_dvd_int @ B9 @ B )
% 5.45/5.80 & ( dvd_dvd_int @ C6 @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % division_decomp
% 5.45/5.80 thf(fact_8053_dvd__productE,axiom,
% 5.45/5.80 ! [P3: nat,A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ P3 @ ( times_times_nat @ A @ B ) )
% 5.45/5.80 => ~ ! [X3: nat,Y3: nat] :
% 5.45/5.80 ( ( P3
% 5.45/5.80 = ( times_times_nat @ X3 @ Y3 ) )
% 5.45/5.80 => ( ( dvd_dvd_nat @ X3 @ A )
% 5.45/5.80 => ~ ( dvd_dvd_nat @ Y3 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_productE
% 5.45/5.80 thf(fact_8054_dvd__productE,axiom,
% 5.45/5.80 ! [P3: int,A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ P3 @ ( times_times_int @ A @ B ) )
% 5.45/5.80 => ~ ! [X3: int,Y3: int] :
% 5.45/5.80 ( ( P3
% 5.45/5.80 = ( times_times_int @ X3 @ Y3 ) )
% 5.45/5.80 => ( ( dvd_dvd_int @ X3 @ A )
% 5.45/5.80 => ~ ( dvd_dvd_int @ Y3 @ B ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_productE
% 5.45/5.80 thf(fact_8055_dvdE,axiom,
% 5.45/5.80 ! [B: code_integer,A: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.45/5.80 => ~ ! [K2: code_integer] :
% 5.45/5.80 ( A
% 5.45/5.80 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdE
% 5.45/5.80 thf(fact_8056_dvdE,axiom,
% 5.45/5.80 ! [B: assn,A: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ B @ A )
% 5.45/5.80 => ~ ! [K2: assn] :
% 5.45/5.80 ( A
% 5.45/5.80 != ( times_times_assn @ B @ K2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdE
% 5.45/5.80 thf(fact_8057_dvdE,axiom,
% 5.45/5.80 ! [B: rat,A: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ B @ A )
% 5.45/5.80 => ~ ! [K2: rat] :
% 5.45/5.80 ( A
% 5.45/5.80 != ( times_times_rat @ B @ K2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdE
% 5.45/5.80 thf(fact_8058_dvdE,axiom,
% 5.45/5.80 ! [B: nat,A: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ B @ A )
% 5.45/5.80 => ~ ! [K2: nat] :
% 5.45/5.80 ( A
% 5.45/5.80 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdE
% 5.45/5.80 thf(fact_8059_dvdE,axiom,
% 5.45/5.80 ! [B: int,A: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ B @ A )
% 5.45/5.80 => ~ ! [K2: int] :
% 5.45/5.80 ( A
% 5.45/5.80 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdE
% 5.45/5.80 thf(fact_8060_dvdI,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdI
% 5.45/5.80 thf(fact_8061_dvdI,axiom,
% 5.45/5.80 ! [A: assn,B: assn,K: assn] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_assn @ B @ K ) )
% 5.45/5.80 => ( dvd_dvd_assn @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdI
% 5.45/5.80 thf(fact_8062_dvdI,axiom,
% 5.45/5.80 ! [A: rat,B: rat,K: rat] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_rat @ B @ K ) )
% 5.45/5.80 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdI
% 5.45/5.80 thf(fact_8063_dvdI,axiom,
% 5.45/5.80 ! [A: nat,B: nat,K: nat] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_nat @ B @ K ) )
% 5.45/5.80 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdI
% 5.45/5.80 thf(fact_8064_dvdI,axiom,
% 5.45/5.80 ! [A: int,B: int,K: int] :
% 5.45/5.80 ( ( A
% 5.45/5.80 = ( times_times_int @ B @ K ) )
% 5.45/5.80 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvdI
% 5.45/5.80 thf(fact_8065_dvd__def,axiom,
% 5.45/5.80 ( dvd_dvd_Code_integer
% 5.45/5.80 = ( ^ [B5: code_integer,A5: code_integer] :
% 5.45/5.80 ? [K3: code_integer] :
% 5.45/5.80 ( A5
% 5.45/5.80 = ( times_3573771949741848930nteger @ B5 @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_def
% 5.45/5.80 thf(fact_8066_dvd__def,axiom,
% 5.45/5.80 ( dvd_dvd_assn
% 5.45/5.80 = ( ^ [B5: assn,A5: assn] :
% 5.45/5.80 ? [K3: assn] :
% 5.45/5.80 ( A5
% 5.45/5.80 = ( times_times_assn @ B5 @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_def
% 5.45/5.80 thf(fact_8067_dvd__def,axiom,
% 5.45/5.80 ( dvd_dvd_rat
% 5.45/5.80 = ( ^ [B5: rat,A5: rat] :
% 5.45/5.80 ? [K3: rat] :
% 5.45/5.80 ( A5
% 5.45/5.80 = ( times_times_rat @ B5 @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_def
% 5.45/5.80 thf(fact_8068_dvd__def,axiom,
% 5.45/5.80 ( dvd_dvd_nat
% 5.45/5.80 = ( ^ [B5: nat,A5: nat] :
% 5.45/5.80 ? [K3: nat] :
% 5.45/5.80 ( A5
% 5.45/5.80 = ( times_times_nat @ B5 @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_def
% 5.45/5.80 thf(fact_8069_dvd__def,axiom,
% 5.45/5.80 ( dvd_dvd_int
% 5.45/5.80 = ( ^ [B5: int,A5: int] :
% 5.45/5.80 ? [K3: int] :
% 5.45/5.80 ( A5
% 5.45/5.80 = ( times_times_int @ B5 @ K3 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_def
% 5.45/5.80 thf(fact_8070_dvd__mult,axiom,
% 5.45/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult
% 5.45/5.80 thf(fact_8071_dvd__mult,axiom,
% 5.45/5.80 ! [A: assn,C: assn,B: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ A @ C )
% 5.45/5.80 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult
% 5.45/5.80 thf(fact_8072_dvd__mult,axiom,
% 5.45/5.80 ! [A: rat,C: rat,B: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ A @ C )
% 5.45/5.80 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult
% 5.45/5.80 thf(fact_8073_dvd__mult,axiom,
% 5.45/5.80 ! [A: nat,C: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ C )
% 5.45/5.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult
% 5.45/5.80 thf(fact_8074_dvd__mult,axiom,
% 5.45/5.80 ! [A: int,C: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ C )
% 5.45/5.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult
% 5.45/5.80 thf(fact_8075_dvd__mult2,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult2
% 5.45/5.80 thf(fact_8076_dvd__mult2,axiom,
% 5.45/5.80 ! [A: assn,B: assn,C: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ A @ B )
% 5.45/5.80 => ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult2
% 5.45/5.80 thf(fact_8077_dvd__mult2,axiom,
% 5.45/5.80 ! [A: rat,B: rat,C: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.45/5.80 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult2
% 5.45/5.80 thf(fact_8078_dvd__mult2,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.80 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult2
% 5.45/5.80 thf(fact_8079_dvd__mult2,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.45/5.80 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult2
% 5.45/5.80 thf(fact_8080_dvd__mult__left,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_left
% 5.45/5.80 thf(fact_8081_dvd__mult__left,axiom,
% 5.45/5.80 ! [A: assn,B: assn,C: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_assn @ A @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_left
% 5.45/5.80 thf(fact_8082_dvd__mult__left,axiom,
% 5.45/5.80 ! [A: rat,B: rat,C: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_left
% 5.45/5.80 thf(fact_8083_dvd__mult__left,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_left
% 5.45/5.80 thf(fact_8084_dvd__mult__left,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_left
% 5.45/5.80 thf(fact_8085_dvd__triv__left,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_left
% 5.45/5.80 thf(fact_8086_dvd__triv__left,axiom,
% 5.45/5.80 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_left
% 5.45/5.80 thf(fact_8087_dvd__triv__left,axiom,
% 5.45/5.80 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_left
% 5.45/5.80 thf(fact_8088_dvd__triv__left,axiom,
% 5.45/5.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_left
% 5.45/5.80 thf(fact_8089_dvd__triv__left,axiom,
% 5.45/5.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_left
% 5.45/5.80 thf(fact_8090_mult__dvd__mono,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer,D2: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_dvd_mono
% 5.45/5.80 thf(fact_8091_mult__dvd__mono,axiom,
% 5.45/5.80 ! [A: assn,B: assn,C: assn,D2: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ A @ B )
% 5.45/5.80 => ( ( dvd_dvd_assn @ C @ D2 )
% 5.45/5.80 => ( dvd_dvd_assn @ ( times_times_assn @ A @ C ) @ ( times_times_assn @ B @ D2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_dvd_mono
% 5.45/5.80 thf(fact_8092_mult__dvd__mono,axiom,
% 5.45/5.80 ! [A: rat,B: rat,C: rat,D2: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ A @ B )
% 5.45/5.80 => ( ( dvd_dvd_rat @ C @ D2 )
% 5.45/5.80 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_dvd_mono
% 5.45/5.80 thf(fact_8093_mult__dvd__mono,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat,D2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.80 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.45/5.80 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_dvd_mono
% 5.45/5.80 thf(fact_8094_mult__dvd__mono,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int,D2: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ B )
% 5.45/5.80 => ( ( dvd_dvd_int @ C @ D2 )
% 5.45/5.80 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_dvd_mono
% 5.45/5.80 thf(fact_8095_dvd__mult__right,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_right
% 5.45/5.80 thf(fact_8096_dvd__mult__right,axiom,
% 5.45/5.80 ! [A: assn,B: assn,C: assn] :
% 5.45/5.80 ( ( dvd_dvd_assn @ ( times_times_assn @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_assn @ B @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_right
% 5.45/5.80 thf(fact_8097_dvd__mult__right,axiom,
% 5.45/5.80 ! [A: rat,B: rat,C: rat] :
% 5.45/5.80 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_right
% 5.45/5.80 thf(fact_8098_dvd__mult__right,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_right
% 5.45/5.80 thf(fact_8099_dvd__mult__right,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.80 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_right
% 5.45/5.80 thf(fact_8100_dvd__triv__right,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_right
% 5.45/5.80 thf(fact_8101_dvd__triv__right,axiom,
% 5.45/5.80 ! [A: assn,B: assn] : ( dvd_dvd_assn @ A @ ( times_times_assn @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_right
% 5.45/5.80 thf(fact_8102_dvd__triv__right,axiom,
% 5.45/5.80 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_right
% 5.45/5.80 thf(fact_8103_dvd__triv__right,axiom,
% 5.45/5.80 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_right
% 5.45/5.80 thf(fact_8104_dvd__triv__right,axiom,
% 5.45/5.80 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_triv_right
% 5.45/5.80 thf(fact_8105_dvd__diff__nat,axiom,
% 5.45/5.80 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ K @ M )
% 5.45/5.80 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.45/5.80 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_diff_nat
% 5.45/5.80 thf(fact_8106_subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( ord_less_eq_set_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % subset_divisors_dvd
% 5.45/5.80 thf(fact_8107_subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( ord_le7084787975880047091nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % subset_divisors_dvd
% 5.45/5.80 thf(fact_8108_subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( ord_less_eq_set_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.45/5.80
% 5.45/5.80 % subset_divisors_dvd
% 5.45/5.80 thf(fact_8109_strict__subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( ord_less_set_nat
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ A ) )
% 5.45/5.80 @ ( collect_nat
% 5.45/5.80 @ ^ [C4: nat] : ( dvd_dvd_nat @ C4 @ B ) ) )
% 5.45/5.80 = ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.80 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % strict_subset_divisors_dvd
% 5.45/5.80 thf(fact_8110_strict__subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( ord_less_set_int
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ A ) )
% 5.45/5.80 @ ( collect_int
% 5.45/5.80 @ ^ [C4: int] : ( dvd_dvd_int @ C4 @ B ) ) )
% 5.45/5.80 = ( ( dvd_dvd_int @ A @ B )
% 5.45/5.80 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % strict_subset_divisors_dvd
% 5.45/5.80 thf(fact_8111_strict__subset__divisors__dvd,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( ord_le1307284697595431911nteger
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ A ) )
% 5.45/5.80 @ ( collect_Code_integer
% 5.45/5.80 @ ^ [C4: code_integer] : ( dvd_dvd_Code_integer @ C4 @ B ) ) )
% 5.45/5.80 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.80 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % strict_subset_divisors_dvd
% 5.45/5.80 thf(fact_8112_pinf_I9_J,axiom,
% 5.45/5.80 ! [D2: code_integer,S2: code_integer] :
% 5.45/5.80 ? [Z2: code_integer] :
% 5.45/5.80 ! [X7: code_integer] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ Z2 @ X7 )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(9)
% 5.45/5.80 thf(fact_8113_pinf_I9_J,axiom,
% 5.45/5.80 ! [D2: rat,S2: rat] :
% 5.45/5.80 ? [Z2: rat] :
% 5.45/5.80 ! [X7: rat] :
% 5.45/5.80 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.80 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(9)
% 5.45/5.80 thf(fact_8114_pinf_I9_J,axiom,
% 5.45/5.80 ! [D2: nat,S2: nat] :
% 5.45/5.80 ? [Z2: nat] :
% 5.45/5.80 ! [X7: nat] :
% 5.45/5.80 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.80 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(9)
% 5.45/5.80 thf(fact_8115_pinf_I9_J,axiom,
% 5.45/5.80 ! [D2: int,S2: int] :
% 5.45/5.80 ? [Z2: int] :
% 5.45/5.80 ! [X7: int] :
% 5.45/5.80 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.80 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(9)
% 5.45/5.80 thf(fact_8116_pinf_I10_J,axiom,
% 5.45/5.80 ! [D2: code_integer,S2: code_integer] :
% 5.45/5.80 ? [Z2: code_integer] :
% 5.45/5.80 ! [X7: code_integer] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ Z2 @ X7 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(10)
% 5.45/5.80 thf(fact_8117_pinf_I10_J,axiom,
% 5.45/5.80 ! [D2: rat,S2: rat] :
% 5.45/5.80 ? [Z2: rat] :
% 5.45/5.80 ! [X7: rat] :
% 5.45/5.80 ( ( ord_less_rat @ Z2 @ X7 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(10)
% 5.45/5.80 thf(fact_8118_pinf_I10_J,axiom,
% 5.45/5.80 ! [D2: nat,S2: nat] :
% 5.45/5.80 ? [Z2: nat] :
% 5.45/5.80 ! [X7: nat] :
% 5.45/5.80 ( ( ord_less_nat @ Z2 @ X7 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(10)
% 5.45/5.80 thf(fact_8119_pinf_I10_J,axiom,
% 5.45/5.80 ! [D2: int,S2: int] :
% 5.45/5.80 ? [Z2: int] :
% 5.45/5.80 ! [X7: int] :
% 5.45/5.80 ( ( ord_less_int @ Z2 @ X7 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % pinf(10)
% 5.45/5.80 thf(fact_8120_minf_I9_J,axiom,
% 5.45/5.80 ! [D2: code_integer,S2: code_integer] :
% 5.45/5.80 ? [Z2: code_integer] :
% 5.45/5.80 ! [X7: code_integer] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ X7 @ Z2 )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(9)
% 5.45/5.80 thf(fact_8121_minf_I9_J,axiom,
% 5.45/5.80 ! [D2: rat,S2: rat] :
% 5.45/5.80 ? [Z2: rat] :
% 5.45/5.80 ! [X7: rat] :
% 5.45/5.80 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.80 => ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(9)
% 5.45/5.80 thf(fact_8122_minf_I9_J,axiom,
% 5.45/5.80 ! [D2: nat,S2: nat] :
% 5.45/5.80 ? [Z2: nat] :
% 5.45/5.80 ! [X7: nat] :
% 5.45/5.80 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.80 => ( ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(9)
% 5.45/5.80 thf(fact_8123_minf_I9_J,axiom,
% 5.45/5.80 ! [D2: int,S2: int] :
% 5.45/5.80 ? [Z2: int] :
% 5.45/5.80 ! [X7: int] :
% 5.45/5.80 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.80 => ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) )
% 5.45/5.80 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(9)
% 5.45/5.80 thf(fact_8124_minf_I10_J,axiom,
% 5.45/5.80 ! [D2: code_integer,S2: code_integer] :
% 5.45/5.80 ? [Z2: code_integer] :
% 5.45/5.80 ! [X7: code_integer] :
% 5.45/5.80 ( ( ord_le6747313008572928689nteger @ X7 @ Z2 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(10)
% 5.45/5.80 thf(fact_8125_minf_I10_J,axiom,
% 5.45/5.80 ! [D2: rat,S2: rat] :
% 5.45/5.80 ? [Z2: rat] :
% 5.45/5.80 ! [X7: rat] :
% 5.45/5.80 ( ( ord_less_rat @ X7 @ Z2 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(10)
% 5.45/5.80 thf(fact_8126_minf_I10_J,axiom,
% 5.45/5.80 ! [D2: nat,S2: nat] :
% 5.45/5.80 ? [Z2: nat] :
% 5.45/5.80 ! [X7: nat] :
% 5.45/5.80 ( ( ord_less_nat @ X7 @ Z2 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_nat @ D2 @ ( plus_plus_nat @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(10)
% 5.45/5.80 thf(fact_8127_minf_I10_J,axiom,
% 5.45/5.80 ! [D2: int,S2: int] :
% 5.45/5.80 ? [Z2: int] :
% 5.45/5.80 ! [X7: int] :
% 5.45/5.80 ( ( ord_less_int @ X7 @ Z2 )
% 5.45/5.80 => ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) )
% 5.45/5.80 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ S2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % minf(10)
% 5.45/5.80 thf(fact_8128_unit__mult__right__cancel,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.45/5.80 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_right_cancel
% 5.45/5.80 thf(fact_8129_unit__mult__right__cancel,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( ( times_times_nat @ B @ A )
% 5.45/5.80 = ( times_times_nat @ C @ A ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_right_cancel
% 5.45/5.80 thf(fact_8130_unit__mult__right__cancel,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( ( times_times_int @ B @ A )
% 5.45/5.80 = ( times_times_int @ C @ A ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_right_cancel
% 5.45/5.80 thf(fact_8131_unit__mult__left__cancel,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.80 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_left_cancel
% 5.45/5.80 thf(fact_8132_unit__mult__left__cancel,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( ( times_times_nat @ A @ B )
% 5.45/5.80 = ( times_times_nat @ A @ C ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_left_cancel
% 5.45/5.80 thf(fact_8133_unit__mult__left__cancel,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( ( times_times_int @ A @ B )
% 5.45/5.80 = ( times_times_int @ A @ C ) )
% 5.45/5.80 = ( B = C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % unit_mult_left_cancel
% 5.45/5.80 thf(fact_8134_mult__unit__dvd__iff_H,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff'
% 5.45/5.80 thf(fact_8135_mult__unit__dvd__iff_H,axiom,
% 5.45/5.80 ! [A: nat,B: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff'
% 5.45/5.80 thf(fact_8136_mult__unit__dvd__iff_H,axiom,
% 5.45/5.80 ! [A: int,B: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff'
% 5.45/5.80 thf(fact_8137_dvd__mult__unit__iff_H,axiom,
% 5.45/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff'
% 5.45/5.80 thf(fact_8138_dvd__mult__unit__iff_H,axiom,
% 5.45/5.80 ! [B: nat,A: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff'
% 5.45/5.80 thf(fact_8139_dvd__mult__unit__iff_H,axiom,
% 5.45/5.80 ! [B: int,A: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff'
% 5.45/5.80 thf(fact_8140_mult__unit__dvd__iff,axiom,
% 5.45/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff
% 5.45/5.80 thf(fact_8141_mult__unit__dvd__iff,axiom,
% 5.45/5.80 ! [B: nat,A: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff
% 5.45/5.80 thf(fact_8142_mult__unit__dvd__iff,axiom,
% 5.45/5.80 ! [B: int,A: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.45/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % mult_unit_dvd_iff
% 5.45/5.80 thf(fact_8143_dvd__mult__unit__iff,axiom,
% 5.45/5.80 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.45/5.80 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff
% 5.45/5.80 thf(fact_8144_dvd__mult__unit__iff,axiom,
% 5.45/5.80 ! [B: nat,A: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.80 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.45/5.80 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff
% 5.45/5.80 thf(fact_8145_dvd__mult__unit__iff,axiom,
% 5.45/5.80 ! [B: int,A: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.80 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.45/5.80 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_unit_iff
% 5.45/5.80 thf(fact_8146_is__unit__mult__iff,axiom,
% 5.45/5.80 ! [A: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.45/5.80 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.80 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % is_unit_mult_iff
% 5.45/5.80 thf(fact_8147_is__unit__mult__iff,axiom,
% 5.45/5.80 ! [A: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.45/5.80 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.80 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % is_unit_mult_iff
% 5.45/5.80 thf(fact_8148_is__unit__mult__iff,axiom,
% 5.45/5.80 ! [A: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.45/5.80 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.80 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % is_unit_mult_iff
% 5.45/5.80 thf(fact_8149_div__mult__div__if__dvd,axiom,
% 5.45/5.80 ! [B: nat,A: nat,D2: nat,C: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ B @ A )
% 5.45/5.80 => ( ( dvd_dvd_nat @ D2 @ C )
% 5.45/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D2 ) )
% 5.45/5.80 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_div_if_dvd
% 5.45/5.80 thf(fact_8150_div__mult__div__if__dvd,axiom,
% 5.45/5.80 ! [B: int,A: int,D2: int,C: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ B @ A )
% 5.45/5.80 => ( ( dvd_dvd_int @ D2 @ C )
% 5.45/5.80 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D2 ) )
% 5.45/5.80 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_div_if_dvd
% 5.45/5.80 thf(fact_8151_div__mult__div__if__dvd,axiom,
% 5.45/5.80 ! [B: code_integer,A: code_integer,D2: code_integer,C: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ D2 @ C )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D2 ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_div_if_dvd
% 5.45/5.80 thf(fact_8152_div__mult__div__if__dvd,axiom,
% 5.45/5.80 ! [B: code_natural,A: code_natural,D2: code_natural,C: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ B @ A )
% 5.45/5.80 => ( ( dvd_dvd_Code_natural @ D2 @ C )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ ( divide5121882707175180666atural @ C @ D2 ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ ( times_2397367101498566445atural @ B @ D2 ) ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_div_if_dvd
% 5.45/5.80 thf(fact_8153_dvd__mult__imp__div,axiom,
% 5.45/5.80 ! [A: nat,C: nat,B: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.45/5.80 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_imp_div
% 5.45/5.80 thf(fact_8154_dvd__mult__imp__div,axiom,
% 5.45/5.80 ! [A: int,C: int,B: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.45/5.80 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_imp_div
% 5.45/5.80 thf(fact_8155_dvd__mult__imp__div,axiom,
% 5.45/5.80 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_imp_div
% 5.45/5.80 thf(fact_8156_dvd__mult__imp__div,axiom,
% 5.45/5.80 ! [A: code_natural,C: code_natural,B: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B )
% 5.45/5.80 => ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_mult_imp_div
% 5.45/5.80 thf(fact_8157_dvd__div__mult2__eq,axiom,
% 5.45/5.80 ! [B: nat,C: nat,A: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.45/5.80 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.80 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult2_eq
% 5.45/5.80 thf(fact_8158_dvd__div__mult2__eq,axiom,
% 5.45/5.80 ! [B: int,C: int,A: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.45/5.80 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.80 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult2_eq
% 5.45/5.80 thf(fact_8159_dvd__div__mult2__eq,axiom,
% 5.45/5.80 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.45/5.80 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult2_eq
% 5.45/5.80 thf(fact_8160_dvd__div__mult2__eq,axiom,
% 5.45/5.80 ! [B: code_natural,C: code_natural,A: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ B @ C ) @ A )
% 5.45/5.80 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult2_eq
% 5.45/5.80 thf(fact_8161_div__div__eq__right,axiom,
% 5.45/5.80 ! [C: nat,B: nat,A: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.45/5.80 => ( ( dvd_dvd_nat @ B @ A )
% 5.45/5.80 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.45/5.80 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_div_eq_right
% 5.45/5.80 thf(fact_8162_div__div__eq__right,axiom,
% 5.45/5.80 ! [C: int,B: int,A: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.45/5.80 => ( ( dvd_dvd_int @ B @ A )
% 5.45/5.80 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.45/5.80 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_div_eq_right
% 5.45/5.80 thf(fact_8163_div__div__eq__right,axiom,
% 5.45/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.45/5.80 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.45/5.80 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.45/5.80 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_div_eq_right
% 5.45/5.80 thf(fact_8164_div__div__eq__right,axiom,
% 5.45/5.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 5.45/5.80 => ( ( dvd_dvd_Code_natural @ B @ A )
% 5.45/5.80 => ( ( divide5121882707175180666atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 5.45/5.80 = ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_div_eq_right
% 5.45/5.80 thf(fact_8165_div__mult__swap,axiom,
% 5.45/5.80 ! [C: nat,B: nat,A: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.45/5.80 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.45/5.80 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_swap
% 5.45/5.80 thf(fact_8166_div__mult__swap,axiom,
% 5.45/5.80 ! [C: int,B: int,A: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.45/5.80 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.45/5.80 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_swap
% 5.45/5.80 thf(fact_8167_div__mult__swap,axiom,
% 5.45/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.45/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_swap
% 5.45/5.80 thf(fact_8168_div__mult__swap,axiom,
% 5.45/5.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 5.45/5.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % div_mult_swap
% 5.45/5.80 thf(fact_8169_dvd__div__mult,axiom,
% 5.45/5.80 ! [C: nat,B: nat,A: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ C @ B )
% 5.45/5.80 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.45/5.80 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult
% 5.45/5.80 thf(fact_8170_dvd__div__mult,axiom,
% 5.45/5.80 ! [C: int,B: int,A: int] :
% 5.45/5.80 ( ( dvd_dvd_int @ C @ B )
% 5.45/5.80 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.45/5.80 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult
% 5.45/5.80 thf(fact_8171_dvd__div__mult,axiom,
% 5.45/5.80 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.45/5.80 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.45/5.80 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult
% 5.45/5.80 thf(fact_8172_dvd__div__mult,axiom,
% 5.45/5.80 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.80 ( ( dvd_dvd_Code_natural @ C @ B )
% 5.45/5.80 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ B @ C ) @ A )
% 5.45/5.80 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ B @ A ) @ C ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_div_mult
% 5.45/5.80 thf(fact_8173_dvd__pos__nat,axiom,
% 5.45/5.80 ! [N2: nat,M: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.80 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.45/5.80 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_pos_nat
% 5.45/5.80 thf(fact_8174_nat__dvd__not__less,axiom,
% 5.45/5.80 ! [M: nat,N2: nat] :
% 5.45/5.80 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.80 => ( ( ord_less_nat @ M @ N2 )
% 5.45/5.80 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % nat_dvd_not_less
% 5.45/5.80 thf(fact_8175_dvd__power__le,axiom,
% 5.45/5.80 ! [X: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.45/5.80 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.45/5.80 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.80 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.45/5.80
% 5.45/5.80 % dvd_power_le
% 5.45/5.80 thf(fact_8176_dvd__power__le,axiom,
% 5.45/5.80 ! [X: nat,Y: nat,N2: nat,M: nat] :
% 5.45/5.80 ( ( dvd_dvd_nat @ X @ Y )
% 5.45/5.80 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.80 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_le
% 5.45/5.81 thf(fact_8177_dvd__power__le,axiom,
% 5.45/5.81 ! [X: int,Y: int,N2: nat,M: nat] :
% 5.45/5.81 ( ( dvd_dvd_int @ X @ Y )
% 5.45/5.81 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_le
% 5.45/5.81 thf(fact_8178_power__le__dvd,axiom,
% 5.45/5.81 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.45/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_dvd
% 5.45/5.81 thf(fact_8179_power__le__dvd,axiom,
% 5.45/5.81 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.45/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_dvd
% 5.45/5.81 thf(fact_8180_power__le__dvd,axiom,
% 5.45/5.81 ! [A: int,N2: nat,B: int,M: nat] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.45/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_dvd
% 5.45/5.81 thf(fact_8181_le__imp__power__dvd,axiom,
% 5.45/5.81 ! [M: nat,N2: nat,A: code_integer] :
% 5.45/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % le_imp_power_dvd
% 5.45/5.81 thf(fact_8182_le__imp__power__dvd,axiom,
% 5.45/5.81 ! [M: nat,N2: nat,A: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % le_imp_power_dvd
% 5.45/5.81 thf(fact_8183_le__imp__power__dvd,axiom,
% 5.45/5.81 ! [M: nat,N2: nat,A: int] :
% 5.45/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % le_imp_power_dvd
% 5.45/5.81 thf(fact_8184_dvd__minus__self,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.45/5.81 = ( ( ord_less_nat @ N2 @ M )
% 5.45/5.81 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_minus_self
% 5.45/5.81 thf(fact_8185_less__eq__dvd__minus,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.45/5.81 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % less_eq_dvd_minus
% 5.45/5.81 thf(fact_8186_dvd__diffD1,axiom,
% 5.45/5.81 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.81 => ( ( dvd_dvd_nat @ K @ M )
% 5.45/5.81 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_diffD1
% 5.45/5.81 thf(fact_8187_dvd__diffD,axiom,
% 5.45/5.81 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.45/5.81 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_diffD
% 5.45/5.81 thf(fact_8188_fact__dvd,axiom,
% 5.45/5.81 ! [N2: nat,M: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_dvd
% 5.45/5.81 thf(fact_8189_fact__dvd,axiom,
% 5.45/5.81 ! [N2: nat,M: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_dvd
% 5.45/5.81 thf(fact_8190_fact__dvd,axiom,
% 5.45/5.81 ! [N2: nat,M: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_dvd
% 5.45/5.81 thf(fact_8191_unity__coeff__ex,axiom,
% 5.45/5.81 ! [P: code_integer > $o,L: code_integer] :
% 5.45/5.81 ( ( ? [X4: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X4 ) ) )
% 5.45/5.81 = ( ? [X4: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X4 @ zero_z3403309356797280102nteger ) )
% 5.45/5.81 & ( P @ X4 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unity_coeff_ex
% 5.45/5.81 thf(fact_8192_unity__coeff__ex,axiom,
% 5.45/5.81 ! [P: rat > $o,L: rat] :
% 5.45/5.81 ( ( ? [X4: rat] : ( P @ ( times_times_rat @ L @ X4 ) ) )
% 5.45/5.81 = ( ? [X4: rat] :
% 5.45/5.81 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X4 @ zero_zero_rat ) )
% 5.45/5.81 & ( P @ X4 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unity_coeff_ex
% 5.45/5.81 thf(fact_8193_unity__coeff__ex,axiom,
% 5.45/5.81 ! [P: nat > $o,L: nat] :
% 5.45/5.81 ( ( ? [X4: nat] : ( P @ ( times_times_nat @ L @ X4 ) ) )
% 5.45/5.81 = ( ? [X4: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X4 @ zero_zero_nat ) )
% 5.45/5.81 & ( P @ X4 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unity_coeff_ex
% 5.45/5.81 thf(fact_8194_unity__coeff__ex,axiom,
% 5.45/5.81 ! [P: int > $o,L: int] :
% 5.45/5.81 ( ( ? [X4: int] : ( P @ ( times_times_int @ L @ X4 ) ) )
% 5.45/5.81 = ( ? [X4: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X4 @ zero_zero_int ) )
% 5.45/5.81 & ( P @ X4 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unity_coeff_ex
% 5.45/5.81 thf(fact_8195_unit__dvdE,axiom,
% 5.45/5.81 ! [A: code_integer,B: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.81 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ! [C2: code_integer] :
% 5.45/5.81 ( B
% 5.45/5.81 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_dvdE
% 5.45/5.81 thf(fact_8196_unit__dvdE,axiom,
% 5.45/5.81 ! [A: nat,B: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.81 => ~ ( ( A != zero_zero_nat )
% 5.45/5.81 => ! [C2: nat] :
% 5.45/5.81 ( B
% 5.45/5.81 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_dvdE
% 5.45/5.81 thf(fact_8197_unit__dvdE,axiom,
% 5.45/5.81 ! [A: int,B: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.81 => ~ ( ( A != zero_zero_int )
% 5.45/5.81 => ! [C2: int] :
% 5.45/5.81 ( B
% 5.45/5.81 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_dvdE
% 5.45/5.81 thf(fact_8198_inf__period_I4_J,axiom,
% 5.45/5.81 ! [D2: code_integer,D3: code_integer,T5: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 5.45/5.81 => ! [X7: code_integer,K4: code_integer] :
% 5.45/5.81 ( ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ T5 ) ) )
% 5.45/5.81 = ( ~ ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T5 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(4)
% 5.45/5.81 thf(fact_8199_inf__period_I4_J,axiom,
% 5.45/5.81 ! [D2: rat,D3: rat,T5: rat] :
% 5.45/5.81 ( ( dvd_dvd_rat @ D2 @ D3 )
% 5.45/5.81 => ! [X7: rat,K4: rat] :
% 5.45/5.81 ( ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ T5 ) ) )
% 5.45/5.81 = ( ~ ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) @ T5 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(4)
% 5.45/5.81 thf(fact_8200_inf__period_I4_J,axiom,
% 5.45/5.81 ! [D2: int,D3: int,T5: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ D2 @ D3 )
% 5.45/5.81 => ! [X7: int,K4: int] :
% 5.45/5.81 ( ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T5 ) ) )
% 5.45/5.81 = ( ~ ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) @ T5 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(4)
% 5.45/5.81 thf(fact_8201_inf__period_I3_J,axiom,
% 5.45/5.81 ! [D2: code_integer,D3: code_integer,T5: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ D2 @ D3 )
% 5.45/5.81 => ! [X7: code_integer,K4: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ X7 @ T5 ) )
% 5.45/5.81 = ( dvd_dvd_Code_integer @ D2 @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X7 @ ( times_3573771949741848930nteger @ K4 @ D3 ) ) @ T5 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(3)
% 5.45/5.81 thf(fact_8202_inf__period_I3_J,axiom,
% 5.45/5.81 ! [D2: rat,D3: rat,T5: rat] :
% 5.45/5.81 ( ( dvd_dvd_rat @ D2 @ D3 )
% 5.45/5.81 => ! [X7: rat,K4: rat] :
% 5.45/5.81 ( ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ X7 @ T5 ) )
% 5.45/5.81 = ( dvd_dvd_rat @ D2 @ ( plus_plus_rat @ ( minus_minus_rat @ X7 @ ( times_times_rat @ K4 @ D3 ) ) @ T5 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(3)
% 5.45/5.81 thf(fact_8203_inf__period_I3_J,axiom,
% 5.45/5.81 ! [D2: int,D3: int,T5: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ D2 @ D3 )
% 5.45/5.81 => ! [X7: int,K4: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ D2 @ ( plus_plus_int @ X7 @ T5 ) )
% 5.45/5.81 = ( dvd_dvd_int @ D2 @ ( plus_plus_int @ ( minus_minus_int @ X7 @ ( times_times_int @ K4 @ D3 ) ) @ T5 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % inf_period(3)
% 5.45/5.81 thf(fact_8204_dvd__div__div__eq__mult,axiom,
% 5.45/5.81 ! [A: nat,C: nat,B: nat,D2: nat] :
% 5.45/5.81 ( ( A != zero_zero_nat )
% 5.45/5.81 => ( ( C != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.81 => ( ( dvd_dvd_nat @ C @ D2 )
% 5.45/5.81 => ( ( ( divide_divide_nat @ B @ A )
% 5.45/5.81 = ( divide_divide_nat @ D2 @ C ) )
% 5.45/5.81 = ( ( times_times_nat @ B @ C )
% 5.45/5.81 = ( times_times_nat @ A @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_div_eq_mult
% 5.45/5.81 thf(fact_8205_dvd__div__div__eq__mult,axiom,
% 5.45/5.81 ! [A: int,C: int,B: int,D2: int] :
% 5.45/5.81 ( ( A != zero_zero_int )
% 5.45/5.81 => ( ( C != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ A @ B )
% 5.45/5.81 => ( ( dvd_dvd_int @ C @ D2 )
% 5.45/5.81 => ( ( ( divide_divide_int @ B @ A )
% 5.45/5.81 = ( divide_divide_int @ D2 @ C ) )
% 5.45/5.81 = ( ( times_times_int @ B @ C )
% 5.45/5.81 = ( times_times_int @ A @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_div_eq_mult
% 5.45/5.81 thf(fact_8206_dvd__div__div__eq__mult,axiom,
% 5.45/5.81 ! [A: code_integer,C: code_integer,B: code_integer,D2: code_integer] :
% 5.45/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ C @ D2 )
% 5.45/5.81 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.45/5.81 = ( divide6298287555418463151nteger @ D2 @ C ) )
% 5.45/5.81 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.45/5.81 = ( times_3573771949741848930nteger @ A @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_div_eq_mult
% 5.45/5.81 thf(fact_8207_dvd__div__div__eq__mult,axiom,
% 5.45/5.81 ! [A: code_natural,C: code_natural,B: code_natural,D2: code_natural] :
% 5.45/5.81 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( C != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ A @ B )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ C @ D2 )
% 5.45/5.81 => ( ( ( divide5121882707175180666atural @ B @ A )
% 5.45/5.81 = ( divide5121882707175180666atural @ D2 @ C ) )
% 5.45/5.81 = ( ( times_2397367101498566445atural @ B @ C )
% 5.45/5.81 = ( times_2397367101498566445atural @ A @ D2 ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_div_eq_mult
% 5.45/5.81 thf(fact_8208_dvd__div__iff__mult,axiom,
% 5.45/5.81 ! [C: nat,B: nat,A: nat] :
% 5.45/5.81 ( ( C != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ C @ B )
% 5.45/5.81 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.45/5.81 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_iff_mult
% 5.45/5.81 thf(fact_8209_dvd__div__iff__mult,axiom,
% 5.45/5.81 ! [C: int,B: int,A: int] :
% 5.45/5.81 ( ( C != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ C @ B )
% 5.45/5.81 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.45/5.81 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_iff_mult
% 5.45/5.81 thf(fact_8210_dvd__div__iff__mult,axiom,
% 5.45/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.81 ( ( C != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.45/5.81 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_iff_mult
% 5.45/5.81 thf(fact_8211_dvd__div__iff__mult,axiom,
% 5.45/5.81 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.81 ( ( C != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ C @ B )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 5.45/5.81 = ( dvd_dvd_Code_natural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_iff_mult
% 5.45/5.81 thf(fact_8212_div__dvd__iff__mult,axiom,
% 5.45/5.81 ! [B: nat,A: nat,C: nat] :
% 5.45/5.81 ( ( B != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ B @ A )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.45/5.81 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_dvd_iff_mult
% 5.45/5.81 thf(fact_8213_div__dvd__iff__mult,axiom,
% 5.45/5.81 ! [B: int,A: int,C: int] :
% 5.45/5.81 ( ( B != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ B @ A )
% 5.45/5.81 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.45/5.81 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_dvd_iff_mult
% 5.45/5.81 thf(fact_8214_div__dvd__iff__mult,axiom,
% 5.45/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.81 ( ( B != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.45/5.81 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_dvd_iff_mult
% 5.45/5.81 thf(fact_8215_div__dvd__iff__mult,axiom,
% 5.45/5.81 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.81 ( ( B != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ B @ A )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 5.45/5.81 = ( dvd_dvd_Code_natural @ A @ ( times_2397367101498566445atural @ C @ B ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_dvd_iff_mult
% 5.45/5.81 thf(fact_8216_dvd__div__eq__mult,axiom,
% 5.45/5.81 ! [A: nat,B: nat,C: nat] :
% 5.45/5.81 ( ( A != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ A @ B )
% 5.45/5.81 => ( ( ( divide_divide_nat @ B @ A )
% 5.45/5.81 = C )
% 5.45/5.81 = ( B
% 5.45/5.81 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_eq_mult
% 5.45/5.81 thf(fact_8217_dvd__div__eq__mult,axiom,
% 5.45/5.81 ! [A: int,B: int,C: int] :
% 5.45/5.81 ( ( A != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ A @ B )
% 5.45/5.81 => ( ( ( divide_divide_int @ B @ A )
% 5.45/5.81 = C )
% 5.45/5.81 = ( B
% 5.45/5.81 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_eq_mult
% 5.45/5.81 thf(fact_8218_dvd__div__eq__mult,axiom,
% 5.45/5.81 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.45/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.45/5.81 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.45/5.81 = C )
% 5.45/5.81 = ( B
% 5.45/5.81 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_eq_mult
% 5.45/5.81 thf(fact_8219_dvd__div__eq__mult,axiom,
% 5.45/5.81 ! [A: code_natural,B: code_natural,C: code_natural] :
% 5.45/5.81 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ A @ B )
% 5.45/5.81 => ( ( ( divide5121882707175180666atural @ B @ A )
% 5.45/5.81 = C )
% 5.45/5.81 = ( B
% 5.45/5.81 = ( times_2397367101498566445atural @ C @ A ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_div_eq_mult
% 5.45/5.81 thf(fact_8220_is__unit__div__mult2__eq,axiom,
% 5.45/5.81 ! [B: nat,C: nat,A: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.45/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.81 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult2_eq
% 5.45/5.81 thf(fact_8221_is__unit__div__mult2__eq,axiom,
% 5.45/5.81 ! [B: int,C: int,A: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.45/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult2_eq
% 5.45/5.81 thf(fact_8222_is__unit__div__mult2__eq,axiom,
% 5.45/5.81 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.81 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult2_eq
% 5.45/5.81 thf(fact_8223_is__unit__div__mult2__eq,axiom,
% 5.45/5.81 ! [B: code_natural,C: code_natural,A: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 5.45/5.81 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult2_eq
% 5.45/5.81 thf(fact_8224_unit__div__mult__swap,axiom,
% 5.45/5.81 ! [C: nat,A: nat,B: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.45/5.81 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.45/5.81 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_mult_swap
% 5.45/5.81 thf(fact_8225_unit__div__mult__swap,axiom,
% 5.45/5.81 ! [C: int,A: int,B: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.45/5.81 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.45/5.81 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_mult_swap
% 5.45/5.81 thf(fact_8226_unit__div__mult__swap,axiom,
% 5.45/5.81 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.45/5.81 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.45/5.81 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_mult_swap
% 5.45/5.81 thf(fact_8227_unit__div__mult__swap,axiom,
% 5.45/5.81 ! [C: code_natural,A: code_natural,B: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 5.45/5.81 => ( ( times_2397367101498566445atural @ A @ ( divide5121882707175180666atural @ B @ C ) )
% 5.45/5.81 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ B ) @ C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_mult_swap
% 5.45/5.81 thf(fact_8228_unit__div__commute,axiom,
% 5.45/5.81 ! [B: nat,A: nat,C: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.45/5.81 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_commute
% 5.45/5.81 thf(fact_8229_unit__div__commute,axiom,
% 5.45/5.81 ! [B: int,A: int,C: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.45/5.81 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_commute
% 5.45/5.81 thf(fact_8230_unit__div__commute,axiom,
% 5.45/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.45/5.81 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_commute
% 5.45/5.81 thf(fact_8231_unit__div__commute,axiom,
% 5.45/5.81 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( times_2397367101498566445atural @ ( divide5121882707175180666atural @ A @ B ) @ C )
% 5.45/5.81 = ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ C ) @ B ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_div_commute
% 5.45/5.81 thf(fact_8232_div__mult__unit2,axiom,
% 5.45/5.81 ! [C: nat,B: nat,A: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ B @ A )
% 5.45/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.45/5.81 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_mult_unit2
% 5.45/5.81 thf(fact_8233_div__mult__unit2,axiom,
% 5.45/5.81 ! [C: int,B: int,A: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ B @ A )
% 5.45/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.45/5.81 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_mult_unit2
% 5.45/5.81 thf(fact_8234_div__mult__unit2,axiom,
% 5.45/5.81 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.45/5.81 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_mult_unit2
% 5.45/5.81 thf(fact_8235_div__mult__unit2,axiom,
% 5.45/5.81 ! [C: code_natural,B: code_natural,A: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ C @ one_one_Code_natural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ B @ A )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ C ) )
% 5.45/5.81 = ( divide5121882707175180666atural @ ( divide5121882707175180666atural @ A @ B ) @ C ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % div_mult_unit2
% 5.45/5.81 thf(fact_8236_unit__eq__div2,axiom,
% 5.45/5.81 ! [B: nat,A: nat,C: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( A
% 5.45/5.81 = ( divide_divide_nat @ C @ B ) )
% 5.45/5.81 = ( ( times_times_nat @ A @ B )
% 5.45/5.81 = C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div2
% 5.45/5.81 thf(fact_8237_unit__eq__div2,axiom,
% 5.45/5.81 ! [B: int,A: int,C: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( A
% 5.45/5.81 = ( divide_divide_int @ C @ B ) )
% 5.45/5.81 = ( ( times_times_int @ A @ B )
% 5.45/5.81 = C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div2
% 5.45/5.81 thf(fact_8238_unit__eq__div2,axiom,
% 5.45/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( A
% 5.45/5.81 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.45/5.81 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.45/5.81 = C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div2
% 5.45/5.81 thf(fact_8239_unit__eq__div2,axiom,
% 5.45/5.81 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( A
% 5.45/5.81 = ( divide5121882707175180666atural @ C @ B ) )
% 5.45/5.81 = ( ( times_2397367101498566445atural @ A @ B )
% 5.45/5.81 = C ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div2
% 5.45/5.81 thf(fact_8240_unit__eq__div1,axiom,
% 5.45/5.81 ! [B: nat,A: nat,C: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( ( divide_divide_nat @ A @ B )
% 5.45/5.81 = C )
% 5.45/5.81 = ( A
% 5.45/5.81 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div1
% 5.45/5.81 thf(fact_8241_unit__eq__div1,axiom,
% 5.45/5.81 ! [B: int,A: int,C: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( ( divide_divide_int @ A @ B )
% 5.45/5.81 = C )
% 5.45/5.81 = ( A
% 5.45/5.81 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div1
% 5.45/5.81 thf(fact_8242_unit__eq__div1,axiom,
% 5.45/5.81 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.45/5.81 = C )
% 5.45/5.81 = ( A
% 5.45/5.81 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div1
% 5.45/5.81 thf(fact_8243_unit__eq__div1,axiom,
% 5.45/5.81 ! [B: code_natural,A: code_natural,C: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( ( divide5121882707175180666atural @ A @ B )
% 5.45/5.81 = C )
% 5.45/5.81 = ( A
% 5.45/5.81 = ( times_2397367101498566445atural @ C @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % unit_eq_div1
% 5.45/5.81 thf(fact_8244_round__mono,axiom,
% 5.45/5.81 ! [X: rat,Y: rat] :
% 5.45/5.81 ( ( ord_less_eq_rat @ X @ Y )
% 5.45/5.81 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % round_mono
% 5.45/5.81 thf(fact_8245_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > nat] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A3 ) @ ( groups3190895334310489300er_nat @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8246_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > int] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A3 ) @ ( groups3188404863801439024er_int @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8247_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_nat,A3: set_nat,F: nat > code_integer] :
% 5.45/5.81 ( ( finite_finite_nat @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A3 ) @ ( groups3455450783089532116nteger @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8248_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > code_integer] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3674199335183972705nteger @ F @ A3 ) @ ( groups3674199335183972705nteger @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8249_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_int,A3: set_int,F: int > nat] :
% 5.45/5.81 ( ( finite_finite_int @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ ( groups1707563613775114915nt_nat @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8250_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_int,A3: set_int,F: int > code_integer] :
% 5.45/5.81 ( ( finite_finite_int @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3827104343326376752nteger @ F @ A3 ) @ ( groups3827104343326376752nteger @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8251_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_nat,A3: set_nat,F: nat > nat] :
% 5.45/5.81 ( ( finite_finite_nat @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ ( groups708209901874060359at_nat @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8252_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_nat,A3: set_nat,F: nat > int] :
% 5.45/5.81 ( ( finite_finite_nat @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_int @ ( groups705719431365010083at_int @ F @ A3 ) @ ( groups705719431365010083at_int @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8253_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_int,A3: set_int,F: int > int] :
% 5.45/5.81 ( ( finite_finite_int @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_int @ ( groups1705073143266064639nt_int @ F @ A3 ) @ ( groups1705073143266064639nt_int @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8254_prod__dvd__prod__subset,axiom,
% 5.45/5.81 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > nat] :
% 5.45/5.81 ( ( finite6177210948735845034at_nat @ B3 )
% 5.45/5.81 => ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups4077766827762148844at_nat @ F @ A3 ) @ ( groups4077766827762148844at_nat @ F @ B3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset
% 5.45/5.81 thf(fact_8255_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_o,A3: set_o,F: $o > nat,G: $o > nat] :
% 5.45/5.81 ( ( finite_finite_o @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: $o] :
% 5.45/5.81 ( ( member_o @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups3504817904513533571_o_nat @ F @ A3 ) @ ( groups3504817904513533571_o_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8256_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > nat,G: code_integer > nat] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: code_integer] :
% 5.45/5.81 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups3190895334310489300er_nat @ F @ A3 ) @ ( groups3190895334310489300er_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8257_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_o,A3: set_o,F: $o > int,G: $o > int] :
% 5.45/5.81 ( ( finite_finite_o @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: $o] :
% 5.45/5.81 ( ( member_o @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_int @ ( groups3502327434004483295_o_int @ F @ A3 ) @ ( groups3502327434004483295_o_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8258_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > int,G: code_integer > int] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: code_integer] :
% 5.45/5.81 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_int @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_int @ ( groups3188404863801439024er_int @ F @ A3 ) @ ( groups3188404863801439024er_int @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8259_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_o,A3: set_o,F: $o > code_integer,G: $o > code_integer] :
% 5.45/5.81 ( ( finite_finite_o @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_o @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: $o] :
% 5.45/5.81 ( ( member_o @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups7694694392188491536nteger @ F @ A3 ) @ ( groups7694694392188491536nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8260_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_nat,A3: set_nat,F: nat > code_integer,G: nat > code_integer] :
% 5.45/5.81 ( ( finite_finite_nat @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: nat] :
% 5.45/5.81 ( ( member_nat @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3455450783089532116nteger @ F @ A3 ) @ ( groups3455450783089532116nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8261_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_Code_integer,A3: set_Code_integer,F: code_integer > code_integer,G: code_integer > code_integer] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ B3 )
% 5.45/5.81 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: code_integer] :
% 5.45/5.81 ( ( member_Code_integer @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3674199335183972705nteger @ F @ A3 ) @ ( groups3674199335183972705nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8262_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_int,A3: set_int,F: int > nat,G: int > nat] :
% 5.45/5.81 ( ( finite_finite_int @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: int] :
% 5.45/5.81 ( ( member_int @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups1707563613775114915nt_nat @ F @ A3 ) @ ( groups1707563613775114915nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8263_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_int,A3: set_int,F: int > code_integer,G: int > code_integer] :
% 5.45/5.81 ( ( finite_finite_int @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: int] :
% 5.45/5.81 ( ( member_int @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( groups3827104343326376752nteger @ F @ A3 ) @ ( groups3827104343326376752nteger @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8264_prod__dvd__prod__subset2,axiom,
% 5.45/5.81 ! [B3: set_nat,A3: set_nat,F: nat > nat,G: nat > nat] :
% 5.45/5.81 ( ( finite_finite_nat @ B3 )
% 5.45/5.81 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.45/5.81 => ( ! [A4: nat] :
% 5.45/5.81 ( ( member_nat @ A4 @ A3 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( F @ A4 ) @ ( G @ A4 ) ) )
% 5.45/5.81 => ( dvd_dvd_nat @ ( groups708209901874060359at_nat @ F @ A3 ) @ ( groups708209901874060359at_nat @ G @ B3 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % prod_dvd_prod_subset2
% 5.45/5.81 thf(fact_8265_dvd__imp__le,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ K @ N2 )
% 5.45/5.81 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_imp_le
% 5.45/5.81 thf(fact_8266_dvd__mult__cancel,axiom,
% 5.45/5.81 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.81 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.81 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_mult_cancel
% 5.45/5.81 thf(fact_8267_nat__mult__dvd__cancel1,axiom,
% 5.45/5.81 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.45/5.81 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % nat_mult_dvd_cancel1
% 5.45/5.81 thf(fact_8268_fact__fact__dvd__fact,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_fact_dvd_fact
% 5.45/5.81 thf(fact_8269_fact__fact__dvd__fact,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] : ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ N2 ) ) @ ( semiri773545260158071498ct_rat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_fact_dvd_fact
% 5.45/5.81 thf(fact_8270_fact__fact__dvd__fact,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_fact_dvd_fact
% 5.45/5.81 thf(fact_8271_fact__fact__dvd__fact,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % fact_fact_dvd_fact
% 5.45/5.81 thf(fact_8272_mod__greater__zero__iff__not__dvd,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.45/5.81 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % mod_greater_zero_iff_not_dvd
% 5.45/5.81 thf(fact_8273_mod__eq__dvd__iff__nat,axiom,
% 5.45/5.81 ! [N2: nat,M: nat,Q6: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ N2 @ M )
% 5.45/5.81 => ( ( ( modulo_modulo_nat @ M @ Q6 )
% 5.45/5.81 = ( modulo_modulo_nat @ N2 @ Q6 ) )
% 5.45/5.81 = ( dvd_dvd_nat @ Q6 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % mod_eq_dvd_iff_nat
% 5.45/5.81 thf(fact_8274_floor__le__round,axiom,
% 5.45/5.81 ! [X: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X ) @ ( archim7778729529865785530nd_rat @ X ) ) ).
% 5.45/5.81
% 5.45/5.81 % floor_le_round
% 5.45/5.81 thf(fact_8275_dvd__fact,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.45/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_fact
% 5.45/5.81 thf(fact_8276_finite__divisors__nat,axiom,
% 5.45/5.81 ! [M: nat] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.81 => ( finite_finite_nat
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_divisors_nat
% 5.45/5.81 thf(fact_8277_gcd__nat_Oordering__top__axioms,axiom,
% 5.45/5.81 ( ordering_top_nat @ dvd_dvd_nat
% 5.45/5.81 @ ^ [M3: nat,N: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ M3 @ N )
% 5.45/5.81 & ( M3 != N ) )
% 5.45/5.81 @ zero_zero_nat ) ).
% 5.45/5.81
% 5.45/5.81 % gcd_nat.ordering_top_axioms
% 5.45/5.81 thf(fact_8278_is__unit__div__mult__cancel__right,axiom,
% 5.45/5.81 ! [A: nat,B: nat] :
% 5.45/5.81 ( ( A != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.45/5.81 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_right
% 5.45/5.81 thf(fact_8279_is__unit__div__mult__cancel__right,axiom,
% 5.45/5.81 ! [A: int,B: int] :
% 5.45/5.81 ( ( A != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.45/5.81 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_right
% 5.45/5.81 thf(fact_8280_is__unit__div__mult__cancel__right,axiom,
% 5.45/5.81 ! [A: code_integer,B: code_integer] :
% 5.45/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.45/5.81 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_right
% 5.45/5.81 thf(fact_8281_is__unit__div__mult__cancel__right,axiom,
% 5.45/5.81 ! [A: code_natural,B: code_natural] :
% 5.45/5.81 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ B @ A ) )
% 5.45/5.81 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_right
% 5.45/5.81 thf(fact_8282_is__unit__div__mult__cancel__left,axiom,
% 5.45/5.81 ! [A: nat,B: nat] :
% 5.45/5.81 ( ( A != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.45/5.81 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.45/5.81 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_left
% 5.45/5.81 thf(fact_8283_is__unit__div__mult__cancel__left,axiom,
% 5.45/5.81 ! [A: int,B: int] :
% 5.45/5.81 ( ( A != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.45/5.81 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.45/5.81 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_left
% 5.45/5.81 thf(fact_8284_is__unit__div__mult__cancel__left,axiom,
% 5.45/5.81 ! [A: code_integer,B: code_integer] :
% 5.45/5.81 ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.45/5.81 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_left
% 5.45/5.81 thf(fact_8285_is__unit__div__mult__cancel__left,axiom,
% 5.45/5.81 ! [A: code_natural,B: code_natural] :
% 5.45/5.81 ( ( A != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ B @ one_one_Code_natural )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ A @ ( times_2397367101498566445atural @ A @ B ) )
% 5.45/5.81 = ( divide5121882707175180666atural @ one_one_Code_natural @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unit_div_mult_cancel_left
% 5.45/5.81 thf(fact_8286_is__unitE,axiom,
% 5.45/5.81 ! [A: nat,C: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.45/5.81 => ~ ( ( A != zero_zero_nat )
% 5.45/5.81 => ! [B4: nat] :
% 5.45/5.81 ( ( B4 != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ B4 @ one_one_nat )
% 5.45/5.81 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.45/5.81 = B4 )
% 5.45/5.81 => ( ( ( divide_divide_nat @ one_one_nat @ B4 )
% 5.45/5.81 = A )
% 5.45/5.81 => ( ( ( times_times_nat @ A @ B4 )
% 5.45/5.81 = one_one_nat )
% 5.45/5.81 => ( ( divide_divide_nat @ C @ A )
% 5.45/5.81 != ( times_times_nat @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unitE
% 5.45/5.81 thf(fact_8287_is__unitE,axiom,
% 5.45/5.81 ! [A: int,C: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.45/5.81 => ~ ( ( A != zero_zero_int )
% 5.45/5.81 => ! [B4: int] :
% 5.45/5.81 ( ( B4 != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ B4 @ one_one_int )
% 5.45/5.81 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.45/5.81 = B4 )
% 5.45/5.81 => ( ( ( divide_divide_int @ one_one_int @ B4 )
% 5.45/5.81 = A )
% 5.45/5.81 => ( ( ( times_times_int @ A @ B4 )
% 5.45/5.81 = one_one_int )
% 5.45/5.81 => ( ( divide_divide_int @ C @ A )
% 5.45/5.81 != ( times_times_int @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unitE
% 5.45/5.81 thf(fact_8288_is__unitE,axiom,
% 5.45/5.81 ! [A: code_integer,C: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.45/5.81 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.45/5.81 => ! [B4: code_integer] :
% 5.45/5.81 ( ( B4 != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ B4 @ one_one_Code_integer )
% 5.45/5.81 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.45/5.81 = B4 )
% 5.45/5.81 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B4 )
% 5.45/5.81 = A )
% 5.45/5.81 => ( ( ( times_3573771949741848930nteger @ A @ B4 )
% 5.45/5.81 = one_one_Code_integer )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.45/5.81 != ( times_3573771949741848930nteger @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unitE
% 5.45/5.81 thf(fact_8289_is__unitE,axiom,
% 5.45/5.81 ! [A: code_natural,C: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ A @ one_one_Code_natural )
% 5.45/5.81 => ~ ( ( A != zero_z2226904508553997617atural )
% 5.45/5.81 => ! [B4: code_natural] :
% 5.45/5.81 ( ( B4 != zero_z2226904508553997617atural )
% 5.45/5.81 => ( ( dvd_dvd_Code_natural @ B4 @ one_one_Code_natural )
% 5.45/5.81 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ A )
% 5.45/5.81 = B4 )
% 5.45/5.81 => ( ( ( divide5121882707175180666atural @ one_one_Code_natural @ B4 )
% 5.45/5.81 = A )
% 5.45/5.81 => ( ( ( times_2397367101498566445atural @ A @ B4 )
% 5.45/5.81 = one_one_Code_natural )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ C @ A )
% 5.45/5.81 != ( times_2397367101498566445atural @ C @ B4 ) ) ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % is_unitE
% 5.45/5.81 thf(fact_8290_evenE,axiom,
% 5.45/5.81 ! [A: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: nat] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % evenE
% 5.45/5.81 thf(fact_8291_evenE,axiom,
% 5.45/5.81 ! [A: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: int] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % evenE
% 5.45/5.81 thf(fact_8292_evenE,axiom,
% 5.45/5.81 ! [A: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: code_integer] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % evenE
% 5.45/5.81 thf(fact_8293_evenE,axiom,
% 5.45/5.81 ! [A: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: code_natural] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B4 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % evenE
% 5.45/5.81 thf(fact_8294_dvd__power__iff,axiom,
% 5.45/5.81 ! [X: code_integer,M: nat,N2: nat] :
% 5.45/5.81 ( ( X != zero_z3403309356797280102nteger )
% 5.45/5.81 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_iff
% 5.45/5.81 thf(fact_8295_dvd__power__iff,axiom,
% 5.45/5.81 ! [X: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( X != zero_zero_nat )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_iff
% 5.45/5.81 thf(fact_8296_dvd__power__iff,axiom,
% 5.45/5.81 ! [X: int,M: nat,N2: nat] :
% 5.45/5.81 ( ( X != zero_zero_int )
% 5.45/5.81 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_iff
% 5.45/5.81 thf(fact_8297_dvd__power,axiom,
% 5.45/5.81 ! [N2: nat,X: code_integer] :
% 5.45/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 | ( X = one_one_Code_integer ) )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power
% 5.45/5.81 thf(fact_8298_dvd__power,axiom,
% 5.45/5.81 ! [N2: nat,X: rat] :
% 5.45/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 | ( X = one_one_rat ) )
% 5.45/5.81 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power
% 5.45/5.81 thf(fact_8299_dvd__power,axiom,
% 5.45/5.81 ! [N2: nat,X: nat] :
% 5.45/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 | ( X = one_one_nat ) )
% 5.45/5.81 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power
% 5.45/5.81 thf(fact_8300_dvd__power,axiom,
% 5.45/5.81 ! [N2: nat,X: int] :
% 5.45/5.81 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 | ( X = one_one_int ) )
% 5.45/5.81 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power
% 5.45/5.81 thf(fact_8301_dvd__mult__cancel1,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.45/5.81 = ( N2 = one_one_nat ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_mult_cancel1
% 5.45/5.81 thf(fact_8302_dvd__mult__cancel2,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.45/5.81 = ( N2 = one_one_nat ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_mult_cancel2
% 5.45/5.81 thf(fact_8303_choose__dvd,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.81 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % choose_dvd
% 5.45/5.81 thf(fact_8304_choose__dvd,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.81 => ( dvd_dvd_rat @ ( times_times_rat @ ( semiri773545260158071498ct_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % choose_dvd
% 5.45/5.81 thf(fact_8305_choose__dvd,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.81 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % choose_dvd
% 5.45/5.81 thf(fact_8306_choose__dvd,axiom,
% 5.45/5.81 ! [K: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ K @ N2 )
% 5.45/5.81 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % choose_dvd
% 5.45/5.81 thf(fact_8307_dvd__minus__add,axiom,
% 5.45/5.81 ! [Q6: nat,N2: nat,R3: nat,M: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ Q6 @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_nat @ Q6 @ ( times_times_nat @ R3 @ M ) )
% 5.45/5.81 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q6 ) )
% 5.45/5.81 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M ) @ Q6 ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_minus_add
% 5.45/5.81 thf(fact_8308_mod__nat__eqI,axiom,
% 5.45/5.81 ! [R3: nat,N2: nat,M: nat] :
% 5.45/5.81 ( ( ord_less_nat @ R3 @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_nat @ R3 @ M )
% 5.45/5.81 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R3 ) )
% 5.45/5.81 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.45/5.81 = R3 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % mod_nat_eqI
% 5.45/5.81 thf(fact_8309_power__dvd__imp__le,axiom,
% 5.45/5.81 ! [I2: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.45/5.81 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.45/5.81 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_dvd_imp_le
% 5.45/5.81 thf(fact_8310_even__two__times__div__two,axiom,
% 5.45/5.81 ! [A: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.45/5.81 = A ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_two_times_div_two
% 5.45/5.81 thf(fact_8311_even__two__times__div__two,axiom,
% 5.45/5.81 ! [A: int] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.45/5.81 = A ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_two_times_div_two
% 5.45/5.81 thf(fact_8312_even__two__times__div__two,axiom,
% 5.45/5.81 ! [A: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.45/5.81 = A ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_two_times_div_two
% 5.45/5.81 thf(fact_8313_even__two__times__div__two,axiom,
% 5.45/5.81 ! [A: code_natural] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ( ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) )
% 5.45/5.81 = A ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_two_times_div_two
% 5.45/5.81 thf(fact_8314_power__mono__odd,axiom,
% 5.45/5.81 ! [N2: nat,A: rat,B: rat] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_rat @ A @ B )
% 5.45/5.81 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_mono_odd
% 5.45/5.81 thf(fact_8315_power__mono__odd,axiom,
% 5.45/5.81 ! [N2: nat,A: int,B: int] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_int @ A @ B )
% 5.45/5.81 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_mono_odd
% 5.45/5.81 thf(fact_8316_odd__pos,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % odd_pos
% 5.45/5.81 thf(fact_8317_dvd__power__iff__le,axiom,
% 5.45/5.81 ! [K: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.45/5.81 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.45/5.81 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % dvd_power_iff_le
% 5.45/5.81 thf(fact_8318_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > nat,B: nat] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( divide_divide_nat @ ( groups4541462559716669496nt_nat @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_plus_nat
% 5.45/5.81 @ ( groups4541462559716669496nt_nat
% 5.45/5.81 @ ^ [A5: int] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide_divide_nat
% 5.45/5.81 @ ( groups4541462559716669496nt_nat @ F
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] :
% 5.45/5.81 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8319_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > nat,B: nat] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( divide_divide_nat @ ( groups7237345082560585321er_nat @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_plus_nat
% 5.45/5.81 @ ( groups7237345082560585321er_nat
% 5.45/5.81 @ ^ [A5: code_integer] : ( divide_divide_nat @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] : ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide_divide_nat
% 5.45/5.81 @ ( groups7237345082560585321er_nat @ F
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] :
% 5.45/5.81 ~ ( dvd_dvd_nat @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8320_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > int,B: int] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( divide_divide_int @ ( groups7234854612051535045er_int @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_plus_int
% 5.45/5.81 @ ( groups7234854612051535045er_int
% 5.45/5.81 @ ^ [A5: code_integer] : ( divide_divide_int @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] : ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide_divide_int
% 5.45/5.81 @ ( groups7234854612051535045er_int @ F
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] :
% 5.45/5.81 ~ ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8321_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > int,B: int] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( divide_divide_int @ ( groups3539618377306564664at_int @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_plus_int
% 5.45/5.81 @ ( groups3539618377306564664at_int
% 5.45/5.81 @ ^ [A5: nat] : ( divide_divide_int @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] : ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide_divide_int
% 5.45/5.81 @ ( groups3539618377306564664at_int @ F
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] :
% 5.45/5.81 ~ ( dvd_dvd_int @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8322_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > code_integer,B: code_integer] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ ( groups7873554091576472773nteger @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p5714425477246183910nteger
% 5.45/5.81 @ ( groups7873554091576472773nteger
% 5.45/5.81 @ ^ [A5: int] : ( divide6298287555418463151nteger @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] : ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide6298287555418463151nteger
% 5.45/5.81 @ ( groups7873554091576472773nteger @ F
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] :
% 5.45/5.81 ~ ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8323_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > code_integer,B: code_integer] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ ( groups879477027807139574nteger @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p5714425477246183910nteger
% 5.45/5.81 @ ( groups879477027807139574nteger
% 5.45/5.81 @ ^ [A5: code_integer] : ( divide6298287555418463151nteger @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] : ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide6298287555418463151nteger
% 5.45/5.81 @ ( groups879477027807139574nteger @ F
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] :
% 5.45/5.81 ~ ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8324_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > code_integer,B: code_integer] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( divide6298287555418463151nteger @ ( groups7501900531339628137nteger @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p5714425477246183910nteger
% 5.45/5.81 @ ( groups7501900531339628137nteger
% 5.45/5.81 @ ^ [A5: nat] : ( divide6298287555418463151nteger @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] : ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide6298287555418463151nteger
% 5.45/5.81 @ ( groups7501900531339628137nteger @ F
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] :
% 5.45/5.81 ~ ( dvd_dvd_Code_integer @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8325_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > code_natural,B: code_natural] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ ( groups6697149243333190288atural @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p4538020629002901425atural
% 5.45/5.81 @ ( groups6697149243333190288atural
% 5.45/5.81 @ ^ [A5: int] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide5121882707175180666atural
% 5.45/5.81 @ ( groups6697149243333190288atural @ F
% 5.45/5.81 @ ( inf_inf_set_int @ A3
% 5.45/5.81 @ ( collect_int
% 5.45/5.81 @ ^ [A5: int] :
% 5.45/5.81 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8326_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > code_natural,B: code_natural] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ ( groups8926444216418632897atural @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p4538020629002901425atural
% 5.45/5.81 @ ( groups8926444216418632897atural
% 5.45/5.81 @ ^ [A5: code_integer] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide5121882707175180666atural
% 5.45/5.81 @ ( groups8926444216418632897atural @ F
% 5.45/5.81 @ ( inf_in1364745209274528805nteger @ A3
% 5.45/5.81 @ ( collect_Code_integer
% 5.45/5.81 @ ^ [A5: code_integer] :
% 5.45/5.81 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8327_sum__div__partition,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > code_natural,B: code_natural] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( divide5121882707175180666atural @ ( groups6325495683096345652atural @ F @ A3 ) @ B )
% 5.45/5.81 = ( plus_p4538020629002901425atural
% 5.45/5.81 @ ( groups6325495683096345652atural
% 5.45/5.81 @ ^ [A5: nat] : ( divide5121882707175180666atural @ ( F @ A5 ) @ B )
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] : ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ ( divide5121882707175180666atural
% 5.45/5.81 @ ( groups6325495683096345652atural @ F
% 5.45/5.81 @ ( inf_inf_set_nat @ A3
% 5.45/5.81 @ ( collect_nat
% 5.45/5.81 @ ^ [A5: nat] :
% 5.45/5.81 ~ ( dvd_dvd_Code_natural @ B @ ( F @ A5 ) ) ) ) )
% 5.45/5.81 @ B ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_div_partition
% 5.45/5.81 thf(fact_8328_round__diff__minimal,axiom,
% 5.45/5.81 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % round_diff_minimal
% 5.45/5.81 thf(fact_8329_oddE,axiom,
% 5.45/5.81 ! [A: nat] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: nat] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B4 ) @ one_one_nat ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % oddE
% 5.45/5.81 thf(fact_8330_oddE,axiom,
% 5.45/5.81 ! [A: int] :
% 5.45/5.81 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: int] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B4 ) @ one_one_int ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % oddE
% 5.45/5.81 thf(fact_8331_oddE,axiom,
% 5.45/5.81 ! [A: code_integer] :
% 5.45/5.81 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: code_integer] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_integer ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % oddE
% 5.45/5.81 thf(fact_8332_oddE,axiom,
% 5.45/5.81 ! [A: code_natural] :
% 5.45/5.81 ( ~ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A )
% 5.45/5.81 => ~ ! [B4: code_natural] :
% 5.45/5.81 ( A
% 5.45/5.81 != ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ B4 ) @ one_one_Code_natural ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % oddE
% 5.45/5.81 thf(fact_8333_zero__le__even__power,axiom,
% 5.45/5.81 ! [N2: nat,A: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_even_power
% 5.45/5.81 thf(fact_8334_zero__le__even__power,axiom,
% 5.45/5.81 ! [N2: nat,A: rat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_even_power
% 5.45/5.81 thf(fact_8335_zero__le__even__power,axiom,
% 5.45/5.81 ! [N2: nat,A: int] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_even_power
% 5.45/5.81 thf(fact_8336_zero__le__odd__power,axiom,
% 5.45/5.81 ! [N2: nat,A: code_integer] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.81 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_odd_power
% 5.45/5.81 thf(fact_8337_zero__le__odd__power,axiom,
% 5.45/5.81 ! [N2: nat,A: rat] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.45/5.81 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_odd_power
% 5.45/5.81 thf(fact_8338_zero__le__odd__power,axiom,
% 5.45/5.81 ! [N2: nat,A: int] :
% 5.45/5.81 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.45/5.81 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_odd_power
% 5.45/5.81 thf(fact_8339_zero__le__power__eq,axiom,
% 5.45/5.81 ! [A: code_integer,N2: nat] :
% 5.45/5.81 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_power_eq
% 5.45/5.81 thf(fact_8340_zero__le__power__eq,axiom,
% 5.45/5.81 ! [A: rat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_power_eq
% 5.45/5.81 thf(fact_8341_zero__le__power__eq,axiom,
% 5.45/5.81 ! [A: int,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.45/5.81 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_le_power_eq
% 5.45/5.81 thf(fact_8342_power__mono__even,axiom,
% 5.45/5.81 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.45/5.81 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_mono_even
% 5.45/5.81 thf(fact_8343_power__mono__even,axiom,
% 5.45/5.81 ! [N2: nat,A: rat,B: rat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.45/5.81 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_mono_even
% 5.45/5.81 thf(fact_8344_power__mono__even,axiom,
% 5.45/5.81 ! [N2: nat,A: int,B: int] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.45/5.81 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_mono_even
% 5.45/5.81 thf(fact_8345_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_set_nat,R: set_nat > set_nat > $o] :
% 5.45/5.81 ( ( finite1152437895449049373et_nat @ A3 )
% 5.45/5.81 => ( ! [X3: set_nat] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: set_nat,Y3: set_nat,Z2: set_nat] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: set_nat] :
% 5.45/5.81 ( ( member_set_nat @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: set_nat] :
% 5.45/5.81 ( ( member_set_nat @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bot_set_set_nat ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8346_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,R: code_integer > code_integer > $o] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ! [X3: code_integer] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: code_integer,Y3: code_integer,Z2: code_integer] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: code_integer] :
% 5.45/5.81 ( ( member_Code_integer @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: code_integer] :
% 5.45/5.81 ( ( member_Code_integer @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bo3990330152332043303nteger ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8347_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_Pr1261947904930325089at_nat,R: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.45/5.81 ( ( finite6177210948735845034at_nat @ A3 )
% 5.45/5.81 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,Z2: product_prod_nat_nat] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: product_prod_nat_nat] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: product_prod_nat_nat] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bo2099793752762293965at_nat ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8348_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_o,R: $o > $o > $o] :
% 5.45/5.81 ( ( finite_finite_o @ A3 )
% 5.45/5.81 => ( ! [X3: $o] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: $o,Y3: $o,Z2: $o] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: $o] :
% 5.45/5.81 ( ( member_o @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: $o] :
% 5.45/5.81 ( ( member_o @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bot_set_o ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8349_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_nat,R: nat > nat > $o] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ! [X3: nat] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: nat,Y3: nat,Z2: nat] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: nat] :
% 5.45/5.81 ( ( member_nat @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: nat] :
% 5.45/5.81 ( ( member_nat @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bot_set_nat ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8350_finite__transitivity__chain,axiom,
% 5.45/5.81 ! [A3: set_int,R: int > int > $o] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ! [X3: int] :
% 5.45/5.81 ~ ( R @ X3 @ X3 )
% 5.45/5.81 => ( ! [X3: int,Y3: int,Z2: int] :
% 5.45/5.81 ( ( R @ X3 @ Y3 )
% 5.45/5.81 => ( ( R @ Y3 @ Z2 )
% 5.45/5.81 => ( R @ X3 @ Z2 ) ) )
% 5.45/5.81 => ( ! [X3: int] :
% 5.45/5.81 ( ( member_int @ X3 @ A3 )
% 5.45/5.81 => ? [Y6: int] :
% 5.45/5.81 ( ( member_int @ Y6 @ A3 )
% 5.45/5.81 & ( R @ X3 @ Y6 ) ) )
% 5.45/5.81 => ( A3 = bot_bot_set_int ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % finite_transitivity_chain
% 5.45/5.81 thf(fact_8351_zero__less__power__eq,axiom,
% 5.45/5.81 ! [A: code_integer,N2: nat] :
% 5.45/5.81 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.45/5.81 = ( ( N2 = zero_zero_nat )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A != zero_z3403309356797280102nteger ) )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_power_eq
% 5.45/5.81 thf(fact_8352_zero__less__power__eq,axiom,
% 5.45/5.81 ! [A: rat,N2: nat] :
% 5.45/5.81 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.45/5.81 = ( ( N2 = zero_zero_nat )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A != zero_zero_rat ) )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_power_eq
% 5.45/5.81 thf(fact_8353_zero__less__power__eq,axiom,
% 5.45/5.81 ! [A: int,N2: nat] :
% 5.45/5.81 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.45/5.81 = ( ( N2 = zero_zero_nat )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A != zero_zero_int ) )
% 5.45/5.81 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_power_eq
% 5.45/5.81 thf(fact_8354_unbounded__k__infinite,axiom,
% 5.45/5.81 ! [K: nat,S: set_nat] :
% 5.45/5.81 ( ! [M5: nat] :
% 5.45/5.81 ( ( ord_less_nat @ K @ M5 )
% 5.45/5.81 => ? [N9: nat] :
% 5.45/5.81 ( ( ord_less_nat @ M5 @ N9 )
% 5.45/5.81 & ( member_nat @ N9 @ S ) ) )
% 5.45/5.81 => ~ ( finite_finite_nat @ S ) ) ).
% 5.45/5.81
% 5.45/5.81 % unbounded_k_infinite
% 5.45/5.81 thf(fact_8355_infinite__nat__iff__unbounded,axiom,
% 5.45/5.81 ! [S: set_nat] :
% 5.45/5.81 ( ( ~ ( finite_finite_nat @ S ) )
% 5.45/5.81 = ( ! [M3: nat] :
% 5.45/5.81 ? [N: nat] :
% 5.45/5.81 ( ( ord_less_nat @ M3 @ N )
% 5.45/5.81 & ( member_nat @ N @ S ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % infinite_nat_iff_unbounded
% 5.45/5.81 thf(fact_8356_infinite__nat__iff__unbounded__le,axiom,
% 5.45/5.81 ! [S: set_nat] :
% 5.45/5.81 ( ( ~ ( finite_finite_nat @ S ) )
% 5.45/5.81 = ( ! [M3: nat] :
% 5.45/5.81 ? [N: nat] :
% 5.45/5.81 ( ( ord_less_eq_nat @ M3 @ N )
% 5.45/5.81 & ( member_nat @ N @ S ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % infinite_nat_iff_unbounded_le
% 5.45/5.81 thf(fact_8357_even__mask__div__iff_H,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff'
% 5.45/5.81 thf(fact_8358_even__mask__div__iff_H,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff'
% 5.45/5.81 thf(fact_8359_even__mask__div__iff_H,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff'
% 5.45/5.81 thf(fact_8360_even__mask__div__iff_H,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff'
% 5.45/5.81 thf(fact_8361_power__le__zero__eq,axiom,
% 5.45/5.81 ! [A: code_integer,N2: nat] :
% 5.45/5.81 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ zero_z3403309356797280102nteger )
% 5.45/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A = zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_zero_eq
% 5.45/5.81 thf(fact_8362_power__le__zero__eq,axiom,
% 5.45/5.81 ! [A: rat,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.45/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_zero_eq
% 5.45/5.81 thf(fact_8363_power__le__zero__eq,axiom,
% 5.45/5.81 ! [A: int,N2: nat] :
% 5.45/5.81 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.45/5.81 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.45/5.81 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.45/5.81 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % power_le_zero_eq
% 5.45/5.81 thf(fact_8364_even__mask__div__iff,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_zero_nat )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff
% 5.45/5.81 thf(fact_8365_even__mask__div__iff,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_zero_int )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff
% 5.45/5.81 thf(fact_8366_even__mask__div__iff,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_z3403309356797280102nteger )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff
% 5.45/5.81 thf(fact_8367_even__mask__div__iff,axiom,
% 5.45/5.81 ! [M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( minus_7197305767214868737atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ one_one_Code_natural ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_z2226904508553997617atural )
% 5.45/5.81 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mask_div_iff
% 5.45/5.81 thf(fact_8368_even__mult__exp__div__exp__iff,axiom,
% 5.45/5.81 ! [A: nat,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ord_less_nat @ N2 @ M )
% 5.45/5.81 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_zero_nat )
% 5.45/5.81 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mult_exp_div_exp_iff
% 5.45/5.81 thf(fact_8369_even__mult__exp__div__exp__iff,axiom,
% 5.45/5.81 ! [A: int,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ord_less_nat @ N2 @ M )
% 5.45/5.81 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_zero_int )
% 5.45/5.81 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mult_exp_div_exp_iff
% 5.45/5.81 thf(fact_8370_even__mult__exp__div__exp__iff,axiom,
% 5.45/5.81 ! [A: code_integer,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ord_less_nat @ N2 @ M )
% 5.45/5.81 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_z3403309356797280102nteger )
% 5.45/5.81 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mult_exp_div_exp_iff
% 5.45/5.81 thf(fact_8371_even__mult__exp__div__exp__iff,axiom,
% 5.45/5.81 ! [A: code_natural,M: nat,N2: nat] :
% 5.45/5.81 ( ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ ( times_2397367101498566445atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.45/5.81 = ( ( ord_less_nat @ N2 @ M )
% 5.45/5.81 | ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 )
% 5.45/5.81 = zero_z2226904508553997617atural )
% 5.45/5.81 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.45/5.81 & ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % even_mult_exp_div_exp_iff
% 5.45/5.81 thf(fact_8372_of__int__round__le,axiom,
% 5.45/5.81 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_int_round_le
% 5.45/5.81 thf(fact_8373_of__int__round__ge,axiom,
% 5.45/5.81 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_int_round_ge
% 5.45/5.81 thf(fact_8374_of__int__round__gt,axiom,
% 5.45/5.81 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_int_round_gt
% 5.45/5.81 thf(fact_8375_infinite__int__iff__unbounded__le,axiom,
% 5.45/5.81 ! [S: set_int] :
% 5.45/5.81 ( ( ~ ( finite_finite_int @ S ) )
% 5.45/5.81 = ( ! [M3: int] :
% 5.45/5.81 ? [N: int] :
% 5.45/5.81 ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N ) )
% 5.45/5.81 & ( member_int @ N @ S ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % infinite_int_iff_unbounded_le
% 5.45/5.81 thf(fact_8376_infinite__int__iff__unbounded,axiom,
% 5.45/5.81 ! [S: set_int] :
% 5.45/5.81 ( ( ~ ( finite_finite_int @ S ) )
% 5.45/5.81 = ( ! [M3: int] :
% 5.45/5.81 ? [N: int] :
% 5.45/5.81 ( ( ord_less_int @ M3 @ ( abs_abs_int @ N ) )
% 5.45/5.81 & ( member_int @ N @ S ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % infinite_int_iff_unbounded
% 5.45/5.81 thf(fact_8377_of__int__round__abs__le,axiom,
% 5.45/5.81 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_int_round_abs_le
% 5.45/5.81 thf(fact_8378_round__unique_H,axiom,
% 5.45/5.81 ! [X: rat,N2: int] :
% 5.45/5.81 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.45/5.81 => ( ( archim7778729529865785530nd_rat @ X )
% 5.45/5.81 = N2 ) ) ).
% 5.45/5.81
% 5.45/5.81 % round_unique'
% 5.45/5.81 thf(fact_8379_in__finite__psubset,axiom,
% 5.45/5.81 ! [A3: set_nat,B3: set_nat] :
% 5.45/5.81 ( ( member8277197624267554838et_nat @ ( produc4532415448927165861et_nat @ A3 @ B3 ) @ finite_psubset_nat )
% 5.45/5.81 = ( ( ord_less_set_nat @ A3 @ B3 )
% 5.45/5.81 & ( finite_finite_nat @ B3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % in_finite_psubset
% 5.45/5.81 thf(fact_8380_in__finite__psubset,axiom,
% 5.45/5.81 ! [A3: set_int,B3: set_int] :
% 5.45/5.81 ( ( member2572552093476627150et_int @ ( produc6363374080413544029et_int @ A3 @ B3 ) @ finite_psubset_int )
% 5.45/5.81 = ( ( ord_less_set_int @ A3 @ B3 )
% 5.45/5.81 & ( finite_finite_int @ B3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % in_finite_psubset
% 5.45/5.81 thf(fact_8381_in__finite__psubset,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,B3: set_Code_integer] :
% 5.45/5.81 ( ( member4307123515891402160nteger @ ( produc7443773368509356479nteger @ A3 @ B3 ) @ finite2416775604798480986nteger )
% 5.45/5.81 = ( ( ord_le1307284697595431911nteger @ A3 @ B3 )
% 5.45/5.81 & ( finite6017078050557962740nteger @ B3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % in_finite_psubset
% 5.45/5.81 thf(fact_8382_in__finite__psubset,axiom,
% 5.45/5.81 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.45/5.81 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ A3 @ B3 ) @ finite469560695537375940at_nat )
% 5.45/5.81 = ( ( ord_le7866589430770878221at_nat @ A3 @ B3 )
% 5.45/5.81 & ( finite6177210948735845034at_nat @ B3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % in_finite_psubset
% 5.45/5.81 thf(fact_8383_flip__bit__0,axiom,
% 5.45/5.81 ! [A: code_integer] :
% 5.45/5.81 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.45/5.81 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % flip_bit_0
% 5.45/5.81 thf(fact_8384_flip__bit__0,axiom,
% 5.45/5.81 ! [A: code_natural] :
% 5.45/5.81 ( ( bit_se168947363167071951atural @ zero_zero_nat @ A )
% 5.45/5.81 = ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ ( dvd_dvd_Code_natural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A ) ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % flip_bit_0
% 5.45/5.81 thf(fact_8385_flip__bit__0,axiom,
% 5.45/5.81 ! [A: nat] :
% 5.45/5.81 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.45/5.81 = ( 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 ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % flip_bit_0
% 5.45/5.81 thf(fact_8386_flip__bit__0,axiom,
% 5.45/5.81 ! [A: int] :
% 5.45/5.81 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.45/5.81 = ( 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 ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % flip_bit_0
% 5.45/5.81 thf(fact_8387_set__decode__def,axiom,
% 5.45/5.81 ( nat_set_decode
% 5.45/5.81 = ( ^ [X4: nat] :
% 5.45/5.81 ( collect_nat
% 5.45/5.81 @ ^ [N: nat] :
% 5.45/5.81 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % set_decode_def
% 5.45/5.81 thf(fact_8388_take__bit__rec,axiom,
% 5.45/5.81 ( bit_se1745604003318907178nteger
% 5.45/5.81 = ( ^ [N: nat,A5: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_rec
% 5.45/5.81 thf(fact_8389_take__bit__rec,axiom,
% 5.45/5.81 ( bit_se569199155075624693atural
% 5.45/5.81 = ( ^ [N: nat,A5: code_natural] : ( if_Code_natural @ ( N = zero_zero_nat ) @ zero_z2226904508553997617atural @ ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide5121882707175180666atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A5 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_rec
% 5.45/5.81 thf(fact_8390_take__bit__rec,axiom,
% 5.45/5.81 ( bit_se2925701944663578781it_nat
% 5.45/5.81 = ( ^ [N: nat,A5: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_rec
% 5.45/5.81 thf(fact_8391_take__bit__rec,axiom,
% 5.45/5.81 ( bit_se2923211474154528505it_int
% 5.45/5.81 = ( ^ [N: nat,A5: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_rec
% 5.45/5.81 thf(fact_8392_divmod__step__def,axiom,
% 5.45/5.81 ( unique5026877609467782581ep_nat
% 5.45/5.81 = ( ^ [L2: num] :
% 5.45/5.81 ( produc2626176000494625587at_nat
% 5.45/5.81 @ ^ [Q7: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q7 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % divmod_step_def
% 5.45/5.81 thf(fact_8393_divmod__step__def,axiom,
% 5.45/5.81 ( unique5024387138958732305ep_int
% 5.45/5.81 = ( ^ [L2: num] :
% 5.45/5.81 ( produc4245557441103728435nt_int
% 5.45/5.81 @ ^ [Q7: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q7 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % divmod_step_def
% 5.45/5.81 thf(fact_8394_divmod__step__def,axiom,
% 5.45/5.81 ( unique4921790084139445826nteger
% 5.45/5.81 = ( ^ [L2: num] :
% 5.45/5.81 ( produc6916734918728496179nteger
% 5.45/5.81 @ ^ [Q7: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q7 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % divmod_step_def
% 5.45/5.81 thf(fact_8395_one__mod__2__pow__eq,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.81 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % one_mod_2_pow_eq
% 5.45/5.81 thf(fact_8396_one__mod__2__pow__eq,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( modulo8411746178871703098atural @ one_one_Code_natural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.81 = ( zero_n8403883297036319079atural @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % one_mod_2_pow_eq
% 5.45/5.81 thf(fact_8397_one__mod__2__pow__eq,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.81 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % one_mod_2_pow_eq
% 5.45/5.81 thf(fact_8398_one__mod__2__pow__eq,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.45/5.81 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % one_mod_2_pow_eq
% 5.45/5.81 thf(fact_8399_of__bool__less__eq__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.45/5.81 = ( P
% 5.45/5.81 => Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_eq_iff
% 5.45/5.81 thf(fact_8400_of__bool__less__eq__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.45/5.81 = ( P
% 5.45/5.81 => Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_eq_iff
% 5.45/5.81 thf(fact_8401_of__bool__less__eq__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.45/5.81 = ( P
% 5.45/5.81 => Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_eq_iff
% 5.45/5.81 thf(fact_8402_of__bool__less__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.45/5.81 = ( ~ P
% 5.45/5.81 & Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_iff
% 5.45/5.81 thf(fact_8403_of__bool__less__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.45/5.81 = ( ~ P
% 5.45/5.81 & Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_iff
% 5.45/5.81 thf(fact_8404_of__bool__less__iff,axiom,
% 5.45/5.81 ! [P: $o,Q: $o] :
% 5.45/5.81 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.45/5.81 = ( ~ P
% 5.45/5.81 & Q ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_iff
% 5.45/5.81 thf(fact_8405_of__nat__of__bool,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.45/5.81 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_nat_of_bool
% 5.45/5.81 thf(fact_8406_of__nat__of__bool,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.45/5.81 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_nat_of_bool
% 5.45/5.81 thf(fact_8407_of__nat__of__bool,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.45/5.81 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.45/5.81
% 5.45/5.81 % of_nat_of_bool
% 5.45/5.81 thf(fact_8408_pair__imageI,axiom,
% 5.45/5.81 ! [A: nat,B: nat,A3: set_Pr1261947904930325089at_nat,F: nat > nat > $o] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_o @ ( F @ A @ B ) @ ( image_3693632289388996572_nat_o @ ( produc6081775807080527818_nat_o @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8409_pair__imageI,axiom,
% 5.45/5.81 ! [A: nat,B: nat,A3: set_Pr1261947904930325089at_nat,F: nat > nat > nat] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_nat @ ( F @ A @ B ) @ ( image_2486076414777270412at_nat @ ( produc6842872674320459806at_nat @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8410_pair__imageI,axiom,
% 5.45/5.81 ! [A: nat,B: nat,A3: set_Pr1261947904930325089at_nat,F: nat > nat > int] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_int @ ( F @ A @ B ) @ ( image_2483585944268220136at_int @ ( produc6840382203811409530at_int @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8411_pair__imageI,axiom,
% 5.45/5.81 ! [A: int,B: int,A3: set_Pr958786334691620121nt_int,F: int > int > $o] :
% 5.45/5.81 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_o @ ( F @ A @ B ) @ ( image_2135063354759101220_int_o @ ( produc4947309494688390418_int_o @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8412_pair__imageI,axiom,
% 5.45/5.81 ! [A: int,B: int,A3: set_Pr958786334691620121nt_int,F: int > int > int] :
% 5.45/5.81 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_int @ ( F @ A @ B ) @ ( image_5042161079198086560nt_int @ ( produc8211389475949308722nt_int @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8413_pair__imageI,axiom,
% 5.45/5.81 ! [A: nat,B: nat,A3: set_Pr1261947904930325089at_nat,F: nat > nat > set_nat] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_set_nat @ ( F @ A @ B ) @ ( image_15824709712370754et_nat @ ( produc6189476227299908564et_nat @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8414_pair__imageI,axiom,
% 5.45/5.81 ! [A: nat,B: nat,A3: set_Pr1261947904930325089at_nat,F: nat > nat > product_prod_nat_nat] :
% 5.45/5.81 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member8440522571783428010at_nat @ ( F @ A @ B ) @ ( image_5168914502847457605at_nat @ ( produc2626176000494625587at_nat @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8415_pair__imageI,axiom,
% 5.45/5.81 ! [A: int,B: int,A3: set_Pr958786334691620121nt_int,F: int > int > product_prod_int_int] :
% 5.45/5.81 ( ( member5262025264175285858nt_int @ ( product_Pair_int_int @ A @ B ) @ A3 )
% 5.45/5.81 => ( member5262025264175285858nt_int @ ( F @ A @ B ) @ ( image_2653370878348428101nt_int @ ( produc4245557441103728435nt_int @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8416_pair__imageI,axiom,
% 5.45/5.81 ! [A: a,B: produc6653097349344004940it_nat,A3: set_Pr7098220151150636591it_nat,F: a > produc6653097349344004940it_nat > $o] :
% 5.45/5.81 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_o @ ( F @ A @ B ) @ ( image_1991556864075471768_nat_o @ ( produc8860486935419594360_nat_o @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8417_pair__imageI,axiom,
% 5.45/5.81 ! [A: a,B: produc6653097349344004940it_nat,A3: set_Pr7098220151150636591it_nat,F: a > produc6653097349344004940it_nat > nat] :
% 5.45/5.81 ( ( member4554412811331277712it_nat @ ( produc9178034014595674355it_nat @ A @ B ) @ A3 )
% 5.45/5.81 => ( member_nat @ ( F @ A @ B ) @ ( image_1030127162643715024at_nat @ ( produc7727125748877983984at_nat @ F ) @ A3 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % pair_imageI
% 5.45/5.81 thf(fact_8418_case__prod__conv,axiom,
% 5.45/5.81 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.45/5.81 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.45/5.81 = ( F @ A @ B ) ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_conv
% 5.45/5.81 thf(fact_8419_case__prod__conv,axiom,
% 5.45/5.81 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.45/5.81 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.45/5.81 = ( F @ A @ B ) ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_conv
% 5.45/5.81 thf(fact_8420_case__prod__conv,axiom,
% 5.45/5.81 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.45/5.81 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.45/5.81 = ( F @ A @ B ) ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_conv
% 5.45/5.81 thf(fact_8421_case__prod__conv,axiom,
% 5.45/5.81 ! [F: int > int > $o,A: int,B: int] :
% 5.45/5.81 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.45/5.81 = ( F @ A @ B ) ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_conv
% 5.45/5.81 thf(fact_8422_case__prod__conv,axiom,
% 5.45/5.81 ! [F: int > int > int,A: int,B: int] :
% 5.45/5.81 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.45/5.81 = ( F @ A @ B ) ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_conv
% 5.45/5.81 thf(fact_8423_curry__case__prod,axiom,
% 5.45/5.81 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.45/5.81 ( ( produc3610074571335452306at_nat @ ( produc27273713700761075at_nat @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % curry_case_prod
% 5.45/5.81 thf(fact_8424_curry__case__prod,axiom,
% 5.45/5.81 ! [F: nat > nat > product_prod_nat_nat > $o] :
% 5.45/5.81 ( ( produc3704529784387675049_nat_o @ ( produc8739625826339149834_nat_o @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % curry_case_prod
% 5.45/5.81 thf(fact_8425_curry__case__prod,axiom,
% 5.45/5.81 ! [F: int > int > product_prod_int_int] :
% 5.45/5.81 ( ( produc8249235968001453780nt_int @ ( produc4245557441103728435nt_int @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % curry_case_prod
% 5.45/5.81 thf(fact_8426_curry__case__prod,axiom,
% 5.45/5.81 ! [F: int > int > $o] :
% 5.45/5.81 ( ( produc175634133007206835_int_o @ ( produc4947309494688390418_int_o @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % curry_case_prod
% 5.45/5.81 thf(fact_8427_curry__case__prod,axiom,
% 5.45/5.81 ! [F: int > int > int] :
% 5.45/5.81 ( ( produc1016772743285680337nt_int @ ( produc8211389475949308722nt_int @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % curry_case_prod
% 5.45/5.81 thf(fact_8428_case__prod__curry,axiom,
% 5.45/5.81 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.45/5.81 ( ( produc27273713700761075at_nat @ ( produc3610074571335452306at_nat @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_curry
% 5.45/5.81 thf(fact_8429_case__prod__curry,axiom,
% 5.45/5.81 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.45/5.81 ( ( produc8739625826339149834_nat_o @ ( produc3704529784387675049_nat_o @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_curry
% 5.45/5.81 thf(fact_8430_case__prod__curry,axiom,
% 5.45/5.81 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.45/5.81 ( ( produc4245557441103728435nt_int @ ( produc8249235968001453780nt_int @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_curry
% 5.45/5.81 thf(fact_8431_case__prod__curry,axiom,
% 5.45/5.81 ! [F: product_prod_int_int > $o] :
% 5.45/5.81 ( ( produc4947309494688390418_int_o @ ( produc175634133007206835_int_o @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_curry
% 5.45/5.81 thf(fact_8432_case__prod__curry,axiom,
% 5.45/5.81 ! [F: product_prod_int_int > int] :
% 5.45/5.81 ( ( produc8211389475949308722nt_int @ ( produc1016772743285680337nt_int @ F ) )
% 5.45/5.81 = F ) ).
% 5.45/5.81
% 5.45/5.81 % case_prod_curry
% 5.45/5.81 thf(fact_8433_take__bit__of__Suc__0,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.45/5.81 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_of_Suc_0
% 5.45/5.81 thf(fact_8434_zero__less__of__bool__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.45/5.81 = P ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_of_bool_iff
% 5.45/5.81 thf(fact_8435_zero__less__of__bool__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.45/5.81 = P ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_of_bool_iff
% 5.45/5.81 thf(fact_8436_zero__less__of__bool__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.45/5.81 = P ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_of_bool_iff
% 5.45/5.81 thf(fact_8437_zero__less__of__bool__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.45/5.81 = P ) ).
% 5.45/5.81
% 5.45/5.81 % zero_less_of_bool_iff
% 5.45/5.81 thf(fact_8438_of__bool__less__one__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.45/5.81 = ~ P ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_one_iff
% 5.45/5.81 thf(fact_8439_of__bool__less__one__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.45/5.81 = ~ P ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_one_iff
% 5.45/5.81 thf(fact_8440_of__bool__less__one__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.45/5.81 = ~ P ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_one_iff
% 5.45/5.81 thf(fact_8441_of__bool__less__one__iff,axiom,
% 5.45/5.81 ! [P: $o] :
% 5.45/5.81 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.45/5.81 = ~ P ) ).
% 5.45/5.81
% 5.45/5.81 % of_bool_less_one_iff
% 5.45/5.81 thf(fact_8442_set__decode__zero,axiom,
% 5.45/5.81 ( ( nat_set_decode @ zero_zero_nat )
% 5.45/5.81 = bot_bot_set_nat ) ).
% 5.45/5.81
% 5.45/5.81 % set_decode_zero
% 5.45/5.81 thf(fact_8443_sgn__mult__self__eq,axiom,
% 5.45/5.81 ! [A: code_integer] :
% 5.45/5.81 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.45/5.81 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_mult_self_eq
% 5.45/5.81 thf(fact_8444_sgn__mult__self__eq,axiom,
% 5.45/5.81 ! [A: rat] :
% 5.45/5.81 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.45/5.81 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_mult_self_eq
% 5.45/5.81 thf(fact_8445_sgn__mult__self__eq,axiom,
% 5.45/5.81 ! [A: int] :
% 5.45/5.81 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.45/5.81 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_mult_self_eq
% 5.45/5.81 thf(fact_8446_take__bit__of__1,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 5.45/5.81 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_of_1
% 5.45/5.81 thf(fact_8447_take__bit__of__1,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.45/5.81 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_of_1
% 5.45/5.81 thf(fact_8448_take__bit__of__1,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.45/5.81 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % take_bit_of_1
% 5.45/5.81 thf(fact_8449_sgn__of__nat,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.45/5.81 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_of_nat
% 5.45/5.81 thf(fact_8450_sgn__of__nat,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.45/5.81 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_of_nat
% 5.45/5.81 thf(fact_8451_sgn__of__nat,axiom,
% 5.45/5.81 ! [N2: nat] :
% 5.45/5.81 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.45/5.81 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sgn_of_nat
% 5.45/5.81 thf(fact_8452_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > code_integer,P: int > $o] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( groups7873554091576472773nteger
% 5.45/5.81 @ ^ [X4: int] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups7873554091576472773nteger @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8453_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > code_integer,P: code_integer > $o] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( groups879477027807139574nteger
% 5.45/5.81 @ ^ [X4: code_integer] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups879477027807139574nteger @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8454_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > code_integer,P: nat > $o] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( groups7501900531339628137nteger
% 5.45/5.81 @ ^ [X4: nat] : ( times_3573771949741848930nteger @ ( F @ X4 ) @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups7501900531339628137nteger @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8455_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > rat,P: int > $o] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( groups3906332499630173760nt_rat
% 5.45/5.81 @ ^ [X4: int] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8456_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > rat,P: code_integer > $o] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( groups6602215022474089585er_rat
% 5.45/5.81 @ ^ [X4: code_integer] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8457_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > rat,P: nat > $o] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( groups2906978787729119204at_rat
% 5.45/5.81 @ ^ [X4: nat] : ( times_times_rat @ ( F @ X4 ) @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8458_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_int,F: int > nat,P: int > $o] :
% 5.45/5.81 ( ( finite_finite_int @ A3 )
% 5.45/5.81 => ( ( groups4541462559716669496nt_nat
% 5.45/5.81 @ ^ [X4: int] : ( times_times_nat @ ( F @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8459_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > nat,P: code_integer > $o] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( groups7237345082560585321er_nat
% 5.45/5.81 @ ^ [X4: code_integer] : ( times_times_nat @ ( F @ X4 ) @ ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8460_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_Code_integer,F: code_integer > int,P: code_integer > $o] :
% 5.45/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.45/5.81 => ( ( groups7234854612051535045er_int
% 5.45/5.81 @ ^ [X4: code_integer] : ( times_times_int @ ( F @ X4 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X4 ) ) )
% 5.45/5.81 @ A3 )
% 5.45/5.81 = ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.45/5.81
% 5.45/5.81 % sum_mult_of_bool_eq
% 5.45/5.81 thf(fact_8461_sum__mult__of__bool__eq,axiom,
% 5.45/5.81 ! [A3: set_nat,F: nat > int,P: nat > $o] :
% 5.45/5.81 ( ( finite_finite_nat @ A3 )
% 5.45/5.81 => ( ( groups3539618377306564664at_int
% 5.45/5.81 @ ^ [X4: nat] : ( times_times_int @ ( F @ X4 ) @ ( zero_n2684676970156552555ol_int @ ( P @ X4 ) ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_mult_of_bool_eq
% 5.49/5.81 thf(fact_8462_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_int,P: int > $o,F: int > code_integer] :
% 5.49/5.81 ( ( finite_finite_int @ A3 )
% 5.49/5.81 => ( ( groups7873554091576472773nteger
% 5.49/5.81 @ ^ [X4: int] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups7873554091576472773nteger @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8463_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_Code_integer,P: code_integer > $o,F: code_integer > code_integer] :
% 5.49/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.81 => ( ( groups879477027807139574nteger
% 5.49/5.81 @ ^ [X4: code_integer] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups879477027807139574nteger @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8464_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_nat,P: nat > $o,F: nat > code_integer] :
% 5.49/5.81 ( ( finite_finite_nat @ A3 )
% 5.49/5.81 => ( ( groups7501900531339628137nteger
% 5.49/5.81 @ ^ [X4: nat] : ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups7501900531339628137nteger @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8465_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_int,P: int > $o,F: int > rat] :
% 5.49/5.81 ( ( finite_finite_int @ A3 )
% 5.49/5.81 => ( ( groups3906332499630173760nt_rat
% 5.49/5.81 @ ^ [X4: int] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups3906332499630173760nt_rat @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8466_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_Code_integer,P: code_integer > $o,F: code_integer > rat] :
% 5.49/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.81 => ( ( groups6602215022474089585er_rat
% 5.49/5.81 @ ^ [X4: code_integer] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups6602215022474089585er_rat @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8467_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_nat,P: nat > $o,F: nat > rat] :
% 5.49/5.81 ( ( finite_finite_nat @ A3 )
% 5.49/5.81 => ( ( groups2906978787729119204at_rat
% 5.49/5.81 @ ^ [X4: nat] : ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups2906978787729119204at_rat @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8468_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_int,P: int > $o,F: int > nat] :
% 5.49/5.81 ( ( finite_finite_int @ A3 )
% 5.49/5.81 => ( ( groups4541462559716669496nt_nat
% 5.49/5.81 @ ^ [X4: int] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups4541462559716669496nt_nat @ F @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8469_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_Code_integer,P: code_integer > $o,F: code_integer > nat] :
% 5.49/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.81 => ( ( groups7237345082560585321er_nat
% 5.49/5.81 @ ^ [X4: code_integer] : ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups7237345082560585321er_nat @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8470_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_Code_integer,P: code_integer > $o,F: code_integer > int] :
% 5.49/5.81 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.81 => ( ( groups7234854612051535045er_int
% 5.49/5.81 @ ^ [X4: code_integer] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups7234854612051535045er_int @ F @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8471_sum__of__bool__mult__eq,axiom,
% 5.49/5.81 ! [A3: set_nat,P: nat > $o,F: nat > int] :
% 5.49/5.81 ( ( finite_finite_nat @ A3 )
% 5.49/5.81 => ( ( groups3539618377306564664at_int
% 5.49/5.81 @ ^ [X4: nat] : ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( P @ X4 ) ) @ ( F @ X4 ) )
% 5.49/5.81 @ A3 )
% 5.49/5.81 = ( groups3539618377306564664at_int @ F @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_of_bool_mult_eq
% 5.49/5.81 thf(fact_8472_take__bit__of__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_exp
% 5.49/5.81 thf(fact_8473_take__bit__of__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ M @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ N2 @ M ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_exp
% 5.49/5.81 thf(fact_8474_take__bit__of__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_exp
% 5.49/5.81 thf(fact_8475_take__bit__of__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_exp
% 5.49/5.81 thf(fact_8476_take__bit__of__2,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_2
% 5.49/5.81 thf(fact_8477_take__bit__of__2,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.49/5.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_2
% 5.49/5.81 thf(fact_8478_take__bit__of__2,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_2
% 5.49/5.81 thf(fact_8479_take__bit__of__2,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_of_2
% 5.49/5.81 thf(fact_8480_nested__case__prod__simp,axiom,
% 5.49/5.81 ( produc27273713700761075at_nat
% 5.49/5.81 = ( ^ [F3: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.49/5.81 ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [A5: nat,B5: nat] : ( F3 @ A5 @ B5 @ Y4 )
% 5.49/5.81 @ X4 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % nested_case_prod_simp
% 5.49/5.81 thf(fact_8481_nested__case__prod__simp,axiom,
% 5.49/5.81 ( produc8739625826339149834_nat_o
% 5.49/5.81 = ( ^ [F3: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.49/5.81 ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [A5: nat,B5: nat] : ( F3 @ A5 @ B5 @ Y4 )
% 5.49/5.81 @ X4 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % nested_case_prod_simp
% 5.49/5.81 thf(fact_8482_case__prod__app,axiom,
% 5.49/5.81 ( produc27273713700761075at_nat
% 5.49/5.81 = ( ^ [F3: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.49/5.81 ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [L2: nat,R4: nat] : ( F3 @ L2 @ R4 @ Y4 )
% 5.49/5.81 @ X4 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_app
% 5.49/5.81 thf(fact_8483_case__prod__app,axiom,
% 5.49/5.81 ( produc8739625826339149834_nat_o
% 5.49/5.81 = ( ^ [F3: nat > nat > product_prod_nat_nat > $o,X4: product_prod_nat_nat,Y4: product_prod_nat_nat] :
% 5.49/5.81 ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [L2: nat,R4: nat] : ( F3 @ L2 @ R4 @ Y4 )
% 5.49/5.81 @ X4 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_app
% 5.49/5.81 thf(fact_8484_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: $o > $o,F: int > int > $o,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.49/5.81 = ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8485_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: $o > int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.49/5.81 = ( produc8211389475949308722nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8486_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: int > $o,F: int > int > int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8487_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: int > int,F: int > int > int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc8211389475949308722nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8488_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: product_prod_int_int > $o,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8489_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: product_prod_int_int > int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc8211389475949308722nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8490_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: $o > product_prod_int_int,F: int > int > $o,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4947309494688390418_int_o @ F @ Prod ) )
% 5.49/5.81 = ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8491_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: int > product_prod_int_int,F: int > int > int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc8211389475949308722nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8492_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: product_prod_int_int > product_prod_int_int,F: int > int > product_prod_int_int,Prod: product_prod_int_int] :
% 5.49/5.81 ( ( H @ ( produc4245557441103728435nt_int @ F @ Prod ) )
% 5.49/5.81 = ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [X13: int,X23: int] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8493_prod_Ocase__distrib,axiom,
% 5.49/5.81 ! [H: ( product_prod_nat_nat > $o ) > product_prod_nat_nat > $o,F: nat > nat > product_prod_nat_nat > $o,Prod: product_prod_nat_nat] :
% 5.49/5.81 ( ( H @ ( produc8739625826339149834_nat_o @ F @ Prod ) )
% 5.49/5.81 = ( produc8739625826339149834_nat_o
% 5.49/5.81 @ ^ [X13: nat,X23: nat] : ( H @ ( F @ X13 @ X23 ) )
% 5.49/5.81 @ Prod ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.case_distrib
% 5.49/5.81 thf(fact_8494_take__bit__tightened,axiom,
% 5.49/5.81 ! [N2: nat,A: nat,B: nat,M: nat] :
% 5.49/5.81 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 5.49/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_tightened
% 5.49/5.81 thf(fact_8495_take__bit__tightened,axiom,
% 5.49/5.81 ! [N2: nat,A: int,B: int,M: nat] :
% 5.49/5.81 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.49/5.81 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_tightened
% 5.49/5.81 thf(fact_8496_take__bit__tightened__less__eq__nat,axiom,
% 5.49/5.81 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.81 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q6 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q6 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_tightened_less_eq_nat
% 5.49/5.81 thf(fact_8497_take__bit__nat__less__eq__self,axiom,
% 5.49/5.81 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_less_eq_self
% 5.49/5.81 thf(fact_8498_of__bool__conj,axiom,
% 5.49/5.81 ! [P: $o,Q: $o] :
% 5.49/5.81 ( ( zero_n356916108424825756nteger
% 5.49/5.81 @ ( P
% 5.49/5.81 & Q ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_conj
% 5.49/5.81 thf(fact_8499_of__bool__conj,axiom,
% 5.49/5.81 ! [P: $o,Q: $o] :
% 5.49/5.81 ( ( zero_n2052037380579107095ol_rat
% 5.49/5.81 @ ( P
% 5.49/5.81 & Q ) )
% 5.49/5.81 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_conj
% 5.49/5.81 thf(fact_8500_of__bool__conj,axiom,
% 5.49/5.81 ! [P: $o,Q: $o] :
% 5.49/5.81 ( ( zero_n2687167440665602831ol_nat
% 5.49/5.81 @ ( P
% 5.49/5.81 & Q ) )
% 5.49/5.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_conj
% 5.49/5.81 thf(fact_8501_of__bool__conj,axiom,
% 5.49/5.81 ! [P: $o,Q: $o] :
% 5.49/5.81 ( ( zero_n2684676970156552555ol_int
% 5.49/5.81 @ ( P
% 5.49/5.81 & Q ) )
% 5.49/5.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_conj
% 5.49/5.81 thf(fact_8502_split__cong,axiom,
% 5.49/5.81 ! [Q6: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: nat > nat > product_prod_nat_nat > product_prod_nat_nat,P3: product_prod_nat_nat] :
% 5.49/5.81 ( ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( ( product_Pair_nat_nat @ X3 @ Y3 )
% 5.49/5.81 = Q6 )
% 5.49/5.81 => ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( P3 = Q6 )
% 5.49/5.81 => ( ( produc27273713700761075at_nat @ F @ P3 )
% 5.49/5.81 = ( produc27273713700761075at_nat @ G @ Q6 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_cong
% 5.49/5.81 thf(fact_8503_split__cong,axiom,
% 5.49/5.81 ! [Q6: product_prod_nat_nat,F: nat > nat > product_prod_nat_nat > $o,G: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat] :
% 5.49/5.81 ( ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( ( product_Pair_nat_nat @ X3 @ Y3 )
% 5.49/5.81 = Q6 )
% 5.49/5.81 => ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( P3 = Q6 )
% 5.49/5.81 => ( ( produc8739625826339149834_nat_o @ F @ P3 )
% 5.49/5.81 = ( produc8739625826339149834_nat_o @ G @ Q6 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_cong
% 5.49/5.81 thf(fact_8504_split__cong,axiom,
% 5.49/5.81 ! [Q6: product_prod_int_int,F: int > int > product_prod_int_int,G: int > int > product_prod_int_int,P3: product_prod_int_int] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 5.49/5.81 = Q6 )
% 5.49/5.81 => ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( P3 = Q6 )
% 5.49/5.81 => ( ( produc4245557441103728435nt_int @ F @ P3 )
% 5.49/5.81 = ( produc4245557441103728435nt_int @ G @ Q6 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_cong
% 5.49/5.81 thf(fact_8505_split__cong,axiom,
% 5.49/5.81 ! [Q6: product_prod_int_int,F: int > int > $o,G: int > int > $o,P3: product_prod_int_int] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 5.49/5.81 = Q6 )
% 5.49/5.81 => ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( P3 = Q6 )
% 5.49/5.81 => ( ( produc4947309494688390418_int_o @ F @ P3 )
% 5.49/5.81 = ( produc4947309494688390418_int_o @ G @ Q6 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_cong
% 5.49/5.81 thf(fact_8506_split__cong,axiom,
% 5.49/5.81 ! [Q6: product_prod_int_int,F: int > int > int,G: int > int > int,P3: product_prod_int_int] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( ( product_Pair_int_int @ X3 @ Y3 )
% 5.49/5.81 = Q6 )
% 5.49/5.81 => ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( P3 = Q6 )
% 5.49/5.81 => ( ( produc8211389475949308722nt_int @ F @ P3 )
% 5.49/5.81 = ( produc8211389475949308722nt_int @ G @ Q6 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_cong
% 5.49/5.81 thf(fact_8507_old_Oprod_Ocase,axiom,
% 5.49/5.81 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X2: nat] :
% 5.49/5.81 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 5.49/5.81 = ( F @ X1 @ X2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % old.prod.case
% 5.49/5.81 thf(fact_8508_old_Oprod_Ocase,axiom,
% 5.49/5.81 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X2: nat] :
% 5.49/5.81 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X2 ) )
% 5.49/5.81 = ( F @ X1 @ X2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % old.prod.case
% 5.49/5.81 thf(fact_8509_old_Oprod_Ocase,axiom,
% 5.49/5.81 ! [F: int > int > product_prod_int_int,X1: int,X2: int] :
% 5.49/5.81 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 5.49/5.81 = ( F @ X1 @ X2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % old.prod.case
% 5.49/5.81 thf(fact_8510_old_Oprod_Ocase,axiom,
% 5.49/5.81 ! [F: int > int > $o,X1: int,X2: int] :
% 5.49/5.81 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 5.49/5.81 = ( F @ X1 @ X2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % old.prod.case
% 5.49/5.81 thf(fact_8511_old_Oprod_Ocase,axiom,
% 5.49/5.81 ! [F: int > int > int,X1: int,X2: int] :
% 5.49/5.81 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X2 ) )
% 5.49/5.81 = ( F @ X1 @ X2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % old.prod.case
% 5.49/5.81 thf(fact_8512_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( produc4058941399401191971et_nat @ produc5001842942810119800et_nat @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8513_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: produc2732055786443039994et_nat] :
% 5.49/5.81 ( ( produc2377985495875741467et_nat @ produc2245416461498447860et_nat @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8514_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: produc2285326912895808259nt_int] :
% 5.49/5.81 ( ( produc8492565224438309093nt_int @ produc5700946648718959541nt_int @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8515_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( produc5122537100556696953nt_int @ produc4305682042979456191nt_int @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8516_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( produc2183267410226956569it_nat @ produc9178034014595674355it_nat @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8517_case__prod__Pair__iden,axiom,
% 5.49/5.81 ! [P3: product_prod_int_int] :
% 5.49/5.81 ( ( produc4245557441103728435nt_int @ product_Pair_int_int @ P3 )
% 5.49/5.81 = P3 ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_Pair_iden
% 5.49/5.81 thf(fact_8518_take__bit__nat__eq,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.49/5.81 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_eq
% 5.49/5.81 thf(fact_8519_nat__take__bit__eq,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.81 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % nat_take_bit_eq
% 5.49/5.81 thf(fact_8520_cond__case__prod__eta,axiom,
% 5.49/5.81 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.49/5.81 ( ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( produc27273713700761075at_nat @ F )
% 5.49/5.81 = G ) ) ).
% 5.49/5.81
% 5.49/5.81 % cond_case_prod_eta
% 5.49/5.81 thf(fact_8521_cond__case__prod__eta,axiom,
% 5.49/5.81 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.49/5.81 ( ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( produc8739625826339149834_nat_o @ F )
% 5.49/5.81 = G ) ) ).
% 5.49/5.81
% 5.49/5.81 % cond_case_prod_eta
% 5.49/5.81 thf(fact_8522_cond__case__prod__eta,axiom,
% 5.49/5.81 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( produc4245557441103728435nt_int @ F )
% 5.49/5.81 = G ) ) ).
% 5.49/5.81
% 5.49/5.81 % cond_case_prod_eta
% 5.49/5.81 thf(fact_8523_cond__case__prod__eta,axiom,
% 5.49/5.81 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( produc4947309494688390418_int_o @ F )
% 5.49/5.81 = G ) ) ).
% 5.49/5.81
% 5.49/5.81 % cond_case_prod_eta
% 5.49/5.81 thf(fact_8524_cond__case__prod__eta,axiom,
% 5.49/5.81 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.49/5.81 ( ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( F @ X3 @ Y3 )
% 5.49/5.81 = ( G @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.49/5.81 => ( ( produc8211389475949308722nt_int @ F )
% 5.49/5.81 = G ) ) ).
% 5.49/5.81
% 5.49/5.81 % cond_case_prod_eta
% 5.49/5.81 thf(fact_8525_case__prod__eta,axiom,
% 5.49/5.81 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.49/5.81 ( ( produc27273713700761075at_nat
% 5.49/5.81 @ ^ [X4: nat,Y4: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) )
% 5.49/5.81 = F ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_eta
% 5.49/5.81 thf(fact_8526_case__prod__eta,axiom,
% 5.49/5.81 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.49/5.81 ( ( produc8739625826339149834_nat_o
% 5.49/5.81 @ ^ [X4: nat,Y4: nat] : ( F @ ( product_Pair_nat_nat @ X4 @ Y4 ) ) )
% 5.49/5.81 = F ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_eta
% 5.49/5.81 thf(fact_8527_case__prod__eta,axiom,
% 5.49/5.81 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.49/5.81 ( ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 5.49/5.81 = F ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_eta
% 5.49/5.81 thf(fact_8528_case__prod__eta,axiom,
% 5.49/5.81 ! [F: product_prod_int_int > $o] :
% 5.49/5.81 ( ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 5.49/5.81 = F ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_eta
% 5.49/5.81 thf(fact_8529_case__prod__eta,axiom,
% 5.49/5.81 ! [F: product_prod_int_int > int] :
% 5.49/5.81 ( ( produc8211389475949308722nt_int
% 5.49/5.81 @ ^ [X4: int,Y4: int] : ( F @ ( product_Pair_int_int @ X4 @ Y4 ) ) )
% 5.49/5.81 = F ) ).
% 5.49/5.81
% 5.49/5.81 % case_prod_eta
% 5.49/5.81 thf(fact_8530_case__prodE2,axiom,
% 5.49/5.81 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.49/5.81 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.49/5.81 => ~ ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( Z
% 5.49/5.81 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE2
% 5.49/5.81 thf(fact_8531_case__prodE2,axiom,
% 5.49/5.81 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.49/5.81 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.49/5.81 => ~ ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( Z
% 5.49/5.81 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE2
% 5.49/5.81 thf(fact_8532_case__prodE2,axiom,
% 5.49/5.81 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.49/5.81 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.49/5.81 => ~ ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( Z
% 5.49/5.81 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE2
% 5.49/5.81 thf(fact_8533_case__prodE2,axiom,
% 5.49/5.81 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.49/5.81 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.49/5.81 => ~ ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( Z
% 5.49/5.81 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE2
% 5.49/5.81 thf(fact_8534_case__prodE2,axiom,
% 5.49/5.81 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.49/5.81 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.49/5.81 => ~ ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( Z
% 5.49/5.81 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( Q @ ( P @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE2
% 5.49/5.81 thf(fact_8535_zero__less__eq__of__bool,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.49/5.81
% 5.49/5.81 % zero_less_eq_of_bool
% 5.49/5.81 thf(fact_8536_zero__less__eq__of__bool,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.49/5.81
% 5.49/5.81 % zero_less_eq_of_bool
% 5.49/5.81 thf(fact_8537_zero__less__eq__of__bool,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.49/5.81
% 5.49/5.81 % zero_less_eq_of_bool
% 5.49/5.81 thf(fact_8538_zero__less__eq__of__bool,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.49/5.81
% 5.49/5.81 % zero_less_eq_of_bool
% 5.49/5.81 thf(fact_8539_of__bool__less__eq__one,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_less_eq_one
% 5.49/5.81 thf(fact_8540_of__bool__less__eq__one,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_less_eq_one
% 5.49/5.81 thf(fact_8541_of__bool__less__eq__one,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_less_eq_one
% 5.49/5.81 thf(fact_8542_of__bool__less__eq__one,axiom,
% 5.49/5.81 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.49/5.81
% 5.49/5.81 % of_bool_less_eq_one
% 5.49/5.81 thf(fact_8543_take__bit__tightened__less__eq__int,axiom,
% 5.49/5.81 ! [M: nat,N2: nat,K: int] :
% 5.49/5.81 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.81 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_tightened_less_eq_int
% 5.49/5.81 thf(fact_8544_take__bit__nonnegative,axiom,
% 5.49/5.81 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nonnegative
% 5.49/5.81 thf(fact_8545_take__bit__int__less__eq__self__iff,axiom,
% 5.49/5.81 ! [N2: nat,K: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.49/5.81 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_less_eq_self_iff
% 5.49/5.81 thf(fact_8546_not__take__bit__negative,axiom,
% 5.49/5.81 ! [N2: nat,K: int] :
% 5.49/5.81 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.49/5.81
% 5.49/5.81 % not_take_bit_negative
% 5.49/5.81 thf(fact_8547_take__bit__int__greater__self__iff,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.49/5.81 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_greater_self_iff
% 5.49/5.81 thf(fact_8548_signed__take__bit__take__bit,axiom,
% 5.49/5.81 ! [M: nat,N2: nat,A: int] :
% 5.49/5.81 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.49/5.81 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % signed_take_bit_take_bit
% 5.49/5.81 thf(fact_8549_take__bit__unset__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: nat] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_unset_bit_eq
% 5.49/5.81 thf(fact_8550_take__bit__unset__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: int] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_unset_bit_eq
% 5.49/5.81 thf(fact_8551_take__bit__set__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: nat] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_set_bit_eq
% 5.49/5.81 thf(fact_8552_take__bit__set__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: int] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_set_bit_eq
% 5.49/5.81 thf(fact_8553_take__bit__flip__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: nat] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.49/5.81 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_flip_bit_eq
% 5.49/5.81 thf(fact_8554_take__bit__flip__bit__eq,axiom,
% 5.49/5.81 ! [N2: nat,M: nat,A: int] :
% 5.49/5.81 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.49/5.81 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_flip_bit_eq
% 5.49/5.81 thf(fact_8555_zdvd__antisym__nonneg,axiom,
% 5.49/5.81 ! [M: int,N2: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.49/5.81 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.49/5.81 => ( ( dvd_dvd_int @ M @ N2 )
% 5.49/5.81 => ( ( dvd_dvd_int @ N2 @ M )
% 5.49/5.81 => ( M = N2 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % zdvd_antisym_nonneg
% 5.49/5.81 thf(fact_8556_zdvd__not__zless,axiom,
% 5.49/5.81 ! [M: int,N2: int] :
% 5.49/5.81 ( ( ord_less_int @ zero_zero_int @ M )
% 5.49/5.81 => ( ( ord_less_int @ M @ N2 )
% 5.49/5.81 => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % zdvd_not_zless
% 5.49/5.81 thf(fact_8557_uncurry__def,axiom,
% 5.49/5.81 uncurr8011562610307062878at_nat = produc27273713700761075at_nat ).
% 5.49/5.81
% 5.49/5.81 % uncurry_def
% 5.49/5.81 thf(fact_8558_uncurry__def,axiom,
% 5.49/5.81 uncurr7511940902602773877_nat_o = produc8739625826339149834_nat_o ).
% 5.49/5.81
% 5.49/5.81 % uncurry_def
% 5.49/5.81 thf(fact_8559_uncurry__def,axiom,
% 5.49/5.81 uncurr7650761721940715016nt_int = produc4245557441103728435nt_int ).
% 5.49/5.81
% 5.49/5.81 % uncurry_def
% 5.49/5.81 thf(fact_8560_uncurry__def,axiom,
% 5.49/5.81 uncurry_int_int_o = produc4947309494688390418_int_o ).
% 5.49/5.81
% 5.49/5.81 % uncurry_def
% 5.49/5.81 thf(fact_8561_uncurry__def,axiom,
% 5.49/5.81 uncurry_int_int_int = produc8211389475949308722nt_int ).
% 5.49/5.81
% 5.49/5.81 % uncurry_def
% 5.49/5.81 thf(fact_8562_internal__case__prod__def,axiom,
% 5.49/5.81 produc1854806715440696265at_nat = produc27273713700761075at_nat ).
% 5.49/5.81
% 5.49/5.81 % internal_case_prod_def
% 5.49/5.81 thf(fact_8563_internal__case__prod__def,axiom,
% 5.49/5.81 produc4780622933104268256_nat_o = produc8739625826339149834_nat_o ).
% 5.49/5.81
% 5.49/5.81 % internal_case_prod_def
% 5.49/5.81 thf(fact_8564_internal__case__prod__def,axiom,
% 5.49/5.81 produc297006045350968285nt_int = produc4245557441103728435nt_int ).
% 5.49/5.81
% 5.49/5.81 % internal_case_prod_def
% 5.49/5.81 thf(fact_8565_internal__case__prod__def,axiom,
% 5.49/5.81 produc8005341501107743676_int_o = produc4947309494688390418_int_o ).
% 5.49/5.81
% 5.49/5.81 % internal_case_prod_def
% 5.49/5.81 thf(fact_8566_internal__case__prod__def,axiom,
% 5.49/5.81 produc7926200574084438792nt_int = produc8211389475949308722nt_int ).
% 5.49/5.81
% 5.49/5.81 % internal_case_prod_def
% 5.49/5.81 thf(fact_8567_finite__divisors__int,axiom,
% 5.49/5.81 ! [I2: int] :
% 5.49/5.81 ( ( I2 != zero_zero_int )
% 5.49/5.81 => ( finite_finite_int
% 5.49/5.81 @ ( collect_int
% 5.49/5.81 @ ^ [D5: int] : ( dvd_dvd_int @ D5 @ I2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_divisors_int
% 5.49/5.81 thf(fact_8568_take__bit__signed__take__bit,axiom,
% 5.49/5.81 ! [M: nat,N2: nat,A: int] :
% 5.49/5.81 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 5.49/5.81 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_signed_take_bit
% 5.49/5.81 thf(fact_8569_zdvd__imp__le,axiom,
% 5.49/5.81 ! [Z: int,N2: int] :
% 5.49/5.81 ( ( dvd_dvd_int @ Z @ N2 )
% 5.49/5.81 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.49/5.81 => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % zdvd_imp_le
% 5.49/5.81 thf(fact_8570_dvd__imp__le__int,axiom,
% 5.49/5.81 ! [I2: int,D2: int] :
% 5.49/5.81 ( ( I2 != zero_zero_int )
% 5.49/5.81 => ( ( dvd_dvd_int @ D2 @ I2 )
% 5.49/5.81 => ( ord_less_eq_int @ ( abs_abs_int @ D2 ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % dvd_imp_le_int
% 5.49/5.81 thf(fact_8571_subset__decode__imp__le,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.49/5.81 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % subset_decode_imp_le
% 5.49/5.81 thf(fact_8572_mod__int__pos__iff,axiom,
% 5.49/5.81 ! [K: int,L: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.49/5.81 = ( ( dvd_dvd_int @ L @ K )
% 5.49/5.81 | ( ( L = zero_zero_int )
% 5.49/5.81 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.49/5.81 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mod_int_pos_iff
% 5.49/5.81 thf(fact_8573_take__bit__Suc__bit0,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit0
% 5.49/5.81 thf(fact_8574_take__bit__Suc__bit0,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 5.49/5.81 = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit0
% 5.49/5.81 thf(fact_8575_take__bit__Suc__bit0,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.49/5.81 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit0
% 5.49/5.81 thf(fact_8576_take__bit__Suc__bit0,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.49/5.81 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit0
% 5.49/5.81 thf(fact_8577_take__bit__nat__eq__self,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.49/5.81 = M ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_eq_self
% 5.49/5.81 thf(fact_8578_take__bit__nat__less__exp,axiom,
% 5.49/5.81 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_less_exp
% 5.49/5.81 thf(fact_8579_take__bit__nat__eq__self__iff,axiom,
% 5.49/5.81 ! [N2: nat,M: nat] :
% 5.49/5.81 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.49/5.81 = M )
% 5.49/5.81 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_eq_self_iff
% 5.49/5.81 thf(fact_8580_take__bit__int__less__exp,axiom,
% 5.49/5.81 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_less_exp
% 5.49/5.81 thf(fact_8581_take__bit__nat__less__self__iff,axiom,
% 5.49/5.81 ! [N2: nat,M: nat] :
% 5.49/5.81 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.49/5.81 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_nat_less_self_iff
% 5.49/5.81 thf(fact_8582_bits__induct,axiom,
% 5.49/5.81 ! [P: code_integer > $o,A: code_integer] :
% 5.49/5.81 ( ! [A4: code_integer] :
% 5.49/5.81 ( ( ( divide6298287555418463151nteger @ A4 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ A4 ) )
% 5.49/5.81 => ( ! [A4: code_integer,B4: $o] :
% 5.49/5.81 ( ( P @ A4 )
% 5.49/5.81 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B4 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.49/5.81 => ( P @ A ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % bits_induct
% 5.49/5.81 thf(fact_8583_bits__induct,axiom,
% 5.49/5.81 ! [P: code_natural > $o,A: code_natural] :
% 5.49/5.81 ( ! [A4: code_natural] :
% 5.49/5.81 ( ( ( divide5121882707175180666atural @ A4 @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ A4 ) )
% 5.49/5.81 => ( ! [A4: code_natural,B4: $o] :
% 5.49/5.81 ( ( P @ A4 )
% 5.49/5.81 => ( ( ( divide5121882707175180666atural @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B4 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A4 ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ ( plus_p4538020629002901425atural @ ( zero_n8403883297036319079atural @ B4 ) @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.49/5.81 => ( P @ A ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % bits_induct
% 5.49/5.81 thf(fact_8584_bits__induct,axiom,
% 5.49/5.81 ! [P: nat > $o,A: nat] :
% 5.49/5.81 ( ! [A4: nat] :
% 5.49/5.81 ( ( ( divide_divide_nat @ A4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ A4 ) )
% 5.49/5.81 => ( ! [A4: nat,B4: $o] :
% 5.49/5.81 ( ( P @ A4 )
% 5.49/5.81 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B4 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.49/5.81 => ( P @ A ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % bits_induct
% 5.49/5.81 thf(fact_8585_bits__induct,axiom,
% 5.49/5.81 ! [P: int > $o,A: int] :
% 5.49/5.81 ( ! [A4: int] :
% 5.49/5.81 ( ( ( divide_divide_int @ A4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ A4 ) )
% 5.49/5.81 => ( ! [A4: int,B4: $o] :
% 5.49/5.81 ( ( P @ A4 )
% 5.49/5.81 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.81 = A4 )
% 5.49/5.81 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B4 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A4 ) ) ) ) )
% 5.49/5.81 => ( P @ A ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % bits_induct
% 5.49/5.81 thf(fact_8586_take__bit__int__greater__eq__self__iff,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.49/5.81 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_greater_eq_self_iff
% 5.49/5.81 thf(fact_8587_take__bit__int__less__self__iff,axiom,
% 5.49/5.81 ! [N2: nat,K: int] :
% 5.49/5.81 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.49/5.81 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_less_self_iff
% 5.49/5.81 thf(fact_8588_divmod__nat__if,axiom,
% 5.49/5.81 ( divmod_nat
% 5.49/5.81 = ( ^ [M3: nat,N: nat] :
% 5.49/5.81 ( if_Pro6206227464963214023at_nat
% 5.49/5.81 @ ( ( N = zero_zero_nat )
% 5.49/5.81 | ( ord_less_nat @ M3 @ N ) )
% 5.49/5.81 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 5.49/5.81 @ ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [Q7: nat] : ( product_Pair_nat_nat @ ( suc @ Q7 ) )
% 5.49/5.81 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N ) @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_nat_if
% 5.49/5.81 thf(fact_8589_nat__dvd__iff,axiom,
% 5.49/5.81 ! [Z: int,M: nat] :
% 5.49/5.81 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.49/5.81 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.49/5.81 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.49/5.81 => ( M = zero_zero_nat ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % nat_dvd_iff
% 5.49/5.81 thf(fact_8590_take__bit__int__eq__self__iff,axiom,
% 5.49/5.81 ! [N2: nat,K: int] :
% 5.49/5.81 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.49/5.81 = K )
% 5.49/5.81 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.81 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_eq_self_iff
% 5.49/5.81 thf(fact_8591_take__bit__int__eq__self,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.81 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.49/5.81 = K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_eq_self
% 5.49/5.81 thf(fact_8592_exp__mod__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_mod_exp
% 5.49/5.81 thf(fact_8593_exp__mod__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( modulo8411746178871703098atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_2397367101498566445atural @ ( zero_n8403883297036319079atural @ ( ord_less_nat @ M @ N2 ) ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_mod_exp
% 5.49/5.81 thf(fact_8594_exp__mod__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_mod_exp
% 5.49/5.81 thf(fact_8595_exp__mod__exp,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_mod_exp
% 5.49/5.81 thf(fact_8596_take__bit__Suc,axiom,
% 5.49/5.81 ! [N2: nat,A: code_integer] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 5.49/5.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc
% 5.49/5.81 thf(fact_8597_take__bit__Suc,axiom,
% 5.49/5.81 ! [N2: nat,A: code_natural] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ A )
% 5.49/5.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( divide5121882707175180666atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ ( modulo8411746178871703098atural @ A @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc
% 5.49/5.81 thf(fact_8598_take__bit__Suc,axiom,
% 5.49/5.81 ! [N2: nat,A: nat] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 5.49/5.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc
% 5.49/5.81 thf(fact_8599_take__bit__Suc,axiom,
% 5.49/5.81 ! [N2: nat,A: int] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.49/5.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc
% 5.49/5.81 thf(fact_8600_take__bit__int__less__eq,axiom,
% 5.49/5.81 ! [N2: nat,K: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.49/5.81 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.81 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_less_eq
% 5.49/5.81 thf(fact_8601_take__bit__int__greater__eq,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.81 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_int_greater_eq
% 5.49/5.81 thf(fact_8602_even__nat__iff,axiom,
% 5.49/5.81 ! [K: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.81 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.49/5.81 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % even_nat_iff
% 5.49/5.81 thf(fact_8603_divmod__step__nat__def,axiom,
% 5.49/5.81 ( unique5026877609467782581ep_nat
% 5.49/5.81 = ( ^ [L2: num] :
% 5.49/5.81 ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [Q7: nat,R4: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R4 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q7 ) @ one_one_nat ) @ ( minus_minus_nat @ R4 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_step_nat_def
% 5.49/5.81 thf(fact_8604_exp__div__exp__eq,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_3573771949741848930nteger
% 5.49/5.81 @ ( zero_n356916108424825756nteger
% 5.49/5.81 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.49/5.81 != zero_z3403309356797280102nteger )
% 5.49/5.81 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.49/5.81 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_div_exp_eq
% 5.49/5.81 thf(fact_8605_exp__div__exp__eq,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( divide5121882707175180666atural @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M ) @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_2397367101498566445atural
% 5.49/5.81 @ ( zero_n8403883297036319079atural
% 5.49/5.81 @ ( ( ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ M )
% 5.49/5.81 != zero_z2226904508553997617atural )
% 5.49/5.81 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.49/5.81 @ ( power_7079662738309270450atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_div_exp_eq
% 5.49/5.81 thf(fact_8606_exp__div__exp__eq,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_nat
% 5.49/5.81 @ ( zero_n2687167440665602831ol_nat
% 5.49/5.81 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.49/5.81 != zero_zero_nat )
% 5.49/5.81 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.49/5.81 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_div_exp_eq
% 5.49/5.81 thf(fact_8607_exp__div__exp__eq,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 = ( times_times_int
% 5.49/5.81 @ ( zero_n2684676970156552555ol_int
% 5.49/5.81 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.49/5.81 != zero_zero_int )
% 5.49/5.81 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.49/5.81 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % exp_div_exp_eq
% 5.49/5.81 thf(fact_8608_divmod__step__int__def,axiom,
% 5.49/5.81 ( unique5024387138958732305ep_int
% 5.49/5.81 = ( ^ [L2: num] :
% 5.49/5.81 ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [Q7: int,R4: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R4 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q7 ) @ one_one_int ) @ ( minus_minus_int @ R4 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_step_int_def
% 5.49/5.81 thf(fact_8609_take__bit__minus__small__eq,axiom,
% 5.49/5.81 ! [K: int,N2: nat] :
% 5.49/5.81 ( ( ord_less_int @ zero_zero_int @ K )
% 5.49/5.81 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.49/5.81 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_minus_small_eq
% 5.49/5.81 thf(fact_8610_take__bit__numeral__minus__numeral__int,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.81 = ( case_option_int_num @ zero_zero_int
% 5.49/5.81 @ ^ [Q7: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q7 ) ) )
% 5.49/5.81 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_minus_numeral_int
% 5.49/5.81 thf(fact_8611_divmod__algorithm__code_I5_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [Q7: int,R4: int] : ( product_Pair_int_int @ Q7 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) )
% 5.49/5.81 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(5)
% 5.49/5.81 thf(fact_8612_divmod__algorithm__code_I5_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [Q7: nat,R4: nat] : ( product_Pair_nat_nat @ Q7 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) )
% 5.49/5.81 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(5)
% 5.49/5.81 thf(fact_8613_divmod__algorithm__code_I5_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc6916734918728496179nteger
% 5.49/5.81 @ ^ [Q7: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q7 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) )
% 5.49/5.81 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(5)
% 5.49/5.81 thf(fact_8614_Divides_Oadjust__div__eq,axiom,
% 5.49/5.81 ! [Q6: int,R3: int] :
% 5.49/5.81 ( ( adjust_div @ ( product_Pair_int_int @ Q6 @ R3 ) )
% 5.49/5.81 = ( plus_plus_int @ Q6 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % Divides.adjust_div_eq
% 5.49/5.81 thf(fact_8615_divmod__divmod__step,axiom,
% 5.49/5.81 ( unique5055182867167087721od_nat
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_divmod_step
% 5.49/5.81 thf(fact_8616_divmod__divmod__step,axiom,
% 5.49/5.81 ( unique5052692396658037445od_int
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_divmod_step
% 5.49/5.81 thf(fact_8617_divmod__divmod__step,axiom,
% 5.49/5.81 ( unique3479559517661332726nteger
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_divmod_step
% 5.49/5.81 thf(fact_8618_divmod__algorithm__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(3)
% 5.49/5.81 thf(fact_8619_divmod__algorithm__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(3)
% 5.49/5.81 thf(fact_8620_divmod__algorithm__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(3)
% 5.49/5.81 thf(fact_8621_case__prodI,axiom,
% 5.49/5.81 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8622_case__prodI,axiom,
% 5.49/5.81 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8623_case__prodI,axiom,
% 5.49/5.81 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8624_case__prodI,axiom,
% 5.49/5.81 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8625_case__prodI,axiom,
% 5.49/5.81 ! [F: a > produc6653097349344004940it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc8860486935419594360_nat_o @ F @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8626_case__prodI,axiom,
% 5.49/5.81 ! [F: int > int > $o,A: int,B: int] :
% 5.49/5.81 ( ( F @ A @ B )
% 5.49/5.81 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI
% 5.49/5.81 thf(fact_8627_case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3925858234332021118et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o] :
% 5.49/5.81 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5001842942810119800et_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc1437786849005270451_nat_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8628_case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc2732055786443039994et_nat,C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o] :
% 5.49/5.81 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc2245416461498447860et_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc838355143741117751_nat_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8629_case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.49/5.81 ( ! [A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc1573362020775583542_int_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8630_case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.49/5.81 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc2558449545302689196_int_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8631_case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,C: a > produc6653097349344004940it_nat > $o] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc8860486935419594360_nat_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8632_case__prodI2,axiom,
% 5.49/5.81 ! [P3: product_prod_int_int,C: int > int > $o] :
% 5.49/5.81 ( ! [A4: int,B4: int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.49/5.81 => ( C @ A4 @ B4 ) )
% 5.49/5.81 => ( produc4947309494688390418_int_o @ C @ P3 ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2
% 5.49/5.81 thf(fact_8633_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: $o,C: a > produc6653097349344004940it_nat > set_o,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( member_o @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc5350075035600711000_set_o @ C @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8634_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: nat,C: a > produc6653097349344004940it_nat > set_nat,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_nat @ Z @ ( produc7315013382793309350et_nat @ C @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8635_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: int,C: a > produc6653097349344004940it_nat > set_int,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_int @ Z @ ( produc3137162363284112642et_int @ C @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8636_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: set_nat,C: a > produc6653097349344004940it_nat > set_set_nat,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( produc8632796428668088668et_nat @ C @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8637_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: product_prod_nat_nat,C: a > produc6653097349344004940it_nat > set_Pr1261947904930325089at_nat,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( member8440522571783428010at_nat @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member8440522571783428010at_nat @ Z @ ( produc8253449849199807809at_nat @ C @ ( produc9178034014595674355it_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8638_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( member_o @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8639_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8640_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8641_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8642_mem__case__prodI,axiom,
% 5.49/5.81 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( member_o @ Z @ ( C @ A @ B ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ ( produc5001842942810119800et_nat @ A @ B ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI
% 5.49/5.81 thf(fact_8643_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,Z: $o,C: a > produc6653097349344004940it_nat > set_o] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member_o @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc5350075035600711000_set_o @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8644_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,Z: nat,C: a > produc6653097349344004940it_nat > set_nat] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member_nat @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_nat @ Z @ ( produc7315013382793309350et_nat @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8645_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,Z: int,C: a > produc6653097349344004940it_nat > set_int] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member_int @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_int @ Z @ ( produc3137162363284112642et_int @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8646_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,Z: set_nat,C: a > produc6653097349344004940it_nat > set_set_nat] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( produc8632796428668088668et_nat @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8647_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3260487557148687353it_nat,Z: product_prod_nat_nat,C: a > produc6653097349344004940it_nat > set_Pr1261947904930325089at_nat] :
% 5.49/5.81 ( ! [A4: a,B4: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member8440522571783428010at_nat @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member8440522571783428010at_nat @ Z @ ( produc8253449849199807809at_nat @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8648_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int,Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o] :
% 5.49/5.81 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( member_o @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8649_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int,Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat] :
% 5.49/5.81 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( member_nat @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8650_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int,Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int] :
% 5.49/5.81 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( member_int @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8651_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc7773217078559923341nt_int,Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat] :
% 5.49/5.81 ( ! [A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8652_mem__case__prodI2,axiom,
% 5.49/5.81 ! [P3: produc3925858234332021118et_nat,Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o] :
% 5.49/5.81 ( ! [A4: produc3658429121746597890et_nat > $o,B4: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5001842942810119800et_nat @ A4 @ B4 ) )
% 5.49/5.81 => ( member_o @ Z @ ( C @ A4 @ B4 ) ) )
% 5.49/5.81 => ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodI2
% 5.49/5.81 thf(fact_8653_case__prodI2_H,axiom,
% 5.49/5.81 ! [P3: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.49/5.81 ( ! [A4: nat,B4: nat] :
% 5.49/5.81 ( ( ( product_Pair_nat_nat @ A4 @ B4 )
% 5.49/5.81 = P3 )
% 5.49/5.81 => ( C @ A4 @ B4 @ X ) )
% 5.49/5.81 => ( produc8739625826339149834_nat_o @ C @ P3 @ X ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodI2'
% 5.49/5.81 thf(fact_8654_take__bit__num__simps_I2_J,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.49/5.81 = ( some_num @ one ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(2)
% 5.49/5.81 thf(fact_8655_take__bit__num__simps_I5_J,axiom,
% 5.49/5.81 ! [R3: num] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ one )
% 5.49/5.81 = ( some_num @ one ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(5)
% 5.49/5.81 thf(fact_8656_take__bit__num__simps_I3_J,axiom,
% 5.49/5.81 ! [N2: nat,M: num] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.49/5.81 = ( case_o6005452278849405969um_num @ none_num
% 5.49/5.81 @ ^ [Q7: num] : ( some_num @ ( bit0 @ Q7 ) )
% 5.49/5.81 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(3)
% 5.49/5.81 thf(fact_8657_divmod__algorithm__code_I2_J,axiom,
% 5.49/5.81 ! [M: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ M @ one )
% 5.49/5.81 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(2)
% 5.49/5.81 thf(fact_8658_divmod__algorithm__code_I2_J,axiom,
% 5.49/5.81 ! [M: num] :
% 5.49/5.81 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.49/5.81 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(2)
% 5.49/5.81 thf(fact_8659_divmod__algorithm__code_I2_J,axiom,
% 5.49/5.81 ! [M: num] :
% 5.49/5.81 ( ( unique3479559517661332726nteger @ M @ one )
% 5.49/5.81 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(2)
% 5.49/5.81 thf(fact_8660_take__bit__numeral__numeral,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.49/5.81 = ( case_o356765784539232260er_num @ zero_z3403309356797280102nteger @ numera6620942414471956472nteger @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_numeral
% 5.49/5.81 thf(fact_8661_take__bit__numeral__numeral,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ M ) @ ( numera5444537566228673987atural @ N2 ) )
% 5.49/5.81 = ( case_o5621594795226839503al_num @ zero_z2226904508553997617atural @ numera5444537566228673987atural @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_numeral
% 5.49/5.81 thf(fact_8662_take__bit__numeral__numeral,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.81 = ( case_option_nat_num @ zero_zero_nat @ numeral_numeral_nat @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_numeral
% 5.49/5.81 thf(fact_8663_take__bit__numeral__numeral,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.81 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_numeral
% 5.49/5.81 thf(fact_8664_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: $o,C: a > produc6653097349344004940it_nat > set_o,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( member_o @ Z @ ( produc5350075035600711000_set_o @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_o @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8665_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: nat,C: a > produc6653097349344004940it_nat > set_nat,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( member_nat @ Z @ ( produc7315013382793309350et_nat @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8666_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: int,C: a > produc6653097349344004940it_nat > set_int,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( member_int @ Z @ ( produc3137162363284112642et_int @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8667_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: set_nat,C: a > produc6653097349344004940it_nat > set_set_nat,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( member_set_nat @ Z @ ( produc8632796428668088668et_nat @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_set_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8668_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: product_prod_nat_nat,C: a > produc6653097349344004940it_nat > set_Pr1261947904930325089at_nat,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( member8440522571783428010at_nat @ Z @ ( produc8253449849199807809at_nat @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member8440522571783428010at_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8669_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: $o,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_o,P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( member_o @ Z @ ( produc8646739037753556108_set_o @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_o @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8670_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_nat,P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( member_nat @ Z @ ( produc8289552606927098482et_nat @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8671_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_int,P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( member_int @ Z @ ( produc4111701587417901774et_int @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_int @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8672_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: set_nat,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_set_nat,P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( member_set_nat @ Z @ ( produc3577156405726439208et_nat @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_set_nat @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8673_mem__case__prodE,axiom,
% 5.49/5.81 ! [Z: $o,C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > set_o,P3: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( member_o @ Z @ ( produc7715693535893868691_set_o @ C @ P3 ) )
% 5.49/5.81 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( member_o @ Z @ ( C @ X3 @ Y3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mem_case_prodE
% 5.49/5.81 thf(fact_8674_case__prodD,axiom,
% 5.49/5.81 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( produc1437786849005270451_nat_o @ F @ ( produc5001842942810119800et_nat @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8675_case__prodD,axiom,
% 5.49/5.81 ! [F: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,A: produc3658429121746597890et_nat > $o,B: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( produc838355143741117751_nat_o @ F @ ( produc2245416461498447860et_nat @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8676_case__prodD,axiom,
% 5.49/5.81 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8677_case__prodD,axiom,
% 5.49/5.81 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.49/5.81 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8678_case__prodD,axiom,
% 5.49/5.81 ! [F: a > produc6653097349344004940it_nat > $o,A: a,B: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( produc8860486935419594360_nat_o @ F @ ( produc9178034014595674355it_nat @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8679_case__prodD,axiom,
% 5.49/5.81 ! [F: int > int > $o,A: int,B: int] :
% 5.49/5.81 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.49/5.81 => ( F @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD
% 5.49/5.81 thf(fact_8680_case__prodE,axiom,
% 5.49/5.81 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3658429121746597890et_nat > $o,P3: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( produc1437786849005270451_nat_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5001842942810119800et_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8681_case__prodE,axiom,
% 5.49/5.81 ! [C: ( produc3658429121746597890et_nat > $o ) > produc3925858234332021118et_nat > $o,P3: produc2732055786443039994et_nat] :
% 5.49/5.81 ( ( produc838355143741117751_nat_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: produc3658429121746597890et_nat > $o,Y3: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc2245416461498447860et_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8682_case__prodE,axiom,
% 5.49/5.81 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P3: produc2285326912895808259nt_int] :
% 5.49/5.81 ( ( produc1573362020775583542_int_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: produc8551481072490612790e_term > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc5700946648718959541nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8683_case__prodE,axiom,
% 5.49/5.81 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P3: produc7773217078559923341nt_int] :
% 5.49/5.81 ( ( produc2558449545302689196_int_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: int > option6357759511663192854e_term,Y3: product_prod_int_int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc4305682042979456191nt_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8684_case__prodE,axiom,
% 5.49/5.81 ! [C: a > produc6653097349344004940it_nat > $o,P3: produc3260487557148687353it_nat] :
% 5.49/5.81 ( ( produc8860486935419594360_nat_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: a,Y3: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( produc9178034014595674355it_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8685_case__prodE,axiom,
% 5.49/5.81 ! [C: int > int > $o,P3: product_prod_int_int] :
% 5.49/5.81 ( ( produc4947309494688390418_int_o @ C @ P3 )
% 5.49/5.81 => ~ ! [X3: int,Y3: int] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( product_Pair_int_int @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE
% 5.49/5.81 thf(fact_8686_case__prodD_H,axiom,
% 5.49/5.81 ! [R: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.49/5.81 ( ( produc8739625826339149834_nat_o @ R @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.49/5.81 => ( R @ A @ B @ C ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodD'
% 5.49/5.81 thf(fact_8687_case__prodE_H,axiom,
% 5.49/5.81 ! [C: nat > nat > product_prod_nat_nat > $o,P3: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.49/5.81 ( ( produc8739625826339149834_nat_o @ C @ P3 @ Z )
% 5.49/5.81 => ~ ! [X3: nat,Y3: nat] :
% 5.49/5.81 ( ( P3
% 5.49/5.81 = ( product_Pair_nat_nat @ X3 @ Y3 ) )
% 5.49/5.81 => ~ ( C @ X3 @ Y3 @ Z ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % case_prodE'
% 5.49/5.81 thf(fact_8688_Divides_Oadjust__div__def,axiom,
% 5.49/5.81 ( adjust_div
% 5.49/5.81 = ( produc8211389475949308722nt_int
% 5.49/5.81 @ ^ [Q7: int,R4: int] : ( plus_plus_int @ Q7 @ ( zero_n2684676970156552555ol_int @ ( R4 != zero_zero_int ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % Divides.adjust_div_def
% 5.49/5.81 thf(fact_8689_Collect__case__prod__mono,axiom,
% 5.49/5.81 ! [A3: int > int > $o,B3: int > int > $o] :
% 5.49/5.81 ( ( ord_le6741204236512500942_int_o @ A3 @ B3 )
% 5.49/5.81 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A3 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % Collect_case_prod_mono
% 5.49/5.81 thf(fact_8690_sum_Otriangle__reindex__eq,axiom,
% 5.49/5.81 ! [G: nat > nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.49/5.81 @ ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [K3: nat] :
% 5.49/5.81 ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.triangle_reindex_eq
% 5.49/5.81 thf(fact_8691_prod_Otriangle__reindex__eq,axiom,
% 5.49/5.81 ! [G: nat > nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.49/5.81 @ ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.81 = ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [K3: nat] :
% 5.49/5.81 ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.triangle_reindex_eq
% 5.49/5.81 thf(fact_8692_prod_Otriangle__reindex__eq,axiom,
% 5.49/5.81 ! [G: nat > nat > int,N2: nat] :
% 5.49/5.81 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.49/5.81 @ ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [I4: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.81 = ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [K3: nat] :
% 5.49/5.81 ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.triangle_reindex_eq
% 5.49/5.81 thf(fact_8693_execute__bind__case,axiom,
% 5.49/5.81 ! [F: heap_Time_Heap_a,G: a > heap_Time_Heap_a,H: heap_e7401611519738050253t_unit] :
% 5.49/5.81 ( ( heap_Time_execute_a @ ( heap_Time_bind_a_a @ F @ G ) @ H )
% 5.49/5.81 = ( case_o6061097939050036047it_nat @ none_P2651198173097904984it_nat
% 5.49/5.81 @ ( produc7850007024774191849it_nat
% 5.49/5.81 @ ^ [X4: a] :
% 5.49/5.81 ( produc5645566021302314940it_nat
% 5.49/5.81 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G @ X4 ) @ H7 ) ) ) )
% 5.49/5.81 @ ( heap_Time_execute_a @ F @ H ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % execute_bind_case
% 5.49/5.81 thf(fact_8694_map__to__set__def,axiom,
% 5.49/5.81 ( map_to_set_int_int
% 5.49/5.81 = ( ^ [M3: int > option_int] :
% 5.49/5.81 ( collec213857154873943460nt_int
% 5.49/5.81 @ ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [K3: int,V2: int] :
% 5.49/5.81 ( ( M3 @ K3 )
% 5.49/5.81 = ( some_int @ V2 ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % map_to_set_def
% 5.49/5.81 thf(fact_8695_take__bit__num__eq__Some__imp,axiom,
% 5.49/5.81 ! [M: nat,N2: num,Q6: num] :
% 5.49/5.81 ( ( ( bit_take_bit_num @ M @ N2 )
% 5.49/5.81 = ( some_num @ Q6 ) )
% 5.49/5.81 => ( ( bit_se1745604003318907178nteger @ M @ ( numera6620942414471956472nteger @ N2 ) )
% 5.49/5.81 = ( numera6620942414471956472nteger @ Q6 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_eq_Some_imp
% 5.49/5.81 thf(fact_8696_take__bit__num__eq__Some__imp,axiom,
% 5.49/5.81 ! [M: nat,N2: num,Q6: num] :
% 5.49/5.81 ( ( ( bit_take_bit_num @ M @ N2 )
% 5.49/5.81 = ( some_num @ Q6 ) )
% 5.49/5.81 => ( ( bit_se569199155075624693atural @ M @ ( numera5444537566228673987atural @ N2 ) )
% 5.49/5.81 = ( numera5444537566228673987atural @ Q6 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_eq_Some_imp
% 5.49/5.81 thf(fact_8697_take__bit__num__eq__Some__imp,axiom,
% 5.49/5.81 ! [M: nat,N2: num,Q6: num] :
% 5.49/5.81 ( ( ( bit_take_bit_num @ M @ N2 )
% 5.49/5.81 = ( some_num @ Q6 ) )
% 5.49/5.81 => ( ( bit_se2925701944663578781it_nat @ M @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.81 = ( numeral_numeral_nat @ Q6 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_eq_Some_imp
% 5.49/5.81 thf(fact_8698_take__bit__num__eq__Some__imp,axiom,
% 5.49/5.81 ! [M: nat,N2: num,Q6: num] :
% 5.49/5.81 ( ( ( bit_take_bit_num @ M @ N2 )
% 5.49/5.81 = ( some_num @ Q6 ) )
% 5.49/5.81 => ( ( bit_se2923211474154528505it_int @ M @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.81 = ( numeral_numeral_int @ Q6 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_eq_Some_imp
% 5.49/5.81 thf(fact_8699_Heap__Time__Monad_Obind__def,axiom,
% 5.49/5.81 ( heap_Time_bind_a_a
% 5.49/5.81 = ( ^ [F3: heap_Time_Heap_a,G3: a > heap_Time_Heap_a] :
% 5.49/5.81 ( heap_Time_Heap_a2
% 5.49/5.81 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 5.49/5.81 ( case_o6061097939050036047it_nat @ none_P2651198173097904984it_nat
% 5.49/5.81 @ ( produc7850007024774191849it_nat
% 5.49/5.81 @ ^ [R4: a] :
% 5.49/5.81 ( produc5645566021302314940it_nat
% 5.49/5.81 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T7616092557645711335rame_a @ N @ ( heap_Time_execute_a @ ( G3 @ R4 ) @ H7 ) ) ) )
% 5.49/5.81 @ ( heap_Time_execute_a @ F3 @ H6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % Heap_Time_Monad.bind_def
% 5.49/5.81 thf(fact_8700_Heap__Time__Monad_Obind__def,axiom,
% 5.49/5.81 ( heap_T8685611227969916822t_unit
% 5.49/5.81 = ( ^ [F3: heap_Time_Heap_a,G3: a > heap_T5738788834812785303t_unit] :
% 5.49/5.81 ( heap_T6183433275982383450t_unit
% 5.49/5.81 @ ^ [H6: heap_e7401611519738050253t_unit] :
% 5.49/5.81 ( case_o7727800614283616222it_nat @ none_P9117596204409417319it_nat
% 5.49/5.81 @ ( produc5648861294512138360it_nat
% 5.49/5.81 @ ^ [R4: a] :
% 5.49/5.81 ( produc7488178964372371019it_nat
% 5.49/5.81 @ ^ [H7: heap_e7401611519738050253t_unit,N: nat] : ( heap_T3616969660504097270t_unit @ N @ ( heap_T875086893843062177t_unit @ ( G3 @ R4 ) @ H7 ) ) ) )
% 5.49/5.81 @ ( heap_Time_execute_a @ F3 @ H6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % Heap_Time_Monad.bind_def
% 5.49/5.81 thf(fact_8701_finite__psubset__def,axiom,
% 5.49/5.81 ( finite_psubset_nat
% 5.49/5.81 = ( collec6662362479098859352et_nat
% 5.49/5.81 @ ( produc6247414631856714078_nat_o
% 5.49/5.81 @ ^ [A6: set_nat,B6: set_nat] :
% 5.49/5.81 ( ( ord_less_set_nat @ A6 @ B6 )
% 5.49/5.81 & ( finite_finite_nat @ B6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_psubset_def
% 5.49/5.81 thf(fact_8702_finite__psubset__def,axiom,
% 5.49/5.81 ( finite_psubset_int
% 5.49/5.81 = ( collec957716948307931664et_int
% 5.49/5.81 @ ( produc4109468873575309990_int_o
% 5.49/5.81 @ ^ [A6: set_int,B6: set_int] :
% 5.49/5.81 ( ( ord_less_set_int @ A6 @ B6 )
% 5.49/5.81 & ( finite_finite_int @ B6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_psubset_def
% 5.49/5.81 thf(fact_8703_finite__psubset__def,axiom,
% 5.49/5.81 ( finite2416775604798480986nteger
% 5.49/5.81 = ( collec2770208431294612722nteger
% 5.49/5.81 @ ( produc1658495936642081476eger_o
% 5.49/5.81 @ ^ [A6: set_Code_integer,B6: set_Code_integer] :
% 5.49/5.81 ( ( ord_le1307284697595431911nteger @ A6 @ B6 )
% 5.49/5.81 & ( finite6017078050557962740nteger @ B6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_psubset_def
% 5.49/5.81 thf(fact_8704_finite__psubset__def,axiom,
% 5.49/5.81 ( finite469560695537375940at_nat
% 5.49/5.81 = ( collec6321179662152712658at_nat
% 5.49/5.81 @ ( produc410239310623530412_nat_o
% 5.49/5.81 @ ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.49/5.81 ( ( ord_le7866589430770878221at_nat @ A6 @ B6 )
% 5.49/5.81 & ( finite6177210948735845034at_nat @ B6 ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_psubset_def
% 5.49/5.81 thf(fact_8705_rel__of__def,axiom,
% 5.49/5.81 ( rel_of4838799251197538391et_nat
% 5.49/5.81 = ( ^ [M3: ( produc3658429121746597890et_nat > $o ) > option936205604648967762et_nat,P4: produc3925858234332021118et_nat > $o] :
% 5.49/5.81 ( collec1402215087704437587et_nat
% 5.49/5.81 @ ( produc1437786849005270451_nat_o
% 5.49/5.81 @ ^ [K3: produc3658429121746597890et_nat > $o,V2: produc3658429121746597890et_nat] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_P624177172695371229et_nat @ V2 ) )
% 5.49/5.81 & ( P4 @ ( produc5001842942810119800et_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8706_rel__of__def,axiom,
% 5.49/5.81 ( rel_of7774016450764239315et_nat
% 5.49/5.81 = ( ^ [M3: ( produc3658429121746597890et_nat > $o ) > option5190343406534369742et_nat,P4: produc2732055786443039994et_nat > $o] :
% 5.49/5.81 ( collec5543584681430388431et_nat
% 5.49/5.81 @ ( produc838355143741117751_nat_o
% 5.49/5.81 @ ^ [K3: produc3658429121746597890et_nat > $o,V2: produc3925858234332021118et_nat] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_P750831030444334937et_nat @ V2 ) )
% 5.49/5.81 & ( P4 @ ( produc2245416461498447860et_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8707_rel__of__def,axiom,
% 5.49/5.81 ( rel_of8306664904814525588nt_int
% 5.49/5.81 = ( ^ [M3: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > option4624381673175914239nt_int,P4: produc2285326912895808259nt_int > $o] :
% 5.49/5.81 ( collec1790188477890212312nt_int
% 5.49/5.81 @ ( produc1573362020775583542_int_o
% 5.49/5.81 @ ^ [K3: produc8551481072490612790e_term > option6357759511663192854e_term,V2: product_prod_int_int] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_P4184893108420464158nt_int @ V2 ) )
% 5.49/5.81 & ( P4 @ ( produc5700946648718959541nt_int @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8708_rel__of__def,axiom,
% 5.49/5.81 ( rel_of5543720577181062686nt_int
% 5.49/5.81 = ( ^ [M3: ( int > option6357759511663192854e_term ) > option4624381673175914239nt_int,P4: produc7773217078559923341nt_int > $o] :
% 5.49/5.81 ( collec506566255779805410nt_int
% 5.49/5.81 @ ( produc2558449545302689196_int_o
% 5.49/5.81 @ ^ [K3: int > option6357759511663192854e_term,V2: product_prod_int_int] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_P4184893108420464158nt_int @ V2 ) )
% 5.49/5.81 & ( P4 @ ( produc4305682042979456191nt_int @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8709_rel__of__def,axiom,
% 5.49/5.81 ( rel_of2761222537318653906it_nat
% 5.49/5.81 = ( ^ [M3: a > option233860712434008220it_nat,P4: produc3260487557148687353it_nat > $o] :
% 5.49/5.81 ( collec4148678073425210574it_nat
% 5.49/5.81 @ ( produc8860486935419594360_nat_o
% 5.49/5.81 @ ^ [K3: a,V2: produc6653097349344004940it_nat] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_P1054239925786823975it_nat @ V2 ) )
% 5.49/5.81 & ( P4 @ ( produc9178034014595674355it_nat @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8710_rel__of__def,axiom,
% 5.49/5.81 ( rel_of_int_int
% 5.49/5.81 = ( ^ [M3: int > option_int,P4: product_prod_int_int > $o] :
% 5.49/5.81 ( collec213857154873943460nt_int
% 5.49/5.81 @ ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [K3: int,V2: int] :
% 5.49/5.81 ( ( ( M3 @ K3 )
% 5.49/5.81 = ( some_int @ V2 ) )
% 5.49/5.81 & ( P4 @ ( product_Pair_int_int @ K3 @ V2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % rel_of_def
% 5.49/5.81 thf(fact_8711_divmod__int__def,axiom,
% 5.49/5.81 ( unique5052692396658037445od_int
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_int_def
% 5.49/5.81 thf(fact_8712_divmod__def,axiom,
% 5.49/5.81 ( unique5052692396658037445od_int
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_def
% 5.49/5.81 thf(fact_8713_divmod__def,axiom,
% 5.49/5.81 ( unique5055182867167087721od_nat
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_def
% 5.49/5.81 thf(fact_8714_divmod__def,axiom,
% 5.49/5.81 ( unique3479559517661332726nteger
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_def
% 5.49/5.81 thf(fact_8715_divmod_H__nat__def,axiom,
% 5.49/5.81 ( unique5055182867167087721od_nat
% 5.49/5.81 = ( ^ [M3: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod'_nat_def
% 5.49/5.81 thf(fact_8716_mlex__eq,axiom,
% 5.49/5.81 ( mlex_prod_nat
% 5.49/5.81 = ( ^ [F3: nat > nat,R6: set_Pr1261947904930325089at_nat] :
% 5.49/5.81 ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.81 ( ( ord_less_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 5.49/5.81 | ( ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 5.49/5.81 & ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X4 @ Y4 ) @ R6 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mlex_eq
% 5.49/5.81 thf(fact_8717_mlex__eq,axiom,
% 5.49/5.81 ( mlex_prod_int
% 5.49/5.81 = ( ^ [F3: int > nat,R6: set_Pr958786334691620121nt_int] :
% 5.49/5.81 ( collec213857154873943460nt_int
% 5.49/5.81 @ ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [X4: int,Y4: int] :
% 5.49/5.81 ( ( ord_less_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 5.49/5.81 | ( ( ord_less_eq_nat @ ( F3 @ X4 ) @ ( F3 @ Y4 ) )
% 5.49/5.81 & ( member5262025264175285858nt_int @ ( product_Pair_int_int @ X4 @ Y4 ) @ R6 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % mlex_eq
% 5.49/5.81 thf(fact_8718_divmod__algorithm__code_I6_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc4245557441103728435nt_int
% 5.49/5.81 @ ^ [Q7: int,R4: int] : ( product_Pair_int_int @ Q7 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R4 ) @ one_one_int ) )
% 5.49/5.81 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(6)
% 5.49/5.81 thf(fact_8719_divmod__algorithm__code_I6_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc2626176000494625587at_nat
% 5.49/5.81 @ ^ [Q7: nat,R4: nat] : ( product_Pair_nat_nat @ Q7 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R4 ) @ one_one_nat ) )
% 5.49/5.81 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(6)
% 5.49/5.81 thf(fact_8720_divmod__algorithm__code_I6_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( produc6916734918728496179nteger
% 5.49/5.81 @ ^ [Q7: code_integer,R4: code_integer] : ( produc1086072967326762835nteger @ Q7 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R4 ) @ one_one_Code_integer ) )
% 5.49/5.81 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(6)
% 5.49/5.81 thf(fact_8721_int__ge__less__than2__def,axiom,
% 5.49/5.81 ( int_ge_less_than2
% 5.49/5.81 = ( ^ [D5: int] :
% 5.49/5.81 ( collec213857154873943460nt_int
% 5.49/5.81 @ ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [Z8: int,Z6: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ D5 @ Z6 )
% 5.49/5.81 & ( ord_less_int @ Z8 @ Z6 ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % int_ge_less_than2_def
% 5.49/5.81 thf(fact_8722_int__ge__less__than__def,axiom,
% 5.49/5.81 ( int_ge_less_than
% 5.49/5.81 = ( ^ [D5: int] :
% 5.49/5.81 ( collec213857154873943460nt_int
% 5.49/5.81 @ ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [Z8: int,Z6: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ D5 @ Z8 )
% 5.49/5.81 & ( ord_less_int @ Z8 @ Z6 ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % int_ge_less_than_def
% 5.49/5.81 thf(fact_8723_divmod__algorithm__code_I8_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(8)
% 5.49/5.81 thf(fact_8724_divmod__algorithm__code_I8_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(8)
% 5.49/5.81 thf(fact_8725_divmod__algorithm__code_I8_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_num @ M @ N2 )
% 5.49/5.81 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(8)
% 5.49/5.81 thf(fact_8726_split__part,axiom,
% 5.49/5.81 ! [P: $o,Q: int > int > $o] :
% 5.49/5.81 ( ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [A5: int,B5: int] :
% 5.49/5.81 ( P
% 5.49/5.81 & ( Q @ A5 @ B5 ) ) )
% 5.49/5.81 = ( ^ [Ab: product_prod_int_int] :
% 5.49/5.81 ( P
% 5.49/5.81 & ( produc4947309494688390418_int_o @ Q @ Ab ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % split_part
% 5.49/5.81 thf(fact_8727_semiring__norm_I80_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( ord_less_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(80)
% 5.49/5.81 thf(fact_8728_semiring__norm_I73_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(73)
% 5.49/5.81 thf(fact_8729_semiring__norm_I72_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(72)
% 5.49/5.81 thf(fact_8730_semiring__norm_I81_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( ord_less_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(81)
% 5.49/5.81 thf(fact_8731_semiring__norm_I70_J,axiom,
% 5.49/5.81 ! [M: num] :
% 5.49/5.81 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(70)
% 5.49/5.81 thf(fact_8732_semiring__norm_I77_J,axiom,
% 5.49/5.81 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(77)
% 5.49/5.81 thf(fact_8733_semiring__norm_I74_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.81 = ( ord_less_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(74)
% 5.49/5.81 thf(fact_8734_semiring__norm_I79_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % semiring_norm(79)
% 5.49/5.81 thf(fact_8735_take__bit__num__simps_I4_J,axiom,
% 5.49/5.81 ! [N2: nat,M: num] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.49/5.81 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(4)
% 5.49/5.81 thf(fact_8736_divmod__algorithm__code_I4_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(4)
% 5.49/5.81 thf(fact_8737_divmod__algorithm__code_I4_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(4)
% 5.49/5.81 thf(fact_8738_divmod__algorithm__code_I4_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(4)
% 5.49/5.81 thf(fact_8739_divmod__algorithm__code_I7_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(7)
% 5.49/5.81 thf(fact_8740_divmod__algorithm__code_I7_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(7)
% 5.49/5.81 thf(fact_8741_divmod__algorithm__code_I7_J,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.49/5.81 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.49/5.81 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_algorithm_code(7)
% 5.49/5.81 thf(fact_8742_prod_Odisc__eq__case,axiom,
% 5.49/5.81 ! [Prod: product_prod_int_int] :
% 5.49/5.81 ( produc4947309494688390418_int_o
% 5.49/5.81 @ ^ [Uu2: int,Uv: int] : $true
% 5.49/5.81 @ Prod ) ).
% 5.49/5.81
% 5.49/5.81 % prod.disc_eq_case
% 5.49/5.81 thf(fact_8743_xor__num_Ocases,axiom,
% 5.49/5.81 ! [X: product_prod_num_num] :
% 5.49/5.81 ( ( X
% 5.49/5.81 != ( product_Pair_num_num @ one @ one ) )
% 5.49/5.81 => ( ! [N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) )
% 5.49/5.81 => ( ! [N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) )
% 5.49/5.81 => ( ! [M5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.49/5.81 => ( ! [M5: num,N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) )
% 5.49/5.81 => ( ! [M5: num,N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) )
% 5.49/5.81 => ( ! [M5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.49/5.81 => ( ! [M5: num,N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) )
% 5.49/5.81 => ~ ! [M5: num,N5: num] :
% 5.49/5.81 ( X
% 5.49/5.81 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % xor_num.cases
% 5.49/5.81 thf(fact_8744_numeral__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_code(3)
% 5.49/5.81 thf(fact_8745_numeral__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_code(3)
% 5.49/5.81 thf(fact_8746_numeral__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( numera6620942414471956472nteger @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_code(3)
% 5.49/5.81 thf(fact_8747_numeral__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_code(3)
% 5.49/5.81 thf(fact_8748_numeral__code_I3_J,axiom,
% 5.49/5.81 ! [N2: num] :
% 5.49/5.81 ( ( numera5444537566228673987atural @ ( bit1 @ N2 ) )
% 5.49/5.81 = ( plus_p4538020629002901425atural @ ( plus_p4538020629002901425atural @ ( numera5444537566228673987atural @ N2 ) @ ( numera5444537566228673987atural @ N2 ) ) @ one_one_Code_natural ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_code(3)
% 5.49/5.81 thf(fact_8749_power__numeral__odd,axiom,
% 5.49/5.81 ! [Z: code_integer,W2: num] :
% 5.49/5.81 ( ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ Z @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_8256067586552552935nteger @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % power_numeral_odd
% 5.49/5.81 thf(fact_8750_power__numeral__odd,axiom,
% 5.49/5.81 ! [Z: assn,W2: num] :
% 5.49/5.81 ( ( power_power_assn @ Z @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.49/5.81 = ( times_times_assn @ ( times_times_assn @ Z @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_assn @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % power_numeral_odd
% 5.49/5.81 thf(fact_8751_power__numeral__odd,axiom,
% 5.49/5.81 ! [Z: rat,W2: num] :
% 5.49/5.81 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.49/5.81 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % power_numeral_odd
% 5.49/5.81 thf(fact_8752_power__numeral__odd,axiom,
% 5.49/5.81 ! [Z: nat,W2: num] :
% 5.49/5.81 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.49/5.81 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % power_numeral_odd
% 5.49/5.81 thf(fact_8753_power__numeral__odd,axiom,
% 5.49/5.81 ! [Z: int,W2: num] :
% 5.49/5.81 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W2 ) ) )
% 5.49/5.81 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W2 ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % power_numeral_odd
% 5.49/5.81 thf(fact_8754_power3__eq__cube,axiom,
% 5.49/5.81 ! [A: code_integer] :
% 5.49/5.81 ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ A @ A ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % power3_eq_cube
% 5.49/5.81 thf(fact_8755_power3__eq__cube,axiom,
% 5.49/5.81 ! [A: assn] :
% 5.49/5.81 ( ( power_power_assn @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.49/5.81 = ( times_times_assn @ ( times_times_assn @ A @ A ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % power3_eq_cube
% 5.49/5.81 thf(fact_8756_power3__eq__cube,axiom,
% 5.49/5.81 ! [A: rat] :
% 5.49/5.81 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.49/5.81 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % power3_eq_cube
% 5.49/5.81 thf(fact_8757_power3__eq__cube,axiom,
% 5.49/5.81 ! [A: nat] :
% 5.49/5.81 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.49/5.81 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % power3_eq_cube
% 5.49/5.81 thf(fact_8758_power3__eq__cube,axiom,
% 5.49/5.81 ! [A: int] :
% 5.49/5.81 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.49/5.81 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.49/5.81
% 5.49/5.81 % power3_eq_cube
% 5.49/5.81 thf(fact_8759_take__bit__Suc__bit1,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit1
% 5.49/5.81 thf(fact_8760_take__bit__Suc__bit1,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ ( suc @ N2 ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ N2 @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit1
% 5.49/5.81 thf(fact_8761_take__bit__Suc__bit1,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit1
% 5.49/5.81 thf(fact_8762_take__bit__Suc__bit1,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_Suc_bit1
% 5.49/5.81 thf(fact_8763_divmod__BitM__2__eq,axiom,
% 5.49/5.81 ! [M: num] :
% 5.49/5.81 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.49/5.81 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % divmod_BitM_2_eq
% 5.49/5.81 thf(fact_8764_take__bit__num__simps_I6_J,axiom,
% 5.49/5.81 ! [R3: num,M: num] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 5.49/5.81 = ( case_o6005452278849405969um_num @ none_num
% 5.49/5.81 @ ^ [Q7: num] : ( some_num @ ( bit0 @ Q7 ) )
% 5.49/5.81 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(6)
% 5.49/5.81 thf(fact_8765_take__bit__numeral__bit1,axiom,
% 5.49/5.81 ! [L: num,K: num] :
% 5.49/5.81 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_bit1
% 5.49/5.81 thf(fact_8766_take__bit__numeral__bit1,axiom,
% 5.49/5.81 ! [L: num,K: num] :
% 5.49/5.81 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_p4538020629002901425atural @ ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) @ one_one_Code_natural ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_bit1
% 5.49/5.81 thf(fact_8767_take__bit__numeral__bit1,axiom,
% 5.49/5.81 ! [L: num,K: num] :
% 5.49/5.81 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_bit1
% 5.49/5.81 thf(fact_8768_take__bit__numeral__bit1,axiom,
% 5.49/5.81 ! [L: num,K: num] :
% 5.49/5.81 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.49/5.81 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_numeral_bit1
% 5.49/5.81 thf(fact_8769_prod_Otriangle__reindex,axiom,
% 5.49/5.81 ! [G: nat > nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups4077766827762148844at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.49/5.81 @ ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.81 = ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [K3: nat] :
% 5.49/5.81 ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.triangle_reindex
% 5.49/5.81 thf(fact_8770_prod_Otriangle__reindex,axiom,
% 5.49/5.81 ! [G: nat > nat > int,N2: nat] :
% 5.49/5.81 ( ( groups4075276357253098568at_int @ ( produc6840382203811409530at_int @ G )
% 5.49/5.81 @ ( collec3392354462482085612at_nat
% 5.49/5.81 @ ( produc6081775807080527818_nat_o
% 5.49/5.81 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.81 = ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [K3: nat] :
% 5.49/5.81 ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.81 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.triangle_reindex
% 5.49/5.81 thf(fact_8771_take__bit__num__def,axiom,
% 5.49/5.81 ( bit_take_bit_num
% 5.49/5.81 = ( ^ [N: nat,M3: num] :
% 5.49/5.81 ( if_option_num
% 5.49/5.81 @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) )
% 5.49/5.81 = zero_zero_nat )
% 5.49/5.81 @ none_num
% 5.49/5.81 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_def
% 5.49/5.81 thf(fact_8772_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: $o,K: $o] :
% 5.49/5.81 ( ( member_o @ I2 @ ( set_ord_lessThan_o @ K ) )
% 5.49/5.81 = ( ord_less_o @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8773_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: set_nat,K: set_nat] :
% 5.49/5.81 ( ( member_set_nat @ I2 @ ( set_or890127255671739683et_nat @ K ) )
% 5.49/5.81 = ( ord_less_set_nat @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8774_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: assn,K: assn] :
% 5.49/5.81 ( ( member_assn @ I2 @ ( set_or7637083652282234053n_assn @ K ) )
% 5.49/5.81 = ( ord_less_assn @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8775_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: rat,K: rat] :
% 5.49/5.81 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.49/5.81 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8776_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: num,K: num] :
% 5.49/5.81 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.49/5.81 = ( ord_less_num @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8777_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: nat,K: nat] :
% 5.49/5.81 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.49/5.81 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8778_lessThan__iff,axiom,
% 5.49/5.81 ! [I2: int,K: int] :
% 5.49/5.81 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.49/5.81 = ( ord_less_int @ I2 @ K ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_iff
% 5.49/5.81 thf(fact_8779_lessThan__subset__iff,axiom,
% 5.49/5.81 ! [X: rat,Y: rat] :
% 5.49/5.81 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.49/5.81 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_subset_iff
% 5.49/5.81 thf(fact_8780_lessThan__subset__iff,axiom,
% 5.49/5.81 ! [X: num,Y: num] :
% 5.49/5.81 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.49/5.81 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_subset_iff
% 5.49/5.81 thf(fact_8781_lessThan__subset__iff,axiom,
% 5.49/5.81 ! [X: nat,Y: nat] :
% 5.49/5.81 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.49/5.81 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_subset_iff
% 5.49/5.81 thf(fact_8782_lessThan__subset__iff,axiom,
% 5.49/5.81 ! [X: int,Y: int] :
% 5.49/5.81 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.49/5.81 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_subset_iff
% 5.49/5.81 thf(fact_8783_lessThan__0,axiom,
% 5.49/5.81 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.49/5.81 = bot_bot_set_nat ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_0
% 5.49/5.81 thf(fact_8784_less__Suc__numeral,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.49/5.81 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % less_Suc_numeral
% 5.49/5.81 thf(fact_8785_less__numeral__Suc,axiom,
% 5.49/5.81 ! [K: num,N2: nat] :
% 5.49/5.81 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.49/5.81 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % less_numeral_Suc
% 5.49/5.81 thf(fact_8786_prod_OlessThan__Suc,axiom,
% 5.49/5.81 ! [G: nat > code_integer,N2: nat] :
% 5.49/5.81 ( ( groups3455450783089532116nteger @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( groups3455450783089532116nteger @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc
% 5.49/5.81 thf(fact_8787_prod_OlessThan__Suc,axiom,
% 5.49/5.81 ! [G: nat > assn,N2: nat] :
% 5.49/5.81 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_assn @ ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc
% 5.49/5.81 thf(fact_8788_prod_OlessThan__Suc,axiom,
% 5.49/5.81 ! [G: nat > rat,N2: nat] :
% 5.49/5.81 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc
% 5.49/5.81 thf(fact_8789_prod_OlessThan__Suc,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc
% 5.49/5.81 thf(fact_8790_prod_OlessThan__Suc,axiom,
% 5.49/5.81 ! [G: nat > int,N2: nat] :
% 5.49/5.81 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc
% 5.49/5.81 thf(fact_8791_le__Suc__numeral,axiom,
% 5.49/5.81 ! [N2: nat,K: num] :
% 5.49/5.81 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.49/5.81 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % le_Suc_numeral
% 5.49/5.81 thf(fact_8792_le__numeral__Suc,axiom,
% 5.49/5.81 ! [K: num,N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.49/5.81 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % le_numeral_Suc
% 5.49/5.81 thf(fact_8793_take__bit__num__simps_I7_J,axiom,
% 5.49/5.81 ! [R3: num,M: num] :
% 5.49/5.81 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 5.49/5.81 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % take_bit_num_simps(7)
% 5.49/5.81 thf(fact_8794_lessThan__non__empty,axiom,
% 5.49/5.81 ! [X: int] :
% 5.49/5.81 ( ( set_ord_lessThan_int @ X )
% 5.49/5.81 != bot_bot_set_int ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_non_empty
% 5.49/5.81 thf(fact_8795_lessThan__def,axiom,
% 5.49/5.81 ( set_or890127255671739683et_nat
% 5.49/5.81 = ( ^ [U2: set_nat] :
% 5.49/5.81 ( collect_set_nat
% 5.49/5.81 @ ^ [X4: set_nat] : ( ord_less_set_nat @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8796_lessThan__def,axiom,
% 5.49/5.81 ( set_or7637083652282234053n_assn
% 5.49/5.81 = ( ^ [U2: assn] :
% 5.49/5.81 ( collect_assn
% 5.49/5.81 @ ^ [X4: assn] : ( ord_less_assn @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8797_lessThan__def,axiom,
% 5.49/5.81 ( set_ord_lessThan_rat
% 5.49/5.81 = ( ^ [U2: rat] :
% 5.49/5.81 ( collect_rat
% 5.49/5.81 @ ^ [X4: rat] : ( ord_less_rat @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8798_lessThan__def,axiom,
% 5.49/5.81 ( set_ord_lessThan_num
% 5.49/5.81 = ( ^ [U2: num] :
% 5.49/5.81 ( collect_num
% 5.49/5.81 @ ^ [X4: num] : ( ord_less_num @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8799_lessThan__def,axiom,
% 5.49/5.81 ( set_ord_lessThan_nat
% 5.49/5.81 = ( ^ [U2: nat] :
% 5.49/5.81 ( collect_nat
% 5.49/5.81 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8800_lessThan__def,axiom,
% 5.49/5.81 ( set_ord_lessThan_int
% 5.49/5.81 = ( ^ [U2: int] :
% 5.49/5.81 ( collect_int
% 5.49/5.81 @ ^ [X4: int] : ( ord_less_int @ X4 @ U2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_def
% 5.49/5.81 thf(fact_8801_lessThan__empty__iff,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( ( set_ord_lessThan_nat @ N2 )
% 5.49/5.81 = bot_bot_set_nat )
% 5.49/5.81 = ( N2 = zero_zero_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_empty_iff
% 5.49/5.81 thf(fact_8802_Iio__eq__empty__iff,axiom,
% 5.49/5.81 ! [N2: $o] :
% 5.49/5.81 ( ( ( set_ord_lessThan_o @ N2 )
% 5.49/5.81 = bot_bot_set_o )
% 5.49/5.81 = ( N2 = bot_bot_o ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iio_eq_empty_iff
% 5.49/5.81 thf(fact_8803_Iio__eq__empty__iff,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( ( set_ord_lessThan_nat @ N2 )
% 5.49/5.81 = bot_bot_set_nat )
% 5.49/5.81 = ( N2 = bot_bot_nat ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iio_eq_empty_iff
% 5.49/5.81 thf(fact_8804_finite__nat__iff__bounded,axiom,
% 5.49/5.81 ( finite_finite_nat
% 5.49/5.81 = ( ^ [S5: set_nat] :
% 5.49/5.81 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_nat_iff_bounded
% 5.49/5.81 thf(fact_8805_finite__nat__bounded,axiom,
% 5.49/5.81 ! [S: set_nat] :
% 5.49/5.81 ( ( finite_finite_nat @ S )
% 5.49/5.81 => ? [K2: nat] : ( ord_less_eq_set_nat @ S @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % finite_nat_bounded
% 5.49/5.81 thf(fact_8806_lessThan__strict__subset__iff,axiom,
% 5.49/5.81 ! [M: rat,N2: rat] :
% 5.49/5.81 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 5.49/5.81 = ( ord_less_rat @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_strict_subset_iff
% 5.49/5.81 thf(fact_8807_lessThan__strict__subset__iff,axiom,
% 5.49/5.81 ! [M: num,N2: num] :
% 5.49/5.81 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.49/5.81 = ( ord_less_num @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_strict_subset_iff
% 5.49/5.81 thf(fact_8808_lessThan__strict__subset__iff,axiom,
% 5.49/5.81 ! [M: nat,N2: nat] :
% 5.49/5.81 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_strict_subset_iff
% 5.49/5.81 thf(fact_8809_lessThan__strict__subset__iff,axiom,
% 5.49/5.81 ! [M: int,N2: int] :
% 5.49/5.81 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.49/5.81 = ( ord_less_int @ M @ N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % lessThan_strict_subset_iff
% 5.49/5.81 thf(fact_8810_sum_Onat__diff__reindex,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.nat_diff_reindex
% 5.49/5.81 thf(fact_8811_prod_Onat__diff__reindex,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.nat_diff_reindex
% 5.49/5.81 thf(fact_8812_prod_Onat__diff__reindex,axiom,
% 5.49/5.81 ! [G: nat > int,N2: nat] :
% 5.49/5.81 ( ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.nat_diff_reindex
% 5.49/5.81 thf(fact_8813_ivl__disj__un__one_I2_J,axiom,
% 5.49/5.81 ! [L: rat,U: rat] :
% 5.49/5.81 ( ( ord_less_eq_rat @ L @ U )
% 5.49/5.81 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or4029947393144176647an_rat @ L @ U ) )
% 5.49/5.81 = ( set_ord_lessThan_rat @ U ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_un_one(2)
% 5.49/5.81 thf(fact_8814_ivl__disj__un__one_I2_J,axiom,
% 5.49/5.81 ! [L: num,U: num] :
% 5.49/5.81 ( ( ord_less_eq_num @ L @ U )
% 5.49/5.81 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or1222409239386451017an_num @ L @ U ) )
% 5.49/5.81 = ( set_ord_lessThan_num @ U ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_un_one(2)
% 5.49/5.81 thf(fact_8815_ivl__disj__un__one_I2_J,axiom,
% 5.49/5.81 ! [L: nat,U: nat] :
% 5.49/5.81 ( ( ord_less_eq_nat @ L @ U )
% 5.49/5.81 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.49/5.81 = ( set_ord_lessThan_nat @ U ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_un_one(2)
% 5.49/5.81 thf(fact_8816_ivl__disj__un__one_I2_J,axiom,
% 5.49/5.81 ! [L: int,U: int] :
% 5.49/5.81 ( ( ord_less_eq_int @ L @ U )
% 5.49/5.81 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.49/5.81 = ( set_ord_lessThan_int @ U ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_un_one(2)
% 5.49/5.81 thf(fact_8817_ivl__disj__un__one_I2_J,axiom,
% 5.49/5.81 ! [L: code_integer,U: code_integer] :
% 5.49/5.81 ( ( ord_le3102999989581377725nteger @ L @ U )
% 5.49/5.81 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 5.49/5.81 = ( set_or5754767410780653050nteger @ U ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_un_one(2)
% 5.49/5.81 thf(fact_8818_ivl__disj__int__one_I4_J,axiom,
% 5.49/5.81 ! [L: $o,U: $o] :
% 5.49/5.81 ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or8904488021354931149Most_o @ L @ U ) )
% 5.49/5.81 = bot_bot_set_o ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(4)
% 5.49/5.81 thf(fact_8819_ivl__disj__int__one_I4_J,axiom,
% 5.49/5.81 ! [L: int,U: int] :
% 5.49/5.81 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.49/5.81 = bot_bot_set_int ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(4)
% 5.49/5.81 thf(fact_8820_ivl__disj__int__one_I4_J,axiom,
% 5.49/5.81 ! [L: nat,U: nat] :
% 5.49/5.81 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.49/5.81 = bot_bot_set_nat ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(4)
% 5.49/5.81 thf(fact_8821_ivl__disj__int__one_I4_J,axiom,
% 5.49/5.81 ! [L: code_integer,U: code_integer] :
% 5.49/5.81 ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 5.49/5.81 = bot_bo3990330152332043303nteger ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(4)
% 5.49/5.81 thf(fact_8822_Iic__subset__Iio__iff,axiom,
% 5.49/5.81 ! [A: rat,B: rat] :
% 5.49/5.81 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.49/5.81 = ( ord_less_rat @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iic_subset_Iio_iff
% 5.49/5.81 thf(fact_8823_Iic__subset__Iio__iff,axiom,
% 5.49/5.81 ! [A: num,B: num] :
% 5.49/5.81 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.49/5.81 = ( ord_less_num @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iic_subset_Iio_iff
% 5.49/5.81 thf(fact_8824_Iic__subset__Iio__iff,axiom,
% 5.49/5.81 ! [A: nat,B: nat] :
% 5.49/5.81 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.49/5.81 = ( ord_less_nat @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iic_subset_Iio_iff
% 5.49/5.81 thf(fact_8825_Iic__subset__Iio__iff,axiom,
% 5.49/5.81 ! [A: int,B: int] :
% 5.49/5.81 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.49/5.81 = ( ord_less_int @ A @ B ) ) ).
% 5.49/5.81
% 5.49/5.81 % Iic_subset_Iio_iff
% 5.49/5.81 thf(fact_8826_ivl__disj__int__one_I2_J,axiom,
% 5.49/5.81 ! [L: $o,U: $o] :
% 5.49/5.81 ( ( inf_inf_set_o @ ( set_ord_lessThan_o @ L ) @ ( set_or7139685690850216873Than_o @ L @ U ) )
% 5.49/5.81 = bot_bot_set_o ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(2)
% 5.49/5.81 thf(fact_8827_ivl__disj__int__one_I2_J,axiom,
% 5.49/5.81 ! [L: nat,U: nat] :
% 5.49/5.81 ( ( inf_inf_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.49/5.81 = bot_bot_set_nat ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(2)
% 5.49/5.81 thf(fact_8828_ivl__disj__int__one_I2_J,axiom,
% 5.49/5.81 ! [L: int,U: int] :
% 5.49/5.81 ( ( inf_inf_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.49/5.81 = bot_bot_set_int ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(2)
% 5.49/5.81 thf(fact_8829_ivl__disj__int__one_I2_J,axiom,
% 5.49/5.81 ! [L: code_integer,U: code_integer] :
% 5.49/5.81 ( ( inf_in1364745209274528805nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or8404916559141939852nteger @ L @ U ) )
% 5.49/5.81 = bot_bo3990330152332043303nteger ) ).
% 5.49/5.81
% 5.49/5.81 % ivl_disj_int_one(2)
% 5.49/5.81 thf(fact_8830_sum__diff__distrib,axiom,
% 5.49/5.81 ! [Q: int > nat,P: int > nat,N2: int] :
% 5.49/5.81 ( ! [X3: int] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.49/5.81 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 5.49/5.81 = ( groups4541462559716669496nt_nat
% 5.49/5.81 @ ^ [X4: int] : ( minus_minus_nat @ ( P @ X4 ) @ ( Q @ X4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_diff_distrib
% 5.49/5.81 thf(fact_8831_sum__diff__distrib,axiom,
% 5.49/5.81 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.49/5.81 ( ! [X3: nat] : ( ord_less_eq_nat @ ( Q @ X3 ) @ ( P @ X3 ) )
% 5.49/5.81 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [X4: nat] : ( minus_minus_nat @ ( P @ X4 ) @ ( Q @ X4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_diff_distrib
% 5.49/5.81 thf(fact_8832_sum_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 5.49/5.81 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups6857163185585827899at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8833_sum_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > rat,N2: nat] :
% 5.49/5.81 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups2906978787729119204at_rat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8834_sum_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > int,N2: nat] :
% 5.49/5.81 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups3539618377306564664at_int
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8835_sum_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8836_sum__lessThan__telescope_H,axiom,
% 5.49/5.81 ! [F: nat > rat,M: nat] :
% 5.49/5.81 ( ( groups2906978787729119204at_rat
% 5.49/5.81 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ M ) )
% 5.49/5.81 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_lessThan_telescope'
% 5.49/5.81 thf(fact_8837_sum__lessThan__telescope_H,axiom,
% 5.49/5.81 ! [F: nat > int,M: nat] :
% 5.49/5.81 ( ( groups3539618377306564664at_int
% 5.49/5.81 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ M ) )
% 5.49/5.81 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_lessThan_telescope'
% 5.49/5.81 thf(fact_8838_sum__lessThan__telescope,axiom,
% 5.49/5.81 ! [F: nat > rat,M: nat] :
% 5.49/5.81 ( ( groups2906978787729119204at_rat
% 5.49/5.81 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ M ) )
% 5.49/5.81 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_lessThan_telescope
% 5.49/5.81 thf(fact_8839_sum__lessThan__telescope,axiom,
% 5.49/5.81 ! [F: nat > int,M: nat] :
% 5.49/5.81 ( ( groups3539618377306564664at_int
% 5.49/5.81 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ M ) )
% 5.49/5.81 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_lessThan_telescope
% 5.49/5.81 thf(fact_8840_prod_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > code_integer,N2: nat] :
% 5.49/5.81 ( ( groups3455450783089532116nteger @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_3573771949741848930nteger @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups3455450783089532116nteger
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8841_prod_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > assn,N2: nat] :
% 5.49/5.81 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_assn @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups6906906614972039071t_assn
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8842_prod_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > rat,N2: nat] :
% 5.49/5.81 ( ( groups73079841787564623at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups73079841787564623at_rat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8843_prod_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8844_prod_OlessThan__Suc__shift,axiom,
% 5.49/5.81 ! [G: nat > int,N2: nat] :
% 5.49/5.81 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.49/5.81 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.49/5.81 @ ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.lessThan_Suc_shift
% 5.49/5.81 thf(fact_8845_numeral__num__of__nat,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.81 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.49/5.81 = N2 ) ) ).
% 5.49/5.81
% 5.49/5.81 % numeral_num_of_nat
% 5.49/5.81 thf(fact_8846_sum_OatLeast1__atMost__eq,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.atLeast1_atMost_eq
% 5.49/5.81 thf(fact_8847_num__of__nat__One,axiom,
% 5.49/5.81 ! [N2: nat] :
% 5.49/5.81 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.49/5.81 => ( ( num_of_nat @ N2 )
% 5.49/5.81 = one ) ) ).
% 5.49/5.81
% 5.49/5.81 % num_of_nat_One
% 5.49/5.81 thf(fact_8848_prod_OatLeast1__atMost__eq,axiom,
% 5.49/5.81 ! [G: nat > nat,N2: nat] :
% 5.49/5.81 ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.49/5.81 = ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.atLeast1_atMost_eq
% 5.49/5.81 thf(fact_8849_prod_OatLeast1__atMost__eq,axiom,
% 5.49/5.81 ! [G: nat > int,N2: nat] :
% 5.49/5.81 ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.49/5.81 = ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.atLeast1_atMost_eq
% 5.49/5.81 thf(fact_8850_sum__bounds__lt__plus1,axiom,
% 5.49/5.81 ! [F: nat > nat,Mm: nat] :
% 5.49/5.81 ( ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum_bounds_lt_plus1
% 5.49/5.81 thf(fact_8851_sum_Onat__group,axiom,
% 5.49/5.81 ! [G: nat > nat,K: nat,N2: nat] :
% 5.49/5.81 ( ( groups3542108847815614940at_nat
% 5.49/5.81 @ ^ [M3: nat] : ( groups3542108847815614940at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K ) @ K ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % sum.nat_group
% 5.49/5.81 thf(fact_8852_prod_Onat__group,axiom,
% 5.49/5.81 ! [G: nat > nat,K: nat,N2: nat] :
% 5.49/5.81 ( ( groups708209901874060359at_nat
% 5.49/5.81 @ ^ [M3: nat] : ( groups708209901874060359at_nat @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K ) @ K ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 5.49/5.81
% 5.49/5.81 % prod.nat_group
% 5.49/5.81 thf(fact_8853_prod_Onat__group,axiom,
% 5.49/5.81 ! [G: nat > int,K: nat,N2: nat] :
% 5.49/5.81 ( ( groups705719431365010083at_int
% 5.49/5.81 @ ^ [M3: nat] : ( groups705719431365010083at_int @ G @ ( set_or4665077453230672383an_nat @ ( times_times_nat @ M3 @ K ) @ ( plus_plus_nat @ ( times_times_nat @ M3 @ K ) @ K ) ) )
% 5.49/5.81 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.81 = ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( times_times_nat @ N2 @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.nat_group
% 5.49/5.82 thf(fact_8854_sum_Onested__swap_H,axiom,
% 5.49/5.82 ! [A: nat > nat > nat,N2: nat] :
% 5.49/5.82 ( ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( groups3542108847815614940at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.49/5.82 @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.49/5.82 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.nested_swap'
% 5.49/5.82 thf(fact_8855_prod_Onested__swap_H,axiom,
% 5.49/5.82 ! [A: nat > nat > nat,N2: nat] :
% 5.49/5.82 ( ( groups708209901874060359at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( groups708209901874060359at_nat @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.49/5.82 @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( groups708209901874060359at_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( groups708209901874060359at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.49/5.82 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.nested_swap'
% 5.49/5.82 thf(fact_8856_prod_Onested__swap_H,axiom,
% 5.49/5.82 ! [A: nat > nat > int,N2: nat] :
% 5.49/5.82 ( ( groups705719431365010083at_int
% 5.49/5.82 @ ^ [I4: nat] : ( groups705719431365010083at_int @ ( A @ I4 ) @ ( set_ord_lessThan_nat @ I4 ) )
% 5.49/5.82 @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( groups705719431365010083at_int
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( groups705719431365010083at_int
% 5.49/5.82 @ ^ [I4: nat] : ( A @ I4 @ J3 )
% 5.49/5.82 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.nested_swap'
% 5.49/5.82 thf(fact_8857_fact__numeral,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % fact_numeral
% 5.49/5.82 thf(fact_8858_fact__numeral,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( semiri3624122377584611663nteger @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ K ) @ ( semiri3624122377584611663nteger @ ( pred_numeral @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % fact_numeral
% 5.49/5.82 thf(fact_8859_fact__numeral,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( semiri773545260158071498ct_rat @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( times_times_rat @ ( numeral_numeral_rat @ K ) @ ( semiri773545260158071498ct_rat @ ( pred_numeral @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % fact_numeral
% 5.49/5.82 thf(fact_8860_fact__numeral,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( semiri2447717529341329178atural @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ K ) @ ( semiri2447717529341329178atural @ ( pred_numeral @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % fact_numeral
% 5.49/5.82 thf(fact_8861_fact__numeral,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % fact_numeral
% 5.49/5.82 thf(fact_8862_ivl__disj__un__one_I4_J,axiom,
% 5.49/5.82 ! [L: rat,U: rat] :
% 5.49/5.82 ( ( ord_less_eq_rat @ L @ U )
% 5.49/5.82 => ( ( sup_sup_set_rat @ ( set_ord_lessThan_rat @ L ) @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.49/5.82 = ( set_ord_atMost_rat @ U ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % ivl_disj_un_one(4)
% 5.49/5.82 thf(fact_8863_ivl__disj__un__one_I4_J,axiom,
% 5.49/5.82 ! [L: num,U: num] :
% 5.49/5.82 ( ( ord_less_eq_num @ L @ U )
% 5.49/5.82 => ( ( sup_sup_set_num @ ( set_ord_lessThan_num @ L ) @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.49/5.82 = ( set_ord_atMost_num @ U ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % ivl_disj_un_one(4)
% 5.49/5.82 thf(fact_8864_ivl__disj__un__one_I4_J,axiom,
% 5.49/5.82 ! [L: int,U: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ L @ U )
% 5.49/5.82 => ( ( sup_sup_set_int @ ( set_ord_lessThan_int @ L ) @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.49/5.82 = ( set_ord_atMost_int @ U ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % ivl_disj_un_one(4)
% 5.49/5.82 thf(fact_8865_ivl__disj__un__one_I4_J,axiom,
% 5.49/5.82 ! [L: nat,U: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ L @ U )
% 5.49/5.82 => ( ( sup_sup_set_nat @ ( set_ord_lessThan_nat @ L ) @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.49/5.82 = ( set_ord_atMost_nat @ U ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % ivl_disj_un_one(4)
% 5.49/5.82 thf(fact_8866_ivl__disj__un__one_I4_J,axiom,
% 5.49/5.82 ! [L: code_integer,U: code_integer] :
% 5.49/5.82 ( ( ord_le3102999989581377725nteger @ L @ U )
% 5.49/5.82 => ( ( sup_su848401254843788991nteger @ ( set_or5754767410780653050nteger @ L ) @ ( set_or189985376899183464nteger @ L @ U ) )
% 5.49/5.82 = ( set_or9101266186257409494nteger @ U ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % ivl_disj_un_one(4)
% 5.49/5.82 thf(fact_8867_one__diff__power__eq,axiom,
% 5.49/5.82 ! [X: code_integer,N2: nat] :
% 5.49/5.82 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq
% 5.49/5.82 thf(fact_8868_one__diff__power__eq,axiom,
% 5.49/5.82 ! [X: rat,N2: nat] :
% 5.49/5.82 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.49/5.82 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq
% 5.49/5.82 thf(fact_8869_one__diff__power__eq,axiom,
% 5.49/5.82 ! [X: int,N2: nat] :
% 5.49/5.82 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.49/5.82 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq
% 5.49/5.82 thf(fact_8870_power__diff__1__eq,axiom,
% 5.49/5.82 ! [X: code_integer,N2: nat] :
% 5.49/5.82 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ one_one_Code_integer )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ one_one_Code_integer ) @ ( groups7501900531339628137nteger @ ( power_8256067586552552935nteger @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_1_eq
% 5.49/5.82 thf(fact_8871_power__diff__1__eq,axiom,
% 5.49/5.82 ! [X: rat,N2: nat] :
% 5.49/5.82 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat )
% 5.49/5.82 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_1_eq
% 5.49/5.82 thf(fact_8872_power__diff__1__eq,axiom,
% 5.49/5.82 ! [X: int,N2: nat] :
% 5.49/5.82 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ one_one_int )
% 5.49/5.82 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_1_eq
% 5.49/5.82 thf(fact_8873_geometric__sum,axiom,
% 5.49/5.82 ! [X: rat,N2: nat] :
% 5.49/5.82 ( ( X != one_one_rat )
% 5.49/5.82 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.82 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % geometric_sum
% 5.49/5.82 thf(fact_8874_image__atLeastZeroLessThan__int,axiom,
% 5.49/5.82 ! [U: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.49/5.82 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.49/5.82 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % image_atLeastZeroLessThan_int
% 5.49/5.82 thf(fact_8875_sum_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > multis2468970476368604999at_nat,N2: nat] :
% 5.49/5.82 ( ( groups6857163185585827899at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( plus_p7104986032573967614at_nat @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups6857163185585827899at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.atMost_shift
% 5.49/5.82 thf(fact_8876_sum_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > rat,N2: nat] :
% 5.49/5.82 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.atMost_shift
% 5.49/5.82 thf(fact_8877_sum_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > int,N2: nat] :
% 5.49/5.82 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.atMost_shift
% 5.49/5.82 thf(fact_8878_sum_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > nat,N2: nat] :
% 5.49/5.82 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.atMost_shift
% 5.49/5.82 thf(fact_8879_prod_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > code_integer,N2: nat] :
% 5.49/5.82 ( ( groups3455450783089532116nteger @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups3455450783089532116nteger
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.atMost_shift
% 5.49/5.82 thf(fact_8880_prod_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > assn,N2: nat] :
% 5.49/5.82 ( ( groups6906906614972039071t_assn @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( times_times_assn @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups6906906614972039071t_assn
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.atMost_shift
% 5.49/5.82 thf(fact_8881_prod_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > rat,N2: nat] :
% 5.49/5.82 ( ( groups73079841787564623at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( times_times_rat @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups73079841787564623at_rat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.atMost_shift
% 5.49/5.82 thf(fact_8882_prod_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > nat,N2: nat] :
% 5.49/5.82 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( times_times_nat @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups708209901874060359at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.atMost_shift
% 5.49/5.82 thf(fact_8883_prod_OatMost__shift,axiom,
% 5.49/5.82 ! [G: nat > int,N2: nat] :
% 5.49/5.82 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.49/5.82 = ( times_times_int @ ( G @ zero_zero_nat )
% 5.49/5.82 @ ( groups705719431365010083at_int
% 5.49/5.82 @ ^ [I4: nat] : ( G @ ( suc @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod.atMost_shift
% 5.49/5.82 thf(fact_8884_num__of__nat__double,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.49/5.82 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % num_of_nat_double
% 5.49/5.82 thf(fact_8885_num__of__nat__plus__distrib,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.49/5.82 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.49/5.82 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % num_of_nat_plus_distrib
% 5.49/5.82 thf(fact_8886_sum__gp__strict,axiom,
% 5.49/5.82 ! [X: rat,N2: nat] :
% 5.49/5.82 ( ( ( X = one_one_rat )
% 5.49/5.82 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.82 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.49/5.82 & ( ( X != one_one_rat )
% 5.49/5.82 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.49/5.82 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_gp_strict
% 5.49/5.82 thf(fact_8887_diff__power__eq__sum,axiom,
% 5.49/5.82 ! [X: code_integer,N2: nat,Y: code_integer] :
% 5.49/5.82 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ ( suc @ N2 ) ) @ ( power_8256067586552552935nteger @ Y @ ( suc @ N2 ) ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 5.49/5.82 @ ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [P7: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ X @ P7 ) @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ P7 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % diff_power_eq_sum
% 5.49/5.82 thf(fact_8888_diff__power__eq__sum,axiom,
% 5.49/5.82 ! [X: rat,N2: nat,Y: rat] :
% 5.49/5.82 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 5.49/5.82 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.49/5.82 @ ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [P7: nat] : ( times_times_rat @ ( power_power_rat @ X @ P7 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P7 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % diff_power_eq_sum
% 5.49/5.82 thf(fact_8889_diff__power__eq__sum,axiom,
% 5.49/5.82 ! [X: int,N2: nat,Y: int] :
% 5.49/5.82 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.49/5.82 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.49/5.82 @ ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [P7: nat] : ( times_times_int @ ( power_power_int @ X @ P7 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P7 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % diff_power_eq_sum
% 5.49/5.82 thf(fact_8890_power__diff__sumr2,axiom,
% 5.49/5.82 ! [X: code_integer,N2: nat,Y: code_integer] :
% 5.49/5.82 ( ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ X @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ X @ Y )
% 5.49/5.82 @ ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [I4: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) ) @ ( power_8256067586552552935nteger @ X @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_sumr2
% 5.49/5.82 thf(fact_8891_power__diff__sumr2,axiom,
% 5.49/5.82 ! [X: rat,N2: nat,Y: rat] :
% 5.49/5.82 ( ( minus_minus_rat @ ( power_power_rat @ X @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.49/5.82 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.49/5.82 @ ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [I4: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) ) @ ( power_power_rat @ X @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_sumr2
% 5.49/5.82 thf(fact_8892_power__diff__sumr2,axiom,
% 5.49/5.82 ! [X: int,N2: nat,Y: int] :
% 5.49/5.82 ( ( minus_minus_int @ ( power_power_int @ X @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.49/5.82 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.49/5.82 @ ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [I4: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) ) @ ( power_power_int @ X @ I4 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % power_diff_sumr2
% 5.49/5.82 thf(fact_8893_take__bit__numeral__bit0,axiom,
% 5.49/5.82 ! [L: num,K: num] :
% 5.49/5.82 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ L ) @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( pred_numeral @ L ) @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_bit_numeral_bit0
% 5.49/5.82 thf(fact_8894_take__bit__numeral__bit0,axiom,
% 5.49/5.82 ! [L: num,K: num] :
% 5.49/5.82 ( ( bit_se569199155075624693atural @ ( numeral_numeral_nat @ L ) @ ( numera5444537566228673987atural @ ( bit0 @ K ) ) )
% 5.49/5.82 = ( times_2397367101498566445atural @ ( bit_se569199155075624693atural @ ( pred_numeral @ L ) @ ( numera5444537566228673987atural @ K ) ) @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_bit_numeral_bit0
% 5.49/5.82 thf(fact_8895_take__bit__numeral__bit0,axiom,
% 5.49/5.82 ! [L: num,K: num] :
% 5.49/5.82 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.49/5.82 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_bit_numeral_bit0
% 5.49/5.82 thf(fact_8896_take__bit__numeral__bit0,axiom,
% 5.49/5.82 ! [L: num,K: num] :
% 5.49/5.82 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.49/5.82 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_bit_numeral_bit0
% 5.49/5.82 thf(fact_8897_one__diff__power__eq_H,axiom,
% 5.49/5.82 ! [X: code_integer,N2: nat] :
% 5.49/5.82 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ X @ N2 ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ one_one_Code_integer @ X )
% 5.49/5.82 @ ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [I4: nat] : ( power_8256067586552552935nteger @ X @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq'
% 5.49/5.82 thf(fact_8898_one__diff__power__eq_H,axiom,
% 5.49/5.82 ! [X: rat,N2: nat] :
% 5.49/5.82 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N2 ) )
% 5.49/5.82 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.49/5.82 @ ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [I4: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq'
% 5.49/5.82 thf(fact_8899_one__diff__power__eq_H,axiom,
% 5.49/5.82 ! [X: int,N2: nat] :
% 5.49/5.82 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N2 ) )
% 5.49/5.82 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.49/5.82 @ ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [I4: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N2 @ ( suc @ I4 ) ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_diff_power_eq'
% 5.49/5.82 thf(fact_8900_sum_Otriangle__reindex,axiom,
% 5.49/5.82 ! [G: nat > nat > nat,N2: nat] :
% 5.49/5.82 ( ( groups977919841031483927at_nat @ ( produc6842872674320459806at_nat @ G )
% 5.49/5.82 @ ( collec3392354462482085612at_nat
% 5.49/5.82 @ ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [I4: nat,J3: nat] : ( ord_less_nat @ ( plus_plus_nat @ I4 @ J3 ) @ N2 ) ) ) )
% 5.49/5.82 = ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [I4: nat] : ( G @ I4 @ ( minus_minus_nat @ K3 @ I4 ) )
% 5.49/5.82 @ ( set_ord_atMost_nat @ K3 ) )
% 5.49/5.82 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum.triangle_reindex
% 5.49/5.82 thf(fact_8901_mask__numeral,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_se2119862282449309892nteger @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_numeral
% 5.49/5.82 thf(fact_8902_mask__numeral,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_se943457434206027407atural @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se943457434206027407atural @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_numeral
% 5.49/5.82 thf(fact_8903_mask__numeral,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_numeral
% 5.49/5.82 thf(fact_8904_mask__numeral,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_numeral
% 5.49/5.82 thf(fact_8905_horner__sum__of__bool__2__less,axiom,
% 5.49/5.82 ! [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 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_of_bool_2_less
% 5.49/5.82 thf(fact_8906_xor__numerals_I4_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(4)
% 5.49/5.82 thf(fact_8907_xor__numerals_I4_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(4)
% 5.49/5.82 thf(fact_8908_xor__numerals_I4_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(4)
% 5.49/5.82 thf(fact_8909_xor__numerals_I4_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(4)
% 5.49/5.82 thf(fact_8910_xor__numerals_I6_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(6)
% 5.49/5.82 thf(fact_8911_xor__numerals_I6_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(6)
% 5.49/5.82 thf(fact_8912_xor__numerals_I6_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(6)
% 5.49/5.82 thf(fact_8913_xor__numerals_I6_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(6)
% 5.49/5.82 thf(fact_8914_divmod__step__integer__def,axiom,
% 5.49/5.82 ( unique4921790084139445826nteger
% 5.49/5.82 = ( ^ [L2: num] :
% 5.49/5.82 ( produc6916734918728496179nteger
% 5.49/5.82 @ ^ [Q7: code_integer,R4: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R4 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q7 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R4 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q7 ) @ R4 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_step_integer_def
% 5.49/5.82 thf(fact_8915_mask__nat__positive__iff,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.49/5.82 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_nat_positive_iff
% 5.49/5.82 thf(fact_8916_xor__nonnegative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.49/5.82 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.82 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_nonnegative_int_iff
% 5.49/5.82 thf(fact_8917_xor__negative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.49/5.82 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.82 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_negative_int_iff
% 5.49/5.82 thf(fact_8918_xor__numerals_I3_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(3)
% 5.49/5.82 thf(fact_8919_xor__numerals_I3_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit0 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(3)
% 5.49/5.82 thf(fact_8920_xor__numerals_I3_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit0 @ X ) ) @ ( numera5444537566228673987atural @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(3)
% 5.49/5.82 thf(fact_8921_xor__numerals_I3_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.49/5.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(3)
% 5.49/5.82 thf(fact_8922_xor__numerals_I7_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(7)
% 5.49/5.82 thf(fact_8923_xor__numerals_I7_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ ( bit1 @ X ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ ( numera6620942414471956472nteger @ X ) @ ( numera6620942414471956472nteger @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(7)
% 5.49/5.82 thf(fact_8924_xor__numerals_I7_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ ( bit1 @ X ) ) @ ( numera5444537566228673987atural @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( times_2397367101498566445atural @ ( numera5444537566228673987atural @ ( bit0 @ one ) ) @ ( bit_se2046307713759805098atural @ ( numera5444537566228673987atural @ X ) @ ( numera5444537566228673987atural @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(7)
% 5.49/5.82 thf(fact_8925_xor__numerals_I7_J,axiom,
% 5.49/5.82 ! [X: num,Y: num] :
% 5.49/5.82 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.49/5.82 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_numerals(7)
% 5.49/5.82 thf(fact_8926_divmod__integer_H__def,axiom,
% 5.49/5.82 ( unique3479559517661332726nteger
% 5.49/5.82 = ( ^ [M3: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_integer'_def
% 5.49/5.82 thf(fact_8927_exhaustive__integer_H_Ocases,axiom,
% 5.49/5.82 ! [X: produc8763457246119570046nteger] :
% 5.49/5.82 ~ ! [F2: code_integer > option6357759511663192854e_term,D: code_integer,I3: code_integer] :
% 5.49/5.82 ( X
% 5.49/5.82 != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D @ I3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % exhaustive_integer'.cases
% 5.49/5.82 thf(fact_8928_full__exhaustive__integer_H_Ocases,axiom,
% 5.49/5.82 ! [X: produc1908205239877642774nteger] :
% 5.49/5.82 ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D: code_integer,I3: code_integer] :
% 5.49/5.82 ( X
% 5.49/5.82 != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D @ I3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % full_exhaustive_integer'.cases
% 5.49/5.82 thf(fact_8929_image__add__integer__atLeastLessThan,axiom,
% 5.49/5.82 ! [L: code_integer,U: code_integer] :
% 5.49/5.82 ( ( image_4470545334726330049nteger
% 5.49/5.82 @ ^ [X4: code_integer] : ( plus_p5714425477246183910nteger @ X4 @ L )
% 5.49/5.82 @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ ( minus_8373710615458151222nteger @ U @ L ) ) )
% 5.49/5.82 = ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 5.49/5.82
% 5.49/5.82 % image_add_integer_atLeastLessThan
% 5.49/5.82 thf(fact_8930_less__eq__integer__code_I1_J,axiom,
% 5.49/5.82 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.49/5.82
% 5.49/5.82 % less_eq_integer_code(1)
% 5.49/5.82 thf(fact_8931_sgn__integer__code,axiom,
% 5.49/5.82 ( sgn_sgn_Code_integer
% 5.49/5.82 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( K3 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sgn_integer_code
% 5.49/5.82 thf(fact_8932_atLeastLessThanPlusOne__atLeastAtMost__integer,axiom,
% 5.49/5.82 ! [L: code_integer,U: code_integer] :
% 5.49/5.82 ( ( set_or8404916559141939852nteger @ L @ ( plus_p5714425477246183910nteger @ U @ one_one_Code_integer ) )
% 5.49/5.82 = ( set_or189985376899183464nteger @ L @ U ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastLessThanPlusOne_atLeastAtMost_integer
% 5.49/5.82 thf(fact_8933_less__eq__mask,axiom,
% 5.49/5.82 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_mask
% 5.49/5.82 thf(fact_8934_XOR__lower,axiom,
% 5.49/5.82 ! [X: int,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % XOR_lower
% 5.49/5.82 thf(fact_8935_mask__nonnegative__int,axiom,
% 5.49/5.82 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_nonnegative_int
% 5.49/5.82 thf(fact_8936_not__mask__negative__int,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.49/5.82
% 5.49/5.82 % not_mask_negative_int
% 5.49/5.82 thf(fact_8937_less__mask,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.49/5.82 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_mask
% 5.49/5.82 thf(fact_8938_mask__nat__less__exp,axiom,
% 5.49/5.82 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % mask_nat_less_exp
% 5.49/5.82 thf(fact_8939_finite__int__iff__bounded,axiom,
% 5.49/5.82 ( finite_finite_int
% 5.49/5.82 = ( ^ [S5: set_int] :
% 5.49/5.82 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_int_iff_bounded
% 5.49/5.82 thf(fact_8940_XOR__upper,axiom,
% 5.49/5.82 ! [X: int,N2: nat,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.82 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.82 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % XOR_upper
% 5.49/5.82 thf(fact_8941_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups8594936613892548326nteger
% 5.49/5.82 = ( ^ [F3: int > code_integer,A5: code_integer,Xs3: list_int] :
% 5.49/5.82 ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [N: nat] : ( times_3573771949741848930nteger @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_8256067586552552935nteger @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8942_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups8223283053655703690nteger
% 5.49/5.82 = ( ^ [F3: nat > code_integer,A5: code_integer,Xs3: list_nat] :
% 5.49/5.82 ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [N: nat] : ( times_3573771949741848930nteger @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_8256067586552552935nteger @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8943_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups3417619833198082522nteger
% 5.49/5.82 = ( ^ [F3: $o > code_integer,A5: code_integer,Xs3: list_o] :
% 5.49/5.82 ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [N: nat] : ( times_3573771949741848930nteger @ ( F3 @ ( nth_o @ Xs3 @ N ) ) @ ( power_8256067586552552935nteger @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8944_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups7852591826665563233nt_rat
% 5.49/5.82 = ( ^ [F3: int > rat,A5: rat,Xs3: list_int] :
% 5.49/5.82 ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8945_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups6853238114764508677at_rat
% 5.49/5.82 = ( ^ [F3: nat > rat,A5: rat,Xs3: list_nat] :
% 5.49/5.82 ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8946_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups8483887719401441109_o_rat
% 5.49/5.82 = ( ^ [F3: $o > rat,A5: rat,Xs3: list_o] :
% 5.49/5.82 ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [N: nat] : ( times_times_rat @ ( F3 @ ( nth_o @ Xs3 @ N ) ) @ ( power_power_rat @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_o @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8947_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups8485231416243008693nt_int
% 5.49/5.82 = ( ^ [F3: int > int,A5: int,Xs3: list_int] :
% 5.49/5.82 ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [N: nat] : ( times_times_int @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_int @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8948_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups7485877704341954137at_int
% 5.49/5.82 = ( ^ [F3: nat > int,A5: int,Xs3: list_nat] :
% 5.49/5.82 ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [N: nat] : ( times_times_int @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_int @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8949_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups8487721886752058969nt_nat
% 5.49/5.82 = ( ^ [F3: int > nat,A5: nat,Xs3: list_int] :
% 5.49/5.82 ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [N: nat] : ( times_times_nat @ ( F3 @ ( nth_int @ Xs3 @ N ) ) @ ( power_power_nat @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_int @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8950_horner__sum__eq__sum,axiom,
% 5.49/5.82 ( groups7488368174851004413at_nat
% 5.49/5.82 = ( ^ [F3: nat > nat,A5: nat,Xs3: list_nat] :
% 5.49/5.82 ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [N: nat] : ( times_times_nat @ ( F3 @ ( nth_nat @ Xs3 @ N ) ) @ ( power_power_nat @ A5 @ N ) )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % horner_sum_eq_sum
% 5.49/5.82 thf(fact_8951_integer__of__int__code,axiom,
% 5.49/5.82 ( code_integer_of_int
% 5.49/5.82 = ( ^ [K3: int] :
% 5.49/5.82 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.49/5.82 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.49/5.82 @ ( if_Code_integer
% 5.49/5.82 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.49/5.82 = zero_zero_int )
% 5.49/5.82 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.49/5.82 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % integer_of_int_code
% 5.49/5.82 thf(fact_8952_integer__of__num_I3_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( code_integer_of_num @ ( bit1 @ N2 ) )
% 5.49/5.82 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.49/5.82
% 5.49/5.82 % integer_of_num(3)
% 5.49/5.82 thf(fact_8953_take__bit__num__code,axiom,
% 5.49/5.82 ( bit_take_bit_num
% 5.49/5.82 = ( ^ [N: nat,M3: num] :
% 5.49/5.82 ( produc478579273971653890on_num
% 5.49/5.82 @ ^ [A5: nat,X4: num] :
% 5.49/5.82 ( case_nat_option_num @ none_num
% 5.49/5.82 @ ^ [O: nat] :
% 5.49/5.82 ( case_num_option_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [P7: num] :
% 5.49/5.82 ( case_o6005452278849405969um_num @ none_num
% 5.49/5.82 @ ^ [Q7: num] : ( some_num @ ( bit0 @ Q7 ) )
% 5.49/5.82 @ ( bit_take_bit_num @ O @ P7 ) )
% 5.49/5.82 @ ^ [P7: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P7 ) ) )
% 5.49/5.82 @ X4 )
% 5.49/5.82 @ A5 )
% 5.49/5.82 @ ( product_Pair_nat_num @ N @ M3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_bit_num_code
% 5.49/5.82 thf(fact_8954_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_o,F: $o > nat] :
% 5.49/5.82 ( ( finite_finite_o @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups8507830703676809646_o_nat @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [A5: $o] :
% 5.49/5.82 ( ( member_o @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8955_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_int,F: int > nat] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups4541462559716669496nt_nat @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [A5: int] :
% 5.49/5.82 ( ( member_int @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8956_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,F: code_integer > nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups7237345082560585321er_nat @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [A5: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8957_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_o,F: $o > int] :
% 5.49/5.82 ( ( finite_finite_o @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups8505340233167759370_o_int @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [A5: $o] :
% 5.49/5.82 ( ( member_o @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8958_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > int] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [A5: nat] :
% 5.49/5.82 ( ( member_nat @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8959_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,F: code_integer > int] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups7234854612051535045er_int @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [A5: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8960_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_o,F: $o > code_integer] :
% 5.49/5.82 ( ( finite_finite_o @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups4406642042086082107nteger @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [A5: $o] :
% 5.49/5.82 ( ( member_o @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8961_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > code_integer] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7501900531339628137nteger @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [A5: nat] :
% 5.49/5.82 ( ( member_nat @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8962_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_int,F: int > code_integer] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups7873554091576472773nteger @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [A5: int] :
% 5.49/5.82 ( ( member_int @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8963_even__sum__iff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,F: code_integer > code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( groups879477027807139574nteger @ F @ A3 ) )
% 5.49/5.82 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.49/5.82 @ ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [A5: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ A5 @ A3 )
% 5.49/5.82 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( F @ A5 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % even_sum_iff
% 5.49/5.82 thf(fact_8964_card__Collect__less__nat,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [I4: nat] : ( ord_less_nat @ I4 @ N2 ) ) )
% 5.49/5.82 = N2 ) ).
% 5.49/5.82
% 5.49/5.82 % card_Collect_less_nat
% 5.49/5.82 thf(fact_8965_finite__atLeastLessThan__integer,axiom,
% 5.49/5.82 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ L @ U ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_atLeastLessThan_integer
% 5.49/5.82 thf(fact_8966_finite__atLeastAtMost__integer,axiom,
% 5.49/5.82 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or189985376899183464nteger @ L @ U ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_atLeastAtMost_integer
% 5.49/5.82 thf(fact_8967_card__Collect__le__nat,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [I4: nat] : ( ord_less_eq_nat @ I4 @ N2 ) ) )
% 5.49/5.82 = ( suc @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Collect_le_nat
% 5.49/5.82 thf(fact_8968_card_Oempty,axiom,
% 5.49/5.82 ( ( finite_card_set_nat @ bot_bot_set_set_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8969_card_Oempty,axiom,
% 5.49/5.82 ( ( finite_card_list_nat @ bot_bot_set_list_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8970_card_Oempty,axiom,
% 5.49/5.82 ( ( finite711546835091564841at_nat @ bot_bo2099793752762293965at_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8971_card_Oempty,axiom,
% 5.49/5.82 ( ( finite_card_o @ bot_bot_set_o )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8972_card_Oempty,axiom,
% 5.49/5.82 ( ( finite_card_nat @ bot_bot_set_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8973_card_Oempty,axiom,
% 5.49/5.82 ( ( finite_card_int @ bot_bot_set_int )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % card.empty
% 5.49/5.82 thf(fact_8974_prod__constant,axiom,
% 5.49/5.82 ! [Y: nat,A3: set_set_nat] :
% 5.49/5.82 ( ( groups4248547760180025341at_nat
% 5.49/5.82 @ ^ [X4: set_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_nat @ Y @ ( finite_card_set_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8975_prod__constant,axiom,
% 5.49/5.82 ! [Y: nat,A3: set_list_nat] :
% 5.49/5.82 ( ( groups2907647131375434839at_nat
% 5.49/5.82 @ ^ [X4: list_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_nat @ Y @ ( finite_card_list_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8976_prod__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_set_nat] :
% 5.49/5.82 ( ( groups4246057289670975065at_int
% 5.49/5.82 @ ^ [X4: set_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_int @ Y @ ( finite_card_set_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8977_prod__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_list_nat] :
% 5.49/5.82 ( ( groups2905156660866384563at_int
% 5.49/5.82 @ ^ [X4: list_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_int @ Y @ ( finite_card_list_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8978_prod__constant,axiom,
% 5.49/5.82 ! [Y: nat,A3: set_nat] :
% 5.49/5.82 ( ( groups708209901874060359at_nat
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_nat @ Y @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8979_prod__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_nat] :
% 5.49/5.82 ( ( groups705719431365010083at_int
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_int @ Y @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8980_prod__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_int] :
% 5.49/5.82 ( ( groups1705073143266064639nt_int
% 5.49/5.82 @ ^ [X4: int] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( power_power_int @ Y @ ( finite_card_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % prod_constant
% 5.49/5.82 thf(fact_8981_case__nat__numeral,axiom,
% 5.49/5.82 ! [A: option_num,F: nat > option_num,V: num] :
% 5.49/5.82 ( ( case_nat_option_num @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.49/5.82 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_numeral
% 5.49/5.82 thf(fact_8982_case__nat__numeral,axiom,
% 5.49/5.82 ! [A: $o,F: nat > $o,V: num] :
% 5.49/5.82 ( ( case_nat_o @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.49/5.82 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_numeral
% 5.49/5.82 thf(fact_8983_case__nat__numeral,axiom,
% 5.49/5.82 ! [A: nat,F: nat > nat,V: num] :
% 5.49/5.82 ( ( case_nat_nat @ A @ F @ ( numeral_numeral_nat @ V ) )
% 5.49/5.82 = ( F @ ( pred_numeral @ V ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_numeral
% 5.49/5.82 thf(fact_8984_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( ( finite_card_set_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bot_set_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8985_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ( ( ( finite_card_list_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bot_set_list_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8986_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( ( finite4902975817058060853nteger @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bo3990330152332043303nteger ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8987_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ A3 )
% 5.49/5.82 => ( ( ( finite711546835091564841at_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bo2099793752762293965at_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8988_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_o] :
% 5.49/5.82 ( ( finite_finite_o @ A3 )
% 5.49/5.82 => ( ( ( finite_card_o @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bot_set_o ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8989_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( ( finite_card_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8990_card__0__eq,axiom,
% 5.49/5.82 ! [A3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( ( finite_card_int @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( A3 = bot_bot_set_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_0_eq
% 5.49/5.82 thf(fact_8991_sum__constant,axiom,
% 5.49/5.82 ! [Y: rat,A3: set_nat] :
% 5.49/5.82 ( ( groups2906978787729119204at_rat
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8992_sum__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_nat] :
% 5.49/5.82 ( ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8993_sum__constant,axiom,
% 5.49/5.82 ! [Y: code_integer,A3: set_nat] :
% 5.49/5.82 ( ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8994_sum__constant,axiom,
% 5.49/5.82 ! [Y: nat,A3: set_nat] :
% 5.49/5.82 ( ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8995_sum__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_int] :
% 5.49/5.82 ( ( groups4538972089207619220nt_int
% 5.49/5.82 @ ^ [X4: int] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_int @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8996_sum__constant,axiom,
% 5.49/5.82 ! [Y: rat,A3: set_set_nat] :
% 5.49/5.82 ( ( groups7659867448343625626at_rat
% 5.49/5.82 @ ^ [X4: set_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_set_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8997_sum__constant,axiom,
% 5.49/5.82 ! [Y: rat,A3: set_list_nat] :
% 5.49/5.82 ( ( groups3760926236672600436at_rat
% 5.49/5.82 @ ^ [X4: list_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_list_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8998_sum__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_set_nat] :
% 5.49/5.82 ( ( groups8292507037921071086at_int
% 5.49/5.82 @ ^ [X4: set_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_set_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_8999_sum__constant,axiom,
% 5.49/5.82 ! [Y: int,A3: set_list_nat] :
% 5.49/5.82 ( ( groups4393565826250045896at_int
% 5.49/5.82 @ ^ [X4: list_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_list_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_9000_sum__constant,axiom,
% 5.49/5.82 ! [Y: nat,A3: set_set_nat] :
% 5.49/5.82 ( ( groups8294997508430121362at_nat
% 5.49/5.82 @ ^ [X4: set_nat] : Y
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_set_nat @ A3 ) ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_constant
% 5.49/5.82 thf(fact_9001_case__nat__add__eq__if,axiom,
% 5.49/5.82 ! [A: option_num,F: nat > option_num,V: num,N2: nat] :
% 5.49/5.82 ( ( case_nat_option_num @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.49/5.82 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_add_eq_if
% 5.49/5.82 thf(fact_9002_case__nat__add__eq__if,axiom,
% 5.49/5.82 ! [A: $o,F: nat > $o,V: num,N2: nat] :
% 5.49/5.82 ( ( case_nat_o @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.49/5.82 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_add_eq_if
% 5.49/5.82 thf(fact_9003_case__nat__add__eq__if,axiom,
% 5.49/5.82 ! [A: nat,F: nat > nat,V: num,N2: nat] :
% 5.49/5.82 ( ( case_nat_nat @ A @ F @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.49/5.82 = ( F @ ( plus_plus_nat @ ( pred_numeral @ V ) @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % case_nat_add_eq_if
% 5.49/5.82 thf(fact_9004_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_int,P: int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( groups7873554091576472773nteger
% 5.49/5.82 @ ^ [X4: int] : ( zero_n356916108424825756nteger @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri4939895301339042750nteger @ ( finite_card_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9005_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,P: code_integer > $o] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( groups879477027807139574nteger
% 5.49/5.82 @ ^ [X4: code_integer] : ( zero_n356916108424825756nteger @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri4939895301339042750nteger @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9006_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_nat,P: nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( groups7501900531339628137nteger
% 5.49/5.82 @ ^ [X4: nat] : ( zero_n356916108424825756nteger @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri4939895301339042750nteger @ ( finite_card_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9007_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_int,P: int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [X4: int] : ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1316708129612266289at_nat @ ( finite_card_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9008_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,P: code_integer > $o] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [X4: code_integer] : ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1316708129612266289at_nat @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9009_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,P: code_integer > $o] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( groups7234854612051535045er_int
% 5.49/5.82 @ ^ [X4: code_integer] : ( zero_n2684676970156552555ol_int @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1314217659103216013at_int @ ( finite4902975817058060853nteger @ ( inf_in1364745209274528805nteger @ A3 @ ( collect_Code_integer @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9010_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_nat,P: nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( groups3539618377306564664at_int
% 5.49/5.82 @ ^ [X4: nat] : ( zero_n2684676970156552555ol_int @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1314217659103216013at_int @ ( finite_card_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9011_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_nat,P: nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : ( zero_n2687167440665602831ol_nat @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1316708129612266289at_nat @ ( finite_card_nat @ ( inf_inf_set_nat @ A3 @ ( collect_nat @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9012_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_int,P: int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( groups4538972089207619220nt_int
% 5.49/5.82 @ ^ [X4: int] : ( zero_n2684676970156552555ol_int @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri1314217659103216013at_int @ ( finite_card_int @ ( inf_inf_set_int @ A3 @ ( collect_int @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9013_sum__of__bool__eq,axiom,
% 5.49/5.82 ! [A3: set_set_nat,P: set_nat > $o] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( groups9190459664516455967nteger
% 5.49/5.82 @ ^ [X4: set_nat] : ( zero_n356916108424825756nteger @ ( P @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( semiri4939895301339042750nteger @ ( finite_card_set_nat @ ( inf_inf_set_set_nat @ A3 @ ( collect_set_nat @ P ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_of_bool_eq
% 5.49/5.82 thf(fact_9014_abs__integer__code,axiom,
% 5.49/5.82 ( abs_abs_Code_integer
% 5.49/5.82 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % abs_integer_code
% 5.49/5.82 thf(fact_9015_less__integer__code_I1_J,axiom,
% 5.49/5.82 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.49/5.82
% 5.49/5.82 % less_integer_code(1)
% 5.49/5.82 thf(fact_9016_less__integer_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: int,X: int] :
% 5.49/5.82 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.49/5.82 = ( ord_less_int @ Xa @ X ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_integer.abs_eq
% 5.49/5.82 thf(fact_9017_finite__atLeastZeroLessThan__integer,axiom,
% 5.49/5.82 ! [U: code_integer] : ( finite6017078050557962740nteger @ ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_atLeastZeroLessThan_integer
% 5.49/5.82 thf(fact_9018_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: option_num > option_num,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_option_num @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9019_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: option_num > $o,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_o @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9020_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: option_num > nat,F1: option_num,F22: nat > option_num,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_option_num @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_nat @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9021_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: $o > option_num,F1: $o,F22: nat > $o,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_option_num @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9022_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: $o > $o,F1: $o,F22: nat > $o,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_o @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9023_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: $o > nat,F1: $o,F22: nat > $o,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_o @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_nat @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9024_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: nat > option_num,F1: nat,F22: nat > nat,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_option_num @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9025_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: nat > $o,F1: nat,F22: nat > nat,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_o @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9026_nat_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: nat > nat,F1: nat,F22: nat > nat,Nat: nat] :
% 5.49/5.82 ( ( H @ ( case_nat_nat @ F1 @ F22 @ Nat ) )
% 5.49/5.82 = ( case_nat_nat @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: nat] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.case_distrib
% 5.49/5.82 thf(fact_9027_num_Ocase__distrib,axiom,
% 5.49/5.82 ! [H: option_num > option_num,F1: option_num,F22: num > option_num,F32: num > option_num,Num: num] :
% 5.49/5.82 ( ( H @ ( case_num_option_num @ F1 @ F22 @ F32 @ Num ) )
% 5.49/5.82 = ( case_num_option_num @ ( H @ F1 )
% 5.49/5.82 @ ^ [X4: num] : ( H @ ( F22 @ X4 ) )
% 5.49/5.82 @ ^ [X4: num] : ( H @ ( F32 @ X4 ) )
% 5.49/5.82 @ Num ) ) ).
% 5.49/5.82
% 5.49/5.82 % num.case_distrib
% 5.49/5.82 thf(fact_9028_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_set_nat,K: nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( finite1149291290879098388et_nat
% 5.49/5.82 @ ( collect_set_set_nat
% 5.49/5.82 @ ^ [B6: set_set_nat] :
% 5.49/5.82 ( ( ord_le6893508408891458716et_nat @ B6 @ A3 )
% 5.49/5.82 & ( ( finite_card_set_nat @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite_card_set_nat @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9029_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_list_nat,K: nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ( ( finite2364142230527598318st_nat
% 5.49/5.82 @ ( collect_set_list_nat
% 5.49/5.82 @ ^ [B6: set_list_nat] :
% 5.49/5.82 ( ( ord_le6045566169113846134st_nat @ B6 @ A3 )
% 5.49/5.82 & ( ( finite_card_list_nat @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite_card_list_nat @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9030_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_nat,K: nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_card_set_nat
% 5.49/5.82 @ ( collect_set_nat
% 5.49/5.82 @ ^ [B6: set_nat] :
% 5.49/5.82 ( ( ord_less_eq_set_nat @ B6 @ A3 )
% 5.49/5.82 & ( ( finite_card_nat @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite_card_nat @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9031_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,K: nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite1340570857867686763nteger
% 5.49/5.82 @ ( collec574505750873337192nteger
% 5.49/5.82 @ ^ [B6: set_Code_integer] :
% 5.49/5.82 ( ( ord_le7084787975880047091nteger @ B6 @ A3 )
% 5.49/5.82 & ( ( finite4902975817058060853nteger @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite4902975817058060853nteger @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9032_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat,K: nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ A3 )
% 5.49/5.82 => ( ( finite4356350796350151305at_nat
% 5.49/5.82 @ ( collec5514110066124741708at_nat
% 5.49/5.82 @ ^ [B6: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_le3146513528884898305at_nat @ B6 @ A3 )
% 5.49/5.82 & ( ( finite711546835091564841at_nat @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite711546835091564841at_nat @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9033_n__subsets,axiom,
% 5.49/5.82 ! [A3: set_int,K: nat] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_card_set_int
% 5.49/5.82 @ ( collect_set_int
% 5.49/5.82 @ ^ [B6: set_int] :
% 5.49/5.82 ( ( ord_less_eq_set_int @ B6 @ A3 )
% 5.49/5.82 & ( ( finite_card_int @ B6 )
% 5.49/5.82 = K ) ) ) )
% 5.49/5.82 = ( binomial @ ( finite_card_int @ A3 ) @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % n_subsets
% 5.49/5.82 thf(fact_9034_old_Onat_Osimps_I4_J,axiom,
% 5.49/5.82 ! [F1: option_num,F22: nat > option_num] :
% 5.49/5.82 ( ( case_nat_option_num @ F1 @ F22 @ zero_zero_nat )
% 5.49/5.82 = F1 ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(4)
% 5.49/5.82 thf(fact_9035_old_Onat_Osimps_I4_J,axiom,
% 5.49/5.82 ! [F1: $o,F22: nat > $o] :
% 5.49/5.82 ( ( case_nat_o @ F1 @ F22 @ zero_zero_nat )
% 5.49/5.82 = F1 ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(4)
% 5.49/5.82 thf(fact_9036_old_Onat_Osimps_I4_J,axiom,
% 5.49/5.82 ! [F1: nat,F22: nat > nat] :
% 5.49/5.82 ( ( case_nat_nat @ F1 @ F22 @ zero_zero_nat )
% 5.49/5.82 = F1 ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(4)
% 5.49/5.82 thf(fact_9037_old_Onat_Osimps_I5_J,axiom,
% 5.49/5.82 ! [F1: option_num,F22: nat > option_num,X2: nat] :
% 5.49/5.82 ( ( case_nat_option_num @ F1 @ F22 @ ( suc @ X2 ) )
% 5.49/5.82 = ( F22 @ X2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(5)
% 5.49/5.82 thf(fact_9038_old_Onat_Osimps_I5_J,axiom,
% 5.49/5.82 ! [F1: $o,F22: nat > $o,X2: nat] :
% 5.49/5.82 ( ( case_nat_o @ F1 @ F22 @ ( suc @ X2 ) )
% 5.49/5.82 = ( F22 @ X2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(5)
% 5.49/5.82 thf(fact_9039_old_Onat_Osimps_I5_J,axiom,
% 5.49/5.82 ! [F1: nat,F22: nat > nat,X2: nat] :
% 5.49/5.82 ( ( case_nat_nat @ F1 @ F22 @ ( suc @ X2 ) )
% 5.49/5.82 = ( F22 @ X2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % old.nat.simps(5)
% 5.49/5.82 thf(fact_9040_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_set_nat,N2: nat] :
% 5.49/5.82 ( ~ ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ? [B10: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ B10 )
% 5.49/5.82 & ( ( finite_card_set_nat @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_le6893508408891458716et_nat @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9041_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_list_nat,N2: nat] :
% 5.49/5.82 ( ~ ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ? [B10: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ B10 )
% 5.49/5.82 & ( ( finite_card_list_nat @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_le6045566169113846134st_nat @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9042_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_nat,N2: nat] :
% 5.49/5.82 ( ~ ( finite_finite_nat @ A3 )
% 5.49/5.82 => ? [B10: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ B10 )
% 5.49/5.82 & ( ( finite_card_nat @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_less_eq_set_nat @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9043_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,N2: nat] :
% 5.49/5.82 ( ~ ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ? [B10: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B10 )
% 5.49/5.82 & ( ( finite4902975817058060853nteger @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_le7084787975880047091nteger @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9044_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat,N2: nat] :
% 5.49/5.82 ( ~ ( finite6177210948735845034at_nat @ A3 )
% 5.49/5.82 => ? [B10: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ B10 )
% 5.49/5.82 & ( ( finite711546835091564841at_nat @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_le3146513528884898305at_nat @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9045_infinite__arbitrarily__large,axiom,
% 5.49/5.82 ! [A3: set_int,N2: nat] :
% 5.49/5.82 ( ~ ( finite_finite_int @ A3 )
% 5.49/5.82 => ? [B10: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ B10 )
% 5.49/5.82 & ( ( finite_card_int @ B10 )
% 5.49/5.82 = N2 )
% 5.49/5.82 & ( ord_less_eq_set_int @ B10 @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % infinite_arbitrarily_large
% 5.49/5.82 thf(fact_9046_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_set_nat,A3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite_card_set_nat @ A3 )
% 5.49/5.82 = ( finite_card_set_nat @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9047_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_list_nat,A3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6045566169113846134st_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite_card_list_nat @ A3 )
% 5.49/5.82 = ( finite_card_list_nat @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9048_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite_card_nat @ A3 )
% 5.49/5.82 = ( finite_card_nat @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9049_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_Code_integer,A3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite4902975817058060853nteger @ A3 )
% 5.49/5.82 = ( finite4902975817058060853nteger @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9050_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite711546835091564841at_nat @ A3 )
% 5.49/5.82 = ( finite711546835091564841at_nat @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9051_card__subset__eq,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.49/5.82 => ( ( ( finite_card_int @ A3 )
% 5.49/5.82 = ( finite_card_int @ B3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_subset_eq
% 5.49/5.82 thf(fact_9052_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_o,A3: set_o,R3: $o > $o > $o] :
% 5.49/5.82 ( ( finite_finite_o @ B3 )
% 5.49/5.82 => ( ! [A4: $o] :
% 5.49/5.82 ( ( member_o @ A4 @ A3 )
% 5.49/5.82 => ? [B11: $o] :
% 5.49/5.82 ( ( member_o @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: $o,A24: $o,B4: $o] :
% 5.49/5.82 ( ( member_o @ A13 @ A3 )
% 5.49/5.82 => ( ( member_o @ A24 @ A3 )
% 5.49/5.82 => ( ( member_o @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_o @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9053_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_o,A3: set_int,R3: int > $o > $o] :
% 5.49/5.82 ( ( finite_finite_o @ B3 )
% 5.49/5.82 => ( ! [A4: int] :
% 5.49/5.82 ( ( member_int @ A4 @ A3 )
% 5.49/5.82 => ? [B11: $o] :
% 5.49/5.82 ( ( member_o @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: int,A24: int,B4: $o] :
% 5.49/5.82 ( ( member_int @ A13 @ A3 )
% 5.49/5.82 => ( ( member_int @ A24 @ A3 )
% 5.49/5.82 => ( ( member_o @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_o @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9054_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_o,A3: set_nat,R3: nat > $o > $o] :
% 5.49/5.82 ( ( finite_finite_o @ B3 )
% 5.49/5.82 => ( ! [A4: nat] :
% 5.49/5.82 ( ( member_nat @ A4 @ A3 )
% 5.49/5.82 => ? [B11: $o] :
% 5.49/5.82 ( ( member_o @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: nat,A24: nat,B4: $o] :
% 5.49/5.82 ( ( member_nat @ A13 @ A3 )
% 5.49/5.82 => ( ( member_nat @ A24 @ A3 )
% 5.49/5.82 => ( ( member_o @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_o @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9055_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_o,R3: $o > nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ! [A4: $o] :
% 5.49/5.82 ( ( member_o @ A4 @ A3 )
% 5.49/5.82 => ? [B11: nat] :
% 5.49/5.82 ( ( member_nat @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: $o,A24: $o,B4: nat] :
% 5.49/5.82 ( ( member_o @ A13 @ A3 )
% 5.49/5.82 => ( ( member_o @ A24 @ A3 )
% 5.49/5.82 => ( ( member_nat @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9056_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_int,R3: int > nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ! [A4: int] :
% 5.49/5.82 ( ( member_int @ A4 @ A3 )
% 5.49/5.82 => ? [B11: nat] :
% 5.49/5.82 ( ( member_nat @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: int,A24: int,B4: nat] :
% 5.49/5.82 ( ( member_int @ A13 @ A3 )
% 5.49/5.82 => ( ( member_int @ A24 @ A3 )
% 5.49/5.82 => ( ( member_nat @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9057_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_nat,R3: nat > nat > $o] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ! [A4: nat] :
% 5.49/5.82 ( ( member_nat @ A4 @ A3 )
% 5.49/5.82 => ? [B11: nat] :
% 5.49/5.82 ( ( member_nat @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: nat,A24: nat,B4: nat] :
% 5.49/5.82 ( ( member_nat @ A13 @ A3 )
% 5.49/5.82 => ( ( member_nat @ A24 @ A3 )
% 5.49/5.82 => ( ( member_nat @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9058_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_o,R3: $o > int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ! [A4: $o] :
% 5.49/5.82 ( ( member_o @ A4 @ A3 )
% 5.49/5.82 => ? [B11: int] :
% 5.49/5.82 ( ( member_int @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: $o,A24: $o,B4: int] :
% 5.49/5.82 ( ( member_o @ A13 @ A3 )
% 5.49/5.82 => ( ( member_o @ A24 @ A3 )
% 5.49/5.82 => ( ( member_int @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite_card_int @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9059_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_int,R3: int > int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ! [A4: int] :
% 5.49/5.82 ( ( member_int @ A4 @ A3 )
% 5.49/5.82 => ? [B11: int] :
% 5.49/5.82 ( ( member_int @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: int,A24: int,B4: int] :
% 5.49/5.82 ( ( member_int @ A13 @ A3 )
% 5.49/5.82 => ( ( member_int @ A24 @ A3 )
% 5.49/5.82 => ( ( member_int @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9060_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_nat,R3: nat > int > $o] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ! [A4: nat] :
% 5.49/5.82 ( ( member_nat @ A4 @ A3 )
% 5.49/5.82 => ? [B11: int] :
% 5.49/5.82 ( ( member_int @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: nat,A24: nat,B4: int] :
% 5.49/5.82 ( ( member_nat @ A13 @ A3 )
% 5.49/5.82 => ( ( member_nat @ A24 @ A3 )
% 5.49/5.82 => ( ( member_int @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_int @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9061_card__le__if__inj__on__rel,axiom,
% 5.49/5.82 ! [B3: set_Code_integer,A3: set_o,R3: $o > code_integer > $o] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ! [A4: $o] :
% 5.49/5.82 ( ( member_o @ A4 @ A3 )
% 5.49/5.82 => ? [B11: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ B11 @ B3 )
% 5.49/5.82 & ( R3 @ A4 @ B11 ) ) )
% 5.49/5.82 => ( ! [A13: $o,A24: $o,B4: code_integer] :
% 5.49/5.82 ( ( member_o @ A13 @ A3 )
% 5.49/5.82 => ( ( member_o @ A24 @ A3 )
% 5.49/5.82 => ( ( member_Code_integer @ B4 @ B3 )
% 5.49/5.82 => ( ( R3 @ A13 @ B4 )
% 5.49/5.82 => ( ( R3 @ A24 @ B4 )
% 5.49/5.82 => ( A13 = A24 ) ) ) ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_o @ A3 ) @ ( finite4902975817058060853nteger @ B3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_if_inj_on_rel
% 5.49/5.82 thf(fact_9062_less__eq__integer_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: int,X: int] :
% 5.49/5.82 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X ) )
% 5.49/5.82 = ( ord_less_eq_int @ Xa @ X ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_integer.abs_eq
% 5.49/5.82 thf(fact_9063_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_o,T5: set_o,R: $o > $o > $o,K: $o > nat] :
% 5.49/5.82 ( ( finite_finite_o @ S2 )
% 5.49/5.82 => ( ( finite_finite_o @ T5 )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups8507830703676809646_o_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9064_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_o,T5: set_int,R: $o > int > $o,K: int > nat] :
% 5.49/5.82 ( ( finite_finite_o @ S2 )
% 5.49/5.82 => ( ( finite_finite_int @ T5 )
% 5.49/5.82 => ( ! [X3: int] :
% 5.49/5.82 ( ( member_int @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [J3: int] :
% 5.49/5.82 ( ( member_int @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups4541462559716669496nt_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9065_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_o,T5: set_Code_integer,R: $o > code_integer > $o,K: code_integer > nat] :
% 5.49/5.82 ( ( finite_finite_o @ S2 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ T5 )
% 5.49/5.82 => ( ! [X3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [J3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups7237345082560585321er_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9066_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_int,T5: set_o,R: int > $o > $o,K: $o > nat] :
% 5.49/5.82 ( ( finite_finite_int @ S2 )
% 5.49/5.82 => ( ( finite_finite_o @ T5 )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups8507830703676809646_o_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9067_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_int,T5: set_int,R: int > int > $o,K: int > nat] :
% 5.49/5.82 ( ( finite_finite_int @ S2 )
% 5.49/5.82 => ( ( finite_finite_int @ T5 )
% 5.49/5.82 => ( ! [X3: int] :
% 5.49/5.82 ( ( member_int @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [J3: int] :
% 5.49/5.82 ( ( member_int @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups4541462559716669496nt_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9068_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_int,T5: set_Code_integer,R: int > code_integer > $o,K: code_integer > nat] :
% 5.49/5.82 ( ( finite_finite_int @ S2 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ T5 )
% 5.49/5.82 => ( ! [X3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [J3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups7237345082560585321er_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9069_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_Code_integer,T5: set_o,R: code_integer > $o > $o,K: $o > nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ S2 )
% 5.49/5.82 => ( ( finite_finite_o @ T5 )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T5 )
% 5.49/5.82 => ( ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups8507830703676809646_o_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9070_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_Code_integer,T5: set_int,R: code_integer > int > $o,K: int > nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ S2 )
% 5.49/5.82 => ( ( finite_finite_int @ T5 )
% 5.49/5.82 => ( ! [X3: int] :
% 5.49/5.82 ( ( member_int @ X3 @ T5 )
% 5.49/5.82 => ( ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [J3: int] :
% 5.49/5.82 ( ( member_int @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups4541462559716669496nt_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9071_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_Code_integer,T5: set_Code_integer,R: code_integer > code_integer > $o,K: code_integer > nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ S2 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ T5 )
% 5.49/5.82 => ( ! [X3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ X3 @ T5 )
% 5.49/5.82 => ( ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [J3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups7237345082560585321er_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9072_sum__multicount__gen,axiom,
% 5.49/5.82 ! [S2: set_o,T5: set_nat,R: $o > nat > $o,K: nat > nat] :
% 5.49/5.82 ( ( finite_finite_o @ S2 )
% 5.49/5.82 => ( ( finite_finite_nat @ T5 )
% 5.49/5.82 => ( ! [X3: nat] :
% 5.49/5.82 ( ( member_nat @ X3 @ T5 )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S2 )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = ( K @ X3 ) ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( ( member_nat @ J3 @ T5 )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S2 )
% 5.49/5.82 = ( groups3542108847815614940at_nat @ K @ T5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount_gen
% 5.49/5.82 thf(fact_9073_card__eq__sum,axiom,
% 5.49/5.82 ( finite_card_set_nat
% 5.49/5.82 = ( groups8294997508430121362at_nat
% 5.49/5.82 @ ^ [X4: set_nat] : one_one_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_sum
% 5.49/5.82 thf(fact_9074_card__eq__sum,axiom,
% 5.49/5.82 ( finite_card_list_nat
% 5.49/5.82 = ( groups4396056296759096172at_nat
% 5.49/5.82 @ ^ [X4: list_nat] : one_one_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_sum
% 5.49/5.82 thf(fact_9075_card__eq__sum,axiom,
% 5.49/5.82 ( finite_card_nat
% 5.49/5.82 = ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : one_one_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_sum
% 5.49/5.82 thf(fact_9076_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_set_nat] :
% 5.49/5.82 ( ( ( finite_card_set_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bot_set_set_nat )
% 5.49/5.82 | ~ ( finite1152437895449049373et_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9077_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_list_nat] :
% 5.49/5.82 ( ( ( finite_card_list_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bot_set_list_nat )
% 5.49/5.82 | ~ ( finite8100373058378681591st_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9078_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer] :
% 5.49/5.82 ( ( ( finite4902975817058060853nteger @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bo3990330152332043303nteger )
% 5.49/5.82 | ~ ( finite6017078050557962740nteger @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9079_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ( finite711546835091564841at_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bo2099793752762293965at_nat )
% 5.49/5.82 | ~ ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9080_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_o] :
% 5.49/5.82 ( ( ( finite_card_o @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bot_set_o )
% 5.49/5.82 | ~ ( finite_finite_o @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9081_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_nat] :
% 5.49/5.82 ( ( ( finite_card_nat @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bot_set_nat )
% 5.49/5.82 | ~ ( finite_finite_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9082_card__eq__0__iff,axiom,
% 5.49/5.82 ! [A3: set_int] :
% 5.49/5.82 ( ( ( finite_card_int @ A3 )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A3 = bot_bot_set_int )
% 5.49/5.82 | ~ ( finite_finite_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_eq_0_iff
% 5.49/5.82 thf(fact_9083_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_set_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A3 ) )
% 5.49/5.82 => ( finite1152437895449049373et_nat @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9084_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_list_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A3 ) )
% 5.49/5.82 => ( finite8100373058378681591st_nat @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9085_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A3 ) )
% 5.49/5.82 => ( finite_finite_nat @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9086_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_int] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.49/5.82 => ( finite_finite_int @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9087_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_Code_integer] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A3 ) )
% 5.49/5.82 => ( finite6017078050557962740nteger @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9088_card__ge__0__finite,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A3 ) )
% 5.49/5.82 => ( finite6177210948735845034at_nat @ A3 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_ge_0_finite
% 5.49/5.82 thf(fact_9089_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > int] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_nat_int @ F @ A3 ) ) @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9090_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_nat_nat @ F @ A3 ) ) @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9091_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_int,F: int > int] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ ( image_int_int @ F @ A3 ) ) @ ( finite_card_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9092_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_int,F: int > nat] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_int_nat @ F @ A3 ) ) @ ( finite_card_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9093_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,F: code_integer > nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_951025933927791156er_nat @ F @ A3 ) ) @ ( finite4902975817058060853nteger @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9094_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_set_nat,F: set_nat > nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_set_nat_nat @ F @ A3 ) ) @ ( finite_card_set_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9095_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_list_nat,F: list_nat > nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( image_list_nat_nat @ F @ A3 ) ) @ ( finite_card_list_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9096_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( image_nat_set_nat @ F @ A3 ) ) @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9097_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_nat,F: nat > list_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( image_nat_list_nat @ F @ A3 ) ) @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9098_card__image__le,axiom,
% 5.49/5.82 ! [A3: set_int,F: int > set_nat] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( image_int_set_nat @ F @ A3 ) ) @ ( finite_card_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_image_le
% 5.49/5.82 thf(fact_9099_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_set_nat,C3: nat] :
% 5.49/5.82 ( ! [G4: set_set_nat] :
% 5.49/5.82 ( ( ord_le6893508408891458716et_nat @ G4 @ F4 )
% 5.49/5.82 => ( ( finite1152437895449049373et_nat @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_set_nat @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite1152437895449049373et_nat @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite_card_set_nat @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9100_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_list_nat,C3: nat] :
% 5.49/5.82 ( ! [G4: set_list_nat] :
% 5.49/5.82 ( ( ord_le6045566169113846134st_nat @ G4 @ F4 )
% 5.49/5.82 => ( ( finite8100373058378681591st_nat @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_list_nat @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite8100373058378681591st_nat @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite_card_list_nat @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9101_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_nat,C3: nat] :
% 5.49/5.82 ( ! [G4: set_nat] :
% 5.49/5.82 ( ( ord_less_eq_set_nat @ G4 @ F4 )
% 5.49/5.82 => ( ( finite_finite_nat @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite_finite_nat @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite_card_nat @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9102_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_Code_integer,C3: nat] :
% 5.49/5.82 ( ! [G4: set_Code_integer] :
% 5.49/5.82 ( ( ord_le7084787975880047091nteger @ G4 @ F4 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9103_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_Pr1261947904930325089at_nat,C3: nat] :
% 5.49/5.82 ( ! [G4: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_le3146513528884898305at_nat @ G4 @ F4 )
% 5.49/5.82 => ( ( finite6177210948735845034at_nat @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite6177210948735845034at_nat @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9104_finite__if__finite__subsets__card__bdd,axiom,
% 5.49/5.82 ! [F4: set_int,C3: nat] :
% 5.49/5.82 ( ! [G4: set_int] :
% 5.49/5.82 ( ( ord_less_eq_set_int @ G4 @ F4 )
% 5.49/5.82 => ( ( finite_finite_int @ G4 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ G4 ) @ C3 ) ) )
% 5.49/5.82 => ( ( finite_finite_int @ F4 )
% 5.49/5.82 & ( ord_less_eq_nat @ ( finite_card_int @ F4 ) @ C3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_if_finite_subsets_card_bdd
% 5.49/5.82 thf(fact_9105_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_set_nat,A3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ B3 ) @ ( finite_card_set_nat @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9106_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_list_nat,A3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6045566169113846134st_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ B3 ) @ ( finite_card_list_nat @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9107_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_nat @ B3 ) @ ( finite_card_nat @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9108_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_Code_integer,A3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ B3 ) @ ( finite4902975817058060853nteger @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9109_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ B3 ) @ ( finite711546835091564841at_nat @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9110_card__seteq,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_int @ B3 ) @ ( finite_card_int @ A3 ) )
% 5.49/5.82 => ( A3 = B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_seteq
% 5.49/5.82 thf(fact_9111_card__mono,axiom,
% 5.49/5.82 ! [B3: set_set_nat,A3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6893508408891458716et_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9112_card__mono,axiom,
% 5.49/5.82 ! [B3: set_list_nat,A3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_le6045566169113846134st_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9113_card__mono,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9114_card__mono,axiom,
% 5.49/5.82 ! [B3: set_Code_integer,A3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_le7084787975880047091nteger @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A3 ) @ ( finite4902975817058060853nteger @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9115_card__mono,axiom,
% 5.49/5.82 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_le3146513528884898305at_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9116_card__mono,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_set_int @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_mono
% 5.49/5.82 thf(fact_9117_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_set_nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite_card_set_nat @ S ) )
% 5.49/5.82 => ~ ! [T6: set_set_nat] :
% 5.49/5.82 ( ( ord_le6893508408891458716et_nat @ T6 @ S )
% 5.49/5.82 => ( ( ( finite_card_set_nat @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite1152437895449049373et_nat @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9118_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_list_nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite_card_list_nat @ S ) )
% 5.49/5.82 => ~ ! [T6: set_list_nat] :
% 5.49/5.82 ( ( ord_le6045566169113846134st_nat @ T6 @ S )
% 5.49/5.82 => ( ( ( finite_card_list_nat @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite8100373058378681591st_nat @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9119_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite_card_nat @ S ) )
% 5.49/5.82 => ~ ! [T6: set_nat] :
% 5.49/5.82 ( ( ord_less_eq_set_nat @ T6 @ S )
% 5.49/5.82 => ( ( ( finite_card_nat @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite_finite_nat @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9120_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_Code_integer] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite4902975817058060853nteger @ S ) )
% 5.49/5.82 => ~ ! [T6: set_Code_integer] :
% 5.49/5.82 ( ( ord_le7084787975880047091nteger @ T6 @ S )
% 5.49/5.82 => ( ( ( finite4902975817058060853nteger @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite6017078050557962740nteger @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9121_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite711546835091564841at_nat @ S ) )
% 5.49/5.82 => ~ ! [T6: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_le3146513528884898305at_nat @ T6 @ S )
% 5.49/5.82 => ( ( ( finite711546835091564841at_nat @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite6177210948735845034at_nat @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9122_obtain__subset__with__card__n,axiom,
% 5.49/5.82 ! [N2: nat,S: set_int] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N2 @ ( finite_card_int @ S ) )
% 5.49/5.82 => ~ ! [T6: set_int] :
% 5.49/5.82 ( ( ord_less_eq_set_int @ T6 @ S )
% 5.49/5.82 => ( ( ( finite_card_int @ T6 )
% 5.49/5.82 = N2 )
% 5.49/5.82 => ~ ( finite_finite_int @ T6 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % obtain_subset_with_card_n
% 5.49/5.82 thf(fact_9123_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9124_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_list_nat,B3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B3 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9125_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_int,B3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9126_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,B3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite4902975817058060853nteger @ A3 ) @ ( finite4902975817058060853nteger @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9127_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ A3 )
% 5.49/5.82 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9128_card__less__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_nat,B3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_sym_Diff
% 5.49/5.82 thf(fact_9129_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_set_nat,B3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ A3 )
% 5.49/5.82 => ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ A3 @ B3 ) ) @ ( finite_card_set_nat @ ( minus_2163939370556025621et_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9130_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_list_nat,B3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ A3 )
% 5.49/5.82 => ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ A3 @ B3 ) ) @ ( finite_card_list_nat @ ( minus_7954133019191499631st_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9131_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_int,B3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ A3 )
% 5.49/5.82 => ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_int @ ( minus_minus_set_int @ A3 @ B3 ) ) @ ( finite_card_int @ ( minus_minus_set_int @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9132_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer,B3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ A3 )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ A3 ) @ ( finite4902975817058060853nteger @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ A3 @ B3 ) ) @ ( finite4902975817058060853nteger @ ( minus_2355218937544613996nteger @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9133_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ A3 )
% 5.49/5.82 => ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ A3 @ B3 ) ) @ ( finite711546835091564841at_nat @ ( minus_1356011639430497352at_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9134_card__le__sym__Diff,axiom,
% 5.49/5.82 ! [A3: set_nat,B3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ A3 )
% 5.49/5.82 => ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_eq_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ ( minus_minus_set_nat @ A3 @ B3 ) ) @ ( finite_card_nat @ ( minus_minus_set_nat @ B3 @ A3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_sym_Diff
% 5.49/5.82 thf(fact_9135_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_set_nat,A3: set_set_nat] :
% 5.49/5.82 ( ( finite1152437895449049373et_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_set_set_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9136_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_list_nat,A3: set_list_nat] :
% 5.49/5.82 ( ( finite8100373058378681591st_nat @ B3 )
% 5.49/5.82 => ( ( ord_le1190675801316882794st_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9137_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_nat,A3: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ B3 )
% 5.49/5.82 => ( ( ord_less_set_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9138_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_int,A3: set_int] :
% 5.49/5.82 ( ( finite_finite_int @ B3 )
% 5.49/5.82 => ( ( ord_less_set_int @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite_card_int @ A3 ) @ ( finite_card_int @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9139_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_Code_integer,A3: set_Code_integer] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ B3 )
% 5.49/5.82 => ( ( ord_le1307284697595431911nteger @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite4902975817058060853nteger @ A3 ) @ ( finite4902975817058060853nteger @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9140_psubset__card__mono,axiom,
% 5.49/5.82 ! [B3: set_Pr1261947904930325089at_nat,A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( finite6177210948735845034at_nat @ B3 )
% 5.49/5.82 => ( ( ord_le7866589430770878221at_nat @ A3 @ B3 )
% 5.49/5.82 => ( ord_less_nat @ ( finite711546835091564841at_nat @ A3 ) @ ( finite711546835091564841at_nat @ B3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % psubset_card_mono
% 5.49/5.82 thf(fact_9141_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_set_nat,B3: set_set_nat] : ( ord_less_eq_nat @ ( finite_card_set_nat @ ( sup_sup_set_set_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite_card_set_nat @ A3 ) @ ( finite_card_set_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9142_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_list_nat,B3: set_list_nat] : ( ord_less_eq_nat @ ( finite_card_list_nat @ ( sup_sup_set_list_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite_card_list_nat @ A3 ) @ ( finite_card_list_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9143_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_Pr8693737435421807431at_nat,B3: set_Pr8693737435421807431at_nat] : ( ord_less_eq_nat @ ( finite1207074278014112911at_nat @ ( sup_su718114333110466843at_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite1207074278014112911at_nat @ A3 ) @ ( finite1207074278014112911at_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9144_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_Pr8551490117392284871at_nat,B3: set_Pr8551490117392284871at_nat] : ( ord_less_eq_nat @ ( finite7007076676225009423at_nat @ ( sup_su3035147773818789531at_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite7007076676225009423at_nat @ A3 ) @ ( finite7007076676225009423at_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9145_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_Pr4329608150637261639at_nat,B3: set_Pr4329608150637261639at_nat] : ( ord_less_eq_nat @ ( finite3771342082235030671at_nat @ ( sup_su5525570899277871387at_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite3771342082235030671at_nat @ A3 ) @ ( finite3771342082235030671at_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9146_card__Un__le,axiom,
% 5.49/5.82 ! [A3: set_nat,B3: set_nat] : ( ord_less_eq_nat @ ( finite_card_nat @ ( sup_sup_set_nat @ A3 @ B3 ) ) @ ( plus_plus_nat @ ( finite_card_nat @ A3 ) @ ( finite_card_nat @ B3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_Un_le
% 5.49/5.82 thf(fact_9147_card__less__Suc2,axiom,
% 5.49/5.82 ! [M6: set_nat,I2: nat] :
% 5.49/5.82 ( ~ ( member_nat @ zero_zero_nat @ M6 )
% 5.49/5.82 => ( ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( ( member_nat @ ( suc @ K3 ) @ M6 )
% 5.49/5.82 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.49/5.82 = ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( ( member_nat @ K3 @ M6 )
% 5.49/5.82 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_Suc2
% 5.49/5.82 thf(fact_9148_card__less__Suc,axiom,
% 5.49/5.82 ! [M6: set_nat,I2: nat] :
% 5.49/5.82 ( ( member_nat @ zero_zero_nat @ M6 )
% 5.49/5.82 => ( ( suc
% 5.49/5.82 @ ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( ( member_nat @ ( suc @ K3 ) @ M6 )
% 5.49/5.82 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.49/5.82 = ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( ( member_nat @ K3 @ M6 )
% 5.49/5.82 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less_Suc
% 5.49/5.82 thf(fact_9149_card__less,axiom,
% 5.49/5.82 ! [M6: set_nat,I2: nat] :
% 5.49/5.82 ( ( member_nat @ zero_zero_nat @ M6 )
% 5.49/5.82 => ( ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] :
% 5.49/5.82 ( ( member_nat @ K3 @ M6 )
% 5.49/5.82 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.49/5.82 != zero_zero_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_less
% 5.49/5.82 thf(fact_9150_subset__card__intvl__is__intvl,axiom,
% 5.49/5.82 ! [A3: set_nat,K: nat] :
% 5.49/5.82 ( ( ord_less_eq_set_nat @ A3 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) )
% 5.49/5.82 => ( A3
% 5.49/5.82 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % subset_card_intvl_is_intvl
% 5.49/5.82 thf(fact_9151_sum__Suc,axiom,
% 5.49/5.82 ! [F: set_nat > nat,A3: set_set_nat] :
% 5.49/5.82 ( ( groups8294997508430121362at_nat
% 5.49/5.82 @ ^ [X4: set_nat] : ( suc @ ( F @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( plus_plus_nat @ ( groups8294997508430121362at_nat @ F @ A3 ) @ ( finite_card_set_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_Suc
% 5.49/5.82 thf(fact_9152_sum__Suc,axiom,
% 5.49/5.82 ! [F: list_nat > nat,A3: set_list_nat] :
% 5.49/5.82 ( ( groups4396056296759096172at_nat
% 5.49/5.82 @ ^ [X4: list_nat] : ( suc @ ( F @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( plus_plus_nat @ ( groups4396056296759096172at_nat @ F @ A3 ) @ ( finite_card_list_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_Suc
% 5.49/5.82 thf(fact_9153_sum__Suc,axiom,
% 5.49/5.82 ! [F: nat > nat,A3: set_nat] :
% 5.49/5.82 ( ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : ( suc @ ( F @ X4 ) )
% 5.49/5.82 @ A3 )
% 5.49/5.82 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ A3 ) @ ( finite_card_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_Suc
% 5.49/5.82 thf(fact_9154_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_o,T: set_o,R: $o > $o > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_o @ S )
% 5.49/5.82 => ( ( finite_finite_o @ T )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_o @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9155_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_o,T: set_nat,R: $o > nat > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_o @ S )
% 5.49/5.82 => ( ( finite_finite_nat @ T )
% 5.49/5.82 => ( ! [X3: nat] :
% 5.49/5.82 ( ( member_nat @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( ( member_nat @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_nat @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9156_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_o,T: set_int,R: $o > int > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_o @ S )
% 5.49/5.82 => ( ( finite_finite_int @ T )
% 5.49/5.82 => ( ! [X3: int] :
% 5.49/5.82 ( ( member_int @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [J3: int] :
% 5.49/5.82 ( ( member_int @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_int @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9157_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_o,T: set_Code_integer,R: $o > code_integer > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_o @ S )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ T )
% 5.49/5.82 => ( ! [X3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( ( member_o @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups8507830703676809646_o_nat
% 5.49/5.82 @ ^ [I4: $o] :
% 5.49/5.82 ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [J3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite4902975817058060853nteger @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9158_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_int,T: set_o,R: int > $o > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_int @ S )
% 5.49/5.82 => ( ( finite_finite_o @ T )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_o @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9159_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_int,T: set_nat,R: int > nat > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_int @ S )
% 5.49/5.82 => ( ( finite_finite_nat @ T )
% 5.49/5.82 => ( ! [X3: nat] :
% 5.49/5.82 ( ( member_nat @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( ( member_nat @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_nat @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9160_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_int,T: set_int,R: int > int > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_int @ S )
% 5.49/5.82 => ( ( finite_finite_int @ T )
% 5.49/5.82 => ( ! [X3: int] :
% 5.49/5.82 ( ( member_int @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [J3: int] :
% 5.49/5.82 ( ( member_int @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_int @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9161_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_int,T: set_Code_integer,R: int > code_integer > $o,K: nat] :
% 5.49/5.82 ( ( finite_finite_int @ S )
% 5.49/5.82 => ( ( finite6017078050557962740nteger @ T )
% 5.49/5.82 => ( ! [X3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ X3 @ T )
% 5.49/5.82 => ( ( finite_card_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( ( member_int @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups4541462559716669496nt_nat
% 5.49/5.82 @ ^ [I4: int] :
% 5.49/5.82 ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [J3: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite4902975817058060853nteger @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9162_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_Code_integer,T: set_o,R: code_integer > $o > $o,K: nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ S )
% 5.49/5.82 => ( ( finite_finite_o @ T )
% 5.49/5.82 => ( ! [X3: $o] :
% 5.49/5.82 ( ( member_o @ X3 @ T )
% 5.49/5.82 => ( ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( finite_card_o
% 5.49/5.82 @ ( collect_o
% 5.49/5.82 @ ^ [J3: $o] :
% 5.49/5.82 ( ( member_o @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_o @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9163_sum__multicount,axiom,
% 5.49/5.82 ! [S: set_Code_integer,T: set_nat,R: code_integer > nat > $o,K: nat] :
% 5.49/5.82 ( ( finite6017078050557962740nteger @ S )
% 5.49/5.82 => ( ( finite_finite_nat @ T )
% 5.49/5.82 => ( ! [X3: nat] :
% 5.49/5.82 ( ( member_nat @ X3 @ T )
% 5.49/5.82 => ( ( finite4902975817058060853nteger
% 5.49/5.82 @ ( collect_Code_integer
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( ( member_Code_integer @ I4 @ S )
% 5.49/5.82 & ( R @ I4 @ X3 ) ) ) )
% 5.49/5.82 = K ) )
% 5.49/5.82 => ( ( groups7237345082560585321er_nat
% 5.49/5.82 @ ^ [I4: code_integer] :
% 5.49/5.82 ( finite_card_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [J3: nat] :
% 5.49/5.82 ( ( member_nat @ J3 @ T )
% 5.49/5.82 & ( R @ I4 @ J3 ) ) ) )
% 5.49/5.82 @ S )
% 5.49/5.82 = ( times_times_nat @ K @ ( finite_card_nat @ T ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_multicount
% 5.49/5.82 thf(fact_9164_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_set_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_set_nat @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bot_set_set_nat )
% 5.49/5.82 & ( finite1152437895449049373et_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9165_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_list_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_list_nat @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bot_set_list_nat )
% 5.49/5.82 & ( finite8100373058378681591st_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9166_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_Code_integer] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite4902975817058060853nteger @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bo3990330152332043303nteger )
% 5.49/5.82 & ( finite6017078050557962740nteger @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9167_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_Pr1261947904930325089at_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite711546835091564841at_nat @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bo2099793752762293965at_nat )
% 5.49/5.82 & ( finite6177210948735845034at_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9168_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_o] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_o @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bot_set_o )
% 5.49/5.82 & ( finite_finite_o @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9169_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_nat @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bot_set_nat )
% 5.49/5.82 & ( finite_finite_nat @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9170_card__gt__0__iff,axiom,
% 5.49/5.82 ! [A3: set_int] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ ( finite_card_int @ A3 ) )
% 5.49/5.82 = ( ( A3 != bot_bot_set_int )
% 5.49/5.82 & ( finite_finite_int @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_gt_0_iff
% 5.49/5.82 thf(fact_9171_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_nat,K5: code_integer,F: nat > code_integer] :
% 5.49/5.82 ( ! [I3: nat] :
% 5.49/5.82 ( ( member_nat @ I3 @ A3 )
% 5.49/5.82 => ( ord_le3102999989581377725nteger @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_le3102999989581377725nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ ( finite_card_nat @ A3 ) ) @ K5 ) @ ( groups7501900531339628137nteger @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9172_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_o,K5: rat,F: $o > rat] :
% 5.49/5.82 ( ! [I3: $o] :
% 5.49/5.82 ( ( member_o @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_rat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_o @ A3 ) ) @ K5 ) @ ( groups7872700643590313910_o_rat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9173_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_int,K5: rat,F: int > rat] :
% 5.49/5.82 ( ! [I3: int] :
% 5.49/5.82 ( ( member_int @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_rat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_int @ A3 ) ) @ K5 ) @ ( groups3906332499630173760nt_rat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9174_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_nat,K5: rat,F: nat > rat] :
% 5.49/5.82 ( ! [I3: nat] :
% 5.49/5.82 ( ( member_nat @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_rat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( finite_card_nat @ A3 ) ) @ K5 ) @ ( groups2906978787729119204at_rat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9175_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_o,K5: nat,F: $o > nat] :
% 5.49/5.82 ( ! [I3: $o] :
% 5.49/5.82 ( ( member_o @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_o @ A3 ) ) @ K5 ) @ ( groups8507830703676809646_o_nat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9176_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_int,K5: nat,F: int > nat] :
% 5.49/5.82 ( ! [I3: int] :
% 5.49/5.82 ( ( member_int @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_int @ A3 ) ) @ K5 ) @ ( groups4541462559716669496nt_nat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9177_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_o,K5: int,F: $o > int] :
% 5.49/5.82 ( ! [I3: $o] :
% 5.49/5.82 ( ( member_o @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_int @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_o @ A3 ) ) @ K5 ) @ ( groups8505340233167759370_o_int @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9178_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_nat,K5: int,F: nat > int] :
% 5.49/5.82 ( ! [I3: nat] :
% 5.49/5.82 ( ( member_nat @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_int @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_nat @ A3 ) ) @ K5 ) @ ( groups3539618377306564664at_int @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9179_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_nat,K5: nat,F: nat > nat] :
% 5.49/5.82 ( ! [I3: nat] :
% 5.49/5.82 ( ( member_nat @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_nat @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( finite_card_nat @ A3 ) ) @ K5 ) @ ( groups3542108847815614940at_nat @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9180_sum__bounded__below,axiom,
% 5.49/5.82 ! [A3: set_int,K5: int,F: int > int] :
% 5.49/5.82 ( ! [I3: int] :
% 5.49/5.82 ( ( member_int @ I3 @ A3 )
% 5.49/5.82 => ( ord_less_eq_int @ K5 @ ( F @ I3 ) ) )
% 5.49/5.82 => ( ord_less_eq_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( finite_card_int @ A3 ) ) @ K5 ) @ ( groups4538972089207619220nt_int @ F @ A3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_bounded_below
% 5.49/5.82 thf(fact_9181_subset__eq__atLeast0__lessThan__card,axiom,
% 5.49/5.82 ! [N7: set_nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_set_nat @ N7 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ N7 ) @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % subset_eq_atLeast0_lessThan_card
% 5.49/5.82 thf(fact_9182_card__sum__le__nat__sum,axiom,
% 5.49/5.82 ! [S: set_nat] :
% 5.49/5.82 ( ord_less_eq_nat
% 5.49/5.82 @ ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : X4
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S ) ) )
% 5.49/5.82 @ ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : X4
% 5.49/5.82 @ S ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_sum_le_nat_sum
% 5.49/5.82 thf(fact_9183_integer__of__num_I2_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.49/5.82 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % integer_of_num(2)
% 5.49/5.82 thf(fact_9184_num__of__integer__code,axiom,
% 5.49/5.82 ( code_num_of_integer
% 5.49/5.82 = ( ^ [K3: code_integer] :
% 5.49/5.82 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.49/5.82 @ ( produc7336495610019696514er_num
% 5.49/5.82 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.49/5.82 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % num_of_integer_code
% 5.49/5.82 thf(fact_9185_bit__cut__integer__def,axiom,
% 5.49/5.82 ( code_bit_cut_integer
% 5.49/5.82 = ( ^ [K3: code_integer] :
% 5.49/5.82 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.49/5.82 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_cut_integer_def
% 5.49/5.82 thf(fact_9186_int__of__integer__code,axiom,
% 5.49/5.82 ( code_int_of_integer
% 5.49/5.82 = ( ^ [K3: code_integer] :
% 5.49/5.82 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.49/5.82 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.49/5.82 @ ( produc1553301316500091796er_int
% 5.49/5.82 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.49/5.82 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_of_integer_code
% 5.49/5.82 thf(fact_9187_divmod__integer__def,axiom,
% 5.49/5.82 ( code_divmod_integer
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L2 ) @ ( modulo364778990260209775nteger @ K3 @ L2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_integer_def
% 5.49/5.82 thf(fact_9188_nat_Odisc__eq__case_I2_J,axiom,
% 5.49/5.82 ! [Nat: nat] :
% 5.49/5.82 ( ( Nat != zero_zero_nat )
% 5.49/5.82 = ( case_nat_o @ $false
% 5.49/5.82 @ ^ [Uu2: nat] : $true
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.disc_eq_case(2)
% 5.49/5.82 thf(fact_9189_nat_Odisc__eq__case_I1_J,axiom,
% 5.49/5.82 ! [Nat: nat] :
% 5.49/5.82 ( ( Nat = zero_zero_nat )
% 5.49/5.82 = ( case_nat_o @ $true
% 5.49/5.82 @ ^ [Uu2: nat] : $false
% 5.49/5.82 @ Nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat.disc_eq_case(1)
% 5.49/5.82 thf(fact_9190_int__of__integer__less__iff,axiom,
% 5.49/5.82 ! [X: code_integer,Y: code_integer] :
% 5.49/5.82 ( ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Y ) )
% 5.49/5.82 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_of_integer_less_iff
% 5.49/5.82 thf(fact_9191_integer__less__iff,axiom,
% 5.49/5.82 ( ord_le6747313008572928689nteger
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % integer_less_iff
% 5.49/5.82 thf(fact_9192_less__integer_Orep__eq,axiom,
% 5.49/5.82 ( ord_le6747313008572928689nteger
% 5.49/5.82 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_integer.rep_eq
% 5.49/5.82 thf(fact_9193_integer__less__eq__iff,axiom,
% 5.49/5.82 ( ord_le3102999989581377725nteger
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % integer_less_eq_iff
% 5.49/5.82 thf(fact_9194_less__eq__integer_Orep__eq,axiom,
% 5.49/5.82 ( ord_le3102999989581377725nteger
% 5.49/5.82 = ( ^ [X4: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_integer.rep_eq
% 5.49/5.82 thf(fact_9195_less__eq__nat_Osimps_I2_J,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.49/5.82 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_nat.simps(2)
% 5.49/5.82 thf(fact_9196_diff__Suc,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = ( case_nat_nat @ zero_zero_nat
% 5.49/5.82 @ ^ [K3: nat] : K3
% 5.49/5.82 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % diff_Suc
% 5.49/5.82 thf(fact_9197_bit__cut__integer__code,axiom,
% 5.49/5.82 ( code_bit_cut_integer
% 5.49/5.82 = ( ^ [K3: code_integer] :
% 5.49/5.82 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.49/5.82 @ ( produc9125791028180074456eger_o
% 5.49/5.82 @ ^ [R4: code_integer,S6: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R4 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ S6 ) ) @ ( S6 = one_one_Code_integer ) )
% 5.49/5.82 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_cut_integer_code
% 5.49/5.82 thf(fact_9198_nat__of__integer__code,axiom,
% 5.49/5.82 ( code_nat_of_integer
% 5.49/5.82 = ( ^ [K3: code_integer] :
% 5.49/5.82 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.49/5.82 @ ( produc1555791787009142072er_nat
% 5.49/5.82 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.49/5.82 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_of_integer_code
% 5.49/5.82 thf(fact_9199_nat__of__integer__non__positive,axiom,
% 5.49/5.82 ! [K: code_integer] :
% 5.49/5.82 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.49/5.82 => ( ( code_nat_of_integer @ K )
% 5.49/5.82 = zero_zero_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_of_integer_non_positive
% 5.49/5.82 thf(fact_9200_divmod__abs__code_I6_J,axiom,
% 5.49/5.82 ! [J: code_integer] :
% 5.49/5.82 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.49/5.82 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_abs_code(6)
% 5.49/5.82 thf(fact_9201_divmod__abs__code_I5_J,axiom,
% 5.49/5.82 ! [J: code_integer] :
% 5.49/5.82 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.49/5.82 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_abs_code(5)
% 5.49/5.82 thf(fact_9202_nat__of__integer__less__iff,axiom,
% 5.49/5.82 ! [X: code_integer,Y: code_integer] :
% 5.49/5.82 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.49/5.82 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.49/5.82 => ( ( ord_less_nat @ ( code_nat_of_integer @ X ) @ ( code_nat_of_integer @ Y ) )
% 5.49/5.82 = ( ord_le6747313008572928689nteger @ X @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_of_integer_less_iff
% 5.49/5.82 thf(fact_9203_image__atLeastZeroLessThan__integer,axiom,
% 5.49/5.82 ! [U: code_integer] :
% 5.49/5.82 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ U )
% 5.49/5.82 => ( ( set_or8404916559141939852nteger @ zero_z3403309356797280102nteger @ U )
% 5.49/5.82 = ( image_1215581382706833972nteger @ semiri4939895301339042750nteger @ ( set_ord_lessThan_nat @ ( code_nat_of_integer @ U ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % image_atLeastZeroLessThan_integer
% 5.49/5.82 thf(fact_9204_divmod__abs__def,axiom,
% 5.49/5.82 ( code_divmod_abs
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_abs_def
% 5.49/5.82 thf(fact_9205_divmod__integer__code,axiom,
% 5.49/5.82 ( code_divmod_integer
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.49/5.82 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.49/5.82 @ ( produc6916734918728496179nteger
% 5.49/5.82 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S6 ) ) )
% 5.49/5.82 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.49/5.82 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.49/5.82 @ ( produc6916734918728496179nteger
% 5.49/5.82 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S6 ) ) )
% 5.49/5.82 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_integer_code
% 5.49/5.82 thf(fact_9206_signed__take__bit__nonnegative__iff,axiom,
% 5.49/5.82 ! [N2: nat,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.49/5.82 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % signed_take_bit_nonnegative_iff
% 5.49/5.82 thf(fact_9207_signed__take__bit__negative__iff,axiom,
% 5.49/5.82 ! [N2: nat,K: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.49/5.82 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % signed_take_bit_negative_iff
% 5.49/5.82 thf(fact_9208_bit__nat__iff,axiom,
% 5.49/5.82 ! [K: int,N2: nat] :
% 5.49/5.82 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.49/5.82 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.82 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_nat_iff
% 5.49/5.82 thf(fact_9209_bit__imp__take__bit__positive,axiom,
% 5.49/5.82 ! [N2: nat,M: nat,K: int] :
% 5.49/5.82 ( ( ord_less_nat @ N2 @ M )
% 5.49/5.82 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.49/5.82 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_imp_take_bit_positive
% 5.49/5.82 thf(fact_9210_int__bit__bound,axiom,
% 5.49/5.82 ! [K: int] :
% 5.49/5.82 ~ ! [N5: nat] :
% 5.49/5.82 ( ! [M4: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ N5 @ M4 )
% 5.49/5.82 => ( ( bit_se1146084159140164899it_int @ K @ M4 )
% 5.49/5.82 = ( bit_se1146084159140164899it_int @ K @ N5 ) ) )
% 5.49/5.82 => ~ ( ( ord_less_nat @ zero_zero_nat @ N5 )
% 5.49/5.82 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N5 @ one_one_nat ) )
% 5.49/5.82 = ( ~ ( bit_se1146084159140164899it_int @ K @ N5 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_bit_bound
% 5.49/5.82 thf(fact_9211_pred__def,axiom,
% 5.49/5.82 ( pred
% 5.49/5.82 = ( case_nat_nat @ zero_zero_nat
% 5.49/5.82 @ ^ [X23: nat] : X23 ) ) ).
% 5.49/5.82
% 5.49/5.82 % pred_def
% 5.49/5.82 thf(fact_9212_finite__enumerate,axiom,
% 5.49/5.82 ! [S: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ S )
% 5.49/5.82 => ? [R2: nat > nat] :
% 5.49/5.82 ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S ) ) )
% 5.49/5.82 & ! [N9: nat] :
% 5.49/5.82 ( ( ord_less_nat @ N9 @ ( finite_card_nat @ S ) )
% 5.49/5.82 => ( member_nat @ ( R2 @ N9 ) @ S ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % finite_enumerate
% 5.49/5.82 thf(fact_9213_or__nonnegative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.49/5.82 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.82 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % or_nonnegative_int_iff
% 5.49/5.82 thf(fact_9214_push__bit__nonnegative__int__iff,axiom,
% 5.49/5.82 ! [N2: nat,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.49/5.82 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.49/5.82
% 5.49/5.82 % push_bit_nonnegative_int_iff
% 5.49/5.82 thf(fact_9215_or__negative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.49/5.82 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.82 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % or_negative_int_iff
% 5.49/5.82 thf(fact_9216_push__bit__negative__int__iff,axiom,
% 5.49/5.82 ! [N2: nat,K: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.49/5.82 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % push_bit_negative_int_iff
% 5.49/5.82 thf(fact_9217_OR__lower,axiom,
% 5.49/5.82 ! [X: int,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % OR_lower
% 5.49/5.82 thf(fact_9218_or__greater__eq,axiom,
% 5.49/5.82 ! [L: int,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.49/5.82 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % or_greater_eq
% 5.49/5.82 thf(fact_9219_bit__push__bit__iff__int,axiom,
% 5.49/5.82 ! [M: nat,K: int,N2: nat] :
% 5.49/5.82 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.49/5.82 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_push_bit_iff_int
% 5.49/5.82 thf(fact_9220_bit__push__bit__iff__nat,axiom,
% 5.49/5.82 ! [M: nat,Q6: nat,N2: nat] :
% 5.49/5.82 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q6 ) @ N2 )
% 5.49/5.82 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 & ( bit_se1148574629649215175it_nat @ Q6 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bit_push_bit_iff_nat
% 5.49/5.82 thf(fact_9221_OR__upper,axiom,
% 5.49/5.82 ! [X: int,N2: nat,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.82 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.49/5.82 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % OR_upper
% 5.49/5.82 thf(fact_9222_Sup__nat__empty,axiom,
% 5.49/5.82 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % Sup_nat_empty
% 5.49/5.82 thf(fact_9223_divmod__integer__eq__cases,axiom,
% 5.49/5.82 ( code_divmod_integer
% 5.49/5.82 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.49/5.82 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.49/5.82 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L2
% 5.49/5.82 @ ( if_Pro6119634080678213985nteger
% 5.49/5.82 @ ( ( sgn_sgn_Code_integer @ K3 )
% 5.49/5.82 = ( sgn_sgn_Code_integer @ L2 ) )
% 5.49/5.82 @ ( code_divmod_abs @ K3 @ L2 )
% 5.49/5.82 @ ( produc6916734918728496179nteger
% 5.49/5.82 @ ^ [R4: code_integer,S6: code_integer] : ( if_Pro6119634080678213985nteger @ ( S6 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R4 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R4 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L2 ) @ S6 ) ) )
% 5.49/5.82 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divmod_integer_eq_cases
% 5.49/5.82 thf(fact_9224_Inf__nat__def1,axiom,
% 5.49/5.82 ! [K5: set_nat] :
% 5.49/5.82 ( ( K5 != bot_bot_set_nat )
% 5.49/5.82 => ( member_nat @ ( complete_Inf_Inf_nat @ K5 ) @ K5 ) ) ).
% 5.49/5.82
% 5.49/5.82 % Inf_nat_def1
% 5.49/5.82 thf(fact_9225_UN__atMost__UNIV,axiom,
% 5.49/5.82 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.49/5.82 = top_top_set_nat ) ).
% 5.49/5.82
% 5.49/5.82 % UN_atMost_UNIV
% 5.49/5.82 thf(fact_9226_UN__lessThan__UNIV,axiom,
% 5.49/5.82 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.49/5.82 = top_top_set_nat ) ).
% 5.49/5.82
% 5.49/5.82 % UN_lessThan_UNIV
% 5.49/5.82 thf(fact_9227_range__mod,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( ( image_nat_nat
% 5.49/5.82 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N2 )
% 5.49/5.82 @ top_top_set_nat )
% 5.49/5.82 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % range_mod
% 5.49/5.82 thf(fact_9228_and__not__num_Osimps_I8_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.82 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.simps(8)
% 5.49/5.82 thf(fact_9229_merge__true__star,axiom,
% 5.49/5.82 ( ( times_times_assn @ top_top_assn @ top_top_assn )
% 5.49/5.82 = top_top_assn ) ).
% 5.49/5.82
% 5.49/5.82 % merge_true_star
% 5.49/5.82 thf(fact_9230_assn__basic__inequalities_I5_J,axiom,
% 5.49/5.82 top_top_assn != bot_bot_assn ).
% 5.49/5.82
% 5.49/5.82 % assn_basic_inequalities(5)
% 5.49/5.82 thf(fact_9231_assn__basic__inequalities_I1_J,axiom,
% 5.49/5.82 top_top_assn != one_one_assn ).
% 5.49/5.82
% 5.49/5.82 % assn_basic_inequalities(1)
% 5.49/5.82 thf(fact_9232_Suc__funpow,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( compow_nat_nat @ N2 @ suc )
% 5.49/5.82 = ( plus_plus_nat @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % Suc_funpow
% 5.49/5.82 thf(fact_9233_and__nonnegative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.49/5.82 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.49/5.82 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_nonnegative_int_iff
% 5.49/5.82 thf(fact_9234_and__negative__int__iff,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.49/5.82 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.49/5.82 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_negative_int_iff
% 5.49/5.82 thf(fact_9235_mod__true,axiom,
% 5.49/5.82 ! [H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ top_top_assn @ H )
% 5.49/5.82 = ( in_range @ H ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_true
% 5.49/5.82 thf(fact_9236_not__negative__int__iff,axiom,
% 5.49/5.82 ! [K: int] :
% 5.49/5.82 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.49/5.82 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.49/5.82
% 5.49/5.82 % not_negative_int_iff
% 5.49/5.82 thf(fact_9237_not__nonnegative__int__iff,axiom,
% 5.49/5.82 ! [K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.49/5.82 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % not_nonnegative_int_iff
% 5.49/5.82 thf(fact_9238_and__minus__numerals_I4_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_minus_numerals(4)
% 5.49/5.82 thf(fact_9239_and__minus__numerals_I8_J,axiom,
% 5.49/5.82 ! [N2: num,M: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_minus_numerals(8)
% 5.49/5.82 thf(fact_9240_and__minus__numerals_I3_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_minus_numerals(3)
% 5.49/5.82 thf(fact_9241_and__minus__numerals_I7_J,axiom,
% 5.49/5.82 ! [N2: num,M: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_minus_numerals(7)
% 5.49/5.82 thf(fact_9242_ent__true,axiom,
% 5.49/5.82 ! [P: assn] : ( entails @ P @ top_top_assn ) ).
% 5.49/5.82
% 5.49/5.82 % ent_true
% 5.49/5.82 thf(fact_9243_and__not__num__eq__Some__iff,axiom,
% 5.49/5.82 ! [M: num,N2: num,Q6: num] :
% 5.49/5.82 ( ( ( bit_and_not_num @ M @ N2 )
% 5.49/5.82 = ( some_num @ Q6 ) )
% 5.49/5.82 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = ( numeral_numeral_int @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num_eq_Some_iff
% 5.49/5.82 thf(fact_9244_int__numeral__not__and__num,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_numeral_not_and_num
% 5.49/5.82 thf(fact_9245_int__numeral__and__not__num,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_numeral_and_not_num
% 5.49/5.82 thf(fact_9246_AND__lower,axiom,
% 5.49/5.82 ! [X: int,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_lower
% 5.49/5.82 thf(fact_9247_AND__upper1,axiom,
% 5.49/5.82 ! [X: int,Y: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper1
% 5.49/5.82 thf(fact_9248_AND__upper2,axiom,
% 5.49/5.82 ! [Y: int,X: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper2
% 5.49/5.82 thf(fact_9249_AND__upper1_H,axiom,
% 5.49/5.82 ! [Y: int,Z: int,Ya: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ( ord_less_eq_int @ Y @ Z )
% 5.49/5.82 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper1'
% 5.49/5.82 thf(fact_9250_AND__upper2_H,axiom,
% 5.49/5.82 ! [Y: int,Z: int,X: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ( ord_less_eq_int @ Y @ Z )
% 5.49/5.82 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper2'
% 5.49/5.82 thf(fact_9251_mod__star__trueI,axiom,
% 5.49/5.82 ! [P: assn,H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ P @ H )
% 5.49/5.82 => ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_star_trueI
% 5.49/5.82 thf(fact_9252_mod__star__trueE,axiom,
% 5.49/5.82 ! [P: assn,H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H )
% 5.49/5.82 => ~ ! [H5: produc3658429121746597890et_nat] :
% 5.49/5.82 ~ ( rep_assn @ P @ H5 ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_star_trueE
% 5.49/5.82 thf(fact_9253_top__assn__def,axiom,
% 5.49/5.82 ( top_top_assn
% 5.49/5.82 = ( abs_assn @ in_range ) ) ).
% 5.49/5.82
% 5.49/5.82 % top_assn_def
% 5.49/5.82 thf(fact_9254_and__less__eq,axiom,
% 5.49/5.82 ! [L: int,K: int] :
% 5.49/5.82 ( ( ord_less_int @ L @ zero_zero_int )
% 5.49/5.82 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_less_eq
% 5.49/5.82 thf(fact_9255_AND__upper1_H_H,axiom,
% 5.49/5.82 ! [Y: int,Z: int,Ya: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ( ord_less_int @ Y @ Z )
% 5.49/5.82 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper1''
% 5.49/5.82 thf(fact_9256_AND__upper2_H_H,axiom,
% 5.49/5.82 ! [Y: int,Z: int,X: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ( ord_less_int @ Y @ Z )
% 5.49/5.82 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % AND_upper2''
% 5.49/5.82 thf(fact_9257_mod__h__bot__iff_I2_J,axiom,
% 5.49/5.82 ! [H: heap_e7401611519738050253t_unit] : ( rep_assn @ top_top_assn @ ( produc7507926704131184380et_nat @ H @ bot_bot_set_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_h_bot_iff(2)
% 5.49/5.82 thf(fact_9258_and__not__num_Osimps_I2_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.49/5.82 = ( some_num @ one ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.simps(2)
% 5.49/5.82 thf(fact_9259_and__not__num_Osimps_I4_J,axiom,
% 5.49/5.82 ! [M: num] :
% 5.49/5.82 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.49/5.82 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.simps(4)
% 5.49/5.82 thf(fact_9260_and__not__num_Osimps_I7_J,axiom,
% 5.49/5.82 ! [M: num] :
% 5.49/5.82 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.49/5.82 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.simps(7)
% 5.49/5.82 thf(fact_9261_and__int_Oelims,axiom,
% 5.49/5.82 ! [X: int,Xa: int,Y: int] :
% 5.49/5.82 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( uminus_uminus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.49/5.82 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( plus_plus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.49/5.82 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_int.elims
% 5.49/5.82 thf(fact_9262_and__int_Osimps,axiom,
% 5.49/5.82 ( bit_se725231765392027082nd_int
% 5.49/5.82 = ( ^ [K3: int,L2: int] :
% 5.49/5.82 ( if_int
% 5.49/5.82 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 @ ( uminus_uminus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.49/5.82 @ ( plus_plus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.49/5.82 @ ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_int.simps
% 5.49/5.82 thf(fact_9263_and__int_Opelims,axiom,
% 5.49/5.82 ! [X: int,Xa: int,Y: int] :
% 5.49/5.82 ( ( ( bit_se725231765392027082nd_int @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.49/5.82 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( uminus_uminus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.49/5.82 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( plus_plus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.49/5.82 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.49/5.82 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_int.pelims
% 5.49/5.82 thf(fact_9264_atLeastAtMostPlus1__int__conv,axiom,
% 5.49/5.82 ! [M: int,N2: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.49/5.82 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.49/5.82 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastAtMostPlus1_int_conv
% 5.49/5.82 thf(fact_9265_simp__from__to,axiom,
% 5.49/5.82 ( set_or1266510415728281911st_int
% 5.49/5.82 = ( ^ [I4: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I4 ) @ bot_bot_set_int @ ( insert_int @ I4 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % simp_from_to
% 5.49/5.82 thf(fact_9266_and__int_Opinduct,axiom,
% 5.49/5.82 ! [A0: int,A1: int,P: int > int > $o] :
% 5.49/5.82 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A1 ) )
% 5.49/5.82 => ( ! [K2: int,L4: int] :
% 5.49/5.82 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.49/5.82 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.49/5.82 => ( P @ K2 @ L4 ) ) )
% 5.49/5.82 => ( P @ A0 @ A1 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_int.pinduct
% 5.49/5.82 thf(fact_9267_and__int_Opsimps,axiom,
% 5.49/5.82 ! [K: int,L: int] :
% 5.49/5.82 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.49/5.82 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.49/5.82 = ( uminus_uminus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.49/5.82 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.49/5.82 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.49/5.82 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.49/5.82 = ( plus_plus_int
% 5.49/5.82 @ ( zero_n2684676970156552555ol_int
% 5.49/5.82 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.49/5.82 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.49/5.82 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_int.psimps
% 5.49/5.82 thf(fact_9268_atLeastLessThan__singleton,axiom,
% 5.49/5.82 ! [M: nat] :
% 5.49/5.82 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.49/5.82 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastLessThan_singleton
% 5.49/5.82 thf(fact_9269_atMost__0,axiom,
% 5.49/5.82 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.49/5.82 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % atMost_0
% 5.49/5.82 thf(fact_9270_UNIV__bool,axiom,
% 5.49/5.82 ( top_top_set_o
% 5.49/5.82 = ( insert_o @ $false @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % UNIV_bool
% 5.49/5.82 thf(fact_9271_atLeastAtMost__insertL,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.49/5.82 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastAtMost_insertL
% 5.49/5.82 thf(fact_9272_atLeastAtMostSuc__conv,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastAtMostSuc_conv
% 5.49/5.82 thf(fact_9273_Icc__eq__insert__lb__nat,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.49/5.82 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Icc_eq_insert_lb_nat
% 5.49/5.82 thf(fact_9274_atLeastLessThanSuc,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastLessThanSuc
% 5.49/5.82 thf(fact_9275_atLeast1__atMost__eq__remove0,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.49/5.82 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeast1_atMost_eq_remove0
% 5.49/5.82 thf(fact_9276_atLeast1__lessThan__eq__remove0,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.49/5.82 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeast1_lessThan_eq_remove0
% 5.49/5.82 thf(fact_9277_atLeastLessThan__nat__numeral,axiom,
% 5.49/5.82 ! [M: nat,K: num] :
% 5.49/5.82 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.49/5.82 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.49/5.82 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.49/5.82 = bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % atLeastLessThan_nat_numeral
% 5.49/5.82 thf(fact_9278_image__minus__const__atLeastLessThan__nat,axiom,
% 5.49/5.82 ! [C: nat,Y: nat,X: nat] :
% 5.49/5.82 ( ( ( ord_less_nat @ C @ Y )
% 5.49/5.82 => ( ( image_nat_nat
% 5.49/5.82 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.49/5.82 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_nat @ C @ Y )
% 5.49/5.82 => ( ( ( ord_less_nat @ X @ Y )
% 5.49/5.82 => ( ( image_nat_nat
% 5.49/5.82 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.49/5.82 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.49/5.82 & ( ~ ( ord_less_nat @ X @ Y )
% 5.49/5.82 => ( ( image_nat_nat
% 5.49/5.82 @ ^ [I4: nat] : ( minus_minus_nat @ I4 @ C )
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.49/5.82 = bot_bot_set_nat ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % image_minus_const_atLeastLessThan_nat
% 5.49/5.82 thf(fact_9279_and__not__num_Oelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_and_not_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y != none_num ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ? [N5: num] :
% 5.49/5.82 ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ one ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ? [N5: num] :
% 5.49/5.82 ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y != none_num ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.elims
% 5.49/5.82 thf(fact_9280_and__not__num_Opelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_and_not_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y = none_num )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ one ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y = none_num )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_not_num.pelims
% 5.49/5.82 thf(fact_9281_and__num_Oelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ one ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ? [N5: num] :
% 5.49/5.82 ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y != none_num ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ? [N5: num] :
% 5.49/5.82 ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ one ) ) ) )
% 5.49/5.82 => ( ( ? [M5: num] :
% 5.49/5.82 ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y != none_num ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ( ? [M5: num] :
% 5.49/5.82 ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ one ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.elims
% 5.49/5.82 thf(fact_9282_xor__num_Oelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y != none_num ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit1 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit0 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( Y
% 5.49/5.82 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.elims
% 5.49/5.82 thf(fact_9283_and__num_Osimps_I1_J,axiom,
% 5.49/5.82 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.49/5.82 = ( some_num @ one ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.simps(1)
% 5.49/5.82 thf(fact_9284_and__num_Osimps_I3_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 5.49/5.82 = ( some_num @ one ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.simps(3)
% 5.49/5.82 thf(fact_9285_and__num_Osimps_I7_J,axiom,
% 5.49/5.82 ! [M: num] :
% 5.49/5.82 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.49/5.82 = ( some_num @ one ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.simps(7)
% 5.49/5.82 thf(fact_9286_xor__num_Osimps_I2_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 5.49/5.82 = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(2)
% 5.49/5.82 thf(fact_9287_xor__num_Osimps_I3_J,axiom,
% 5.49/5.82 ! [N2: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 5.49/5.82 = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(3)
% 5.49/5.82 thf(fact_9288_xor__num_Osimps_I4_J,axiom,
% 5.49/5.82 ! [M: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.49/5.82 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(4)
% 5.49/5.82 thf(fact_9289_xor__num_Osimps_I7_J,axiom,
% 5.49/5.82 ! [M: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.49/5.82 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(7)
% 5.49/5.82 thf(fact_9290_and__num_Osimps_I9_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.82 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.simps(9)
% 5.49/5.82 thf(fact_9291_xor__num_Osimps_I6_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.49/5.82 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(6)
% 5.49/5.82 thf(fact_9292_xor__num_Osimps_I8_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.49/5.82 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.simps(8)
% 5.49/5.82 thf(fact_9293_and__num_Opelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_un7362597486090784418nd_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ one ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y = none_num )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ one ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y = none_num )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ one ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.49/5.82 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.49/5.82 @ ( bit_un7362597486090784418nd_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % and_num.pelims
% 5.49/5.82 thf(fact_9294_xor__num_Opelims,axiom,
% 5.49/5.82 ! [X: num,Xa: num,Y: option_num] :
% 5.49/5.82 ( ( ( bit_un2480387367778600638or_num @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X @ Xa ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y = none_num )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit1 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ( ( X = one )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit0 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit1 @ M5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit0 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ( ( Xa = one )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.49/5.82 => ( ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit0 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N5 ) ) ) ) ) )
% 5.49/5.82 => ~ ! [M5: num] :
% 5.49/5.82 ( ( X
% 5.49/5.82 = ( bit1 @ M5 ) )
% 5.49/5.82 => ! [N5: num] :
% 5.49/5.82 ( ( Xa
% 5.49/5.82 = ( bit1 @ N5 ) )
% 5.49/5.82 => ( ( Y
% 5.49/5.82 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N5 ) ) )
% 5.49/5.82 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % xor_num.pelims
% 5.49/5.82 thf(fact_9295_times__int_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.49/5.82 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( abs_Integ
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) )
% 5.49/5.82 @ Xa
% 5.49/5.82 @ X ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % times_int.abs_eq
% 5.49/5.82 thf(fact_9296_eq__Abs__Integ,axiom,
% 5.49/5.82 ! [Z: int] :
% 5.49/5.82 ~ ! [X3: nat,Y3: nat] :
% 5.49/5.82 ( Z
% 5.49/5.82 != ( abs_Integ @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % eq_Abs_Integ
% 5.49/5.82 thf(fact_9297_zero__int__def,axiom,
% 5.49/5.82 ( zero_zero_int
% 5.49/5.82 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % zero_int_def
% 5.49/5.82 thf(fact_9298_int__def,axiom,
% 5.49/5.82 ( semiri1314217659103216013at_int
% 5.49/5.82 = ( ^ [N: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N @ zero_zero_nat ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % int_def
% 5.49/5.82 thf(fact_9299_uminus__int_Oabs__eq,axiom,
% 5.49/5.82 ! [X: product_prod_nat_nat] :
% 5.49/5.82 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( abs_Integ
% 5.49/5.82 @ ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 )
% 5.49/5.82 @ X ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % uminus_int.abs_eq
% 5.49/5.82 thf(fact_9300_one__int__def,axiom,
% 5.49/5.82 ( one_one_int
% 5.49/5.82 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % one_int_def
% 5.49/5.82 thf(fact_9301_less__int_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.49/5.82 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 5.49/5.82 @ Xa
% 5.49/5.82 @ X ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_int.abs_eq
% 5.49/5.82 thf(fact_9302_less__eq__int_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.49/5.82 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) )
% 5.49/5.82 @ Xa
% 5.49/5.82 @ X ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_int.abs_eq
% 5.49/5.82 thf(fact_9303_plus__int_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.49/5.82 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( abs_Integ
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) )
% 5.49/5.82 @ Xa
% 5.49/5.82 @ X ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % plus_int.abs_eq
% 5.49/5.82 thf(fact_9304_minus__int_Oabs__eq,axiom,
% 5.49/5.82 ! [Xa: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.49/5.82 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X ) )
% 5.49/5.82 = ( abs_Integ
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) )
% 5.49/5.82 @ Xa
% 5.49/5.82 @ X ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % minus_int.abs_eq
% 5.49/5.82 thf(fact_9305_less__eq__int_Orep__eq,axiom,
% 5.49/5.82 ( ord_less_eq_int
% 5.49/5.82 = ( ^ [X4: int,Xa4: int] :
% 5.49/5.82 ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [Y4: nat,Z6: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y4 @ V2 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.49/5.82 @ ( rep_Integ @ X4 )
% 5.49/5.82 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_int.rep_eq
% 5.49/5.82 thf(fact_9306_less__int_Orep__eq,axiom,
% 5.49/5.82 ( ord_less_int
% 5.49/5.82 = ( ^ [X4: int,Xa4: int] :
% 5.49/5.82 ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [Y4: nat,Z6: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y4 @ V2 ) @ ( plus_plus_nat @ U2 @ Z6 ) ) )
% 5.49/5.82 @ ( rep_Integ @ X4 )
% 5.49/5.82 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_int.rep_eq
% 5.49/5.82 thf(fact_9307_uminus__int__def,axiom,
% 5.49/5.82 ( uminus_uminus_int
% 5.49/5.82 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.49/5.82 @ ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % uminus_int_def
% 5.49/5.82 thf(fact_9308_pred__nat__def,axiom,
% 5.49/5.82 ( pred_nat
% 5.49/5.82 = ( collec3392354462482085612at_nat
% 5.49/5.82 @ ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [M3: nat,N: nat] :
% 5.49/5.82 ( N
% 5.49/5.82 = ( suc @ M3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % pred_nat_def
% 5.49/5.82 thf(fact_9309_times__int__def,axiom,
% 5.49/5.82 ( times_times_int
% 5.49/5.82 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % times_int_def
% 5.49/5.82 thf(fact_9310_minus__int__def,axiom,
% 5.49/5.82 ( minus_minus_int
% 5.49/5.82 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % minus_int_def
% 5.49/5.82 thf(fact_9311_plus__int__def,axiom,
% 5.49/5.82 ( plus_plus_int
% 5.49/5.82 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.49/5.82 @ ( produc27273713700761075at_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc2626176000494625587at_nat
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % plus_int_def
% 5.49/5.82 thf(fact_9312_Gcd__remove0__nat,axiom,
% 5.49/5.82 ! [M6: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ M6 )
% 5.49/5.82 => ( ( gcd_Gcd_nat @ M6 )
% 5.49/5.82 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M6 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_remove0_nat
% 5.49/5.82 thf(fact_9313_num__of__nat_Osimps_I2_J,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.49/5.82 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.49/5.82 = one ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % num_of_nat.simps(2)
% 5.49/5.82 thf(fact_9314_Gcd__eq__Max,axiom,
% 5.49/5.82 ! [M6: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ M6 )
% 5.49/5.82 => ( ( M6 != bot_bot_set_nat )
% 5.49/5.82 => ( ~ ( member_nat @ zero_zero_nat @ M6 )
% 5.49/5.82 => ( ( gcd_Gcd_nat @ M6 )
% 5.49/5.82 = ( lattic8265883725875713057ax_nat
% 5.49/5.82 @ ( comple7806235888213564991et_nat
% 5.49/5.82 @ ( image_nat_set_nat
% 5.49/5.82 @ ^ [M3: nat] :
% 5.49/5.82 ( collect_nat
% 5.49/5.82 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M3 ) )
% 5.49/5.82 @ M6 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_eq_Max
% 5.49/5.82 thf(fact_9315_Gcd__abs__eq,axiom,
% 5.49/5.82 ! [K5: set_int] :
% 5.49/5.82 ( ( gcd_Gcd_int @ ( image_int_int @ abs_abs_int @ K5 ) )
% 5.49/5.82 = ( gcd_Gcd_int @ K5 ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_abs_eq
% 5.49/5.82 thf(fact_9316_Gcd__nat__abs__eq,axiom,
% 5.49/5.82 ! [K5: set_int] :
% 5.49/5.82 ( ( gcd_Gcd_nat
% 5.49/5.82 @ ( image_int_nat
% 5.49/5.82 @ ^ [K3: int] : ( nat2 @ ( abs_abs_int @ K3 ) )
% 5.49/5.82 @ K5 ) )
% 5.49/5.82 = ( nat2 @ ( gcd_Gcd_int @ K5 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_nat_abs_eq
% 5.49/5.82 thf(fact_9317_Max__divisors__self__nat,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( N2 != zero_zero_nat )
% 5.49/5.82 => ( ( lattic8265883725875713057ax_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ N2 ) ) )
% 5.49/5.82 = N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % Max_divisors_self_nat
% 5.49/5.82 thf(fact_9318_Gcd__int__eq,axiom,
% 5.49/5.82 ! [N7: set_nat] :
% 5.49/5.82 ( ( gcd_Gcd_int @ ( image_nat_int @ semiri1314217659103216013at_int @ N7 ) )
% 5.49/5.82 = ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ N7 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_int_eq
% 5.49/5.82 thf(fact_9319_Gcd__int__greater__eq__0,axiom,
% 5.49/5.82 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_int_greater_eq_0
% 5.49/5.82 thf(fact_9320_Sup__nat__def,axiom,
% 5.49/5.82 ( complete_Sup_Sup_nat
% 5.49/5.82 = ( ^ [X11: set_nat] : ( if_nat @ ( X11 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X11 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Sup_nat_def
% 5.49/5.82 thf(fact_9321_card__le__Suc__Max,axiom,
% 5.49/5.82 ! [S: set_nat] :
% 5.49/5.82 ( ( finite_finite_nat @ S )
% 5.49/5.82 => ( ord_less_eq_nat @ ( finite_card_nat @ S ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_le_Suc_Max
% 5.49/5.82 thf(fact_9322_divide__nat__def,axiom,
% 5.49/5.82 ( divide_divide_nat
% 5.49/5.82 = ( ^ [M3: nat,N: nat] :
% 5.49/5.82 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.49/5.82 @ ( lattic8265883725875713057ax_nat
% 5.49/5.82 @ ( collect_nat
% 5.49/5.82 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % divide_nat_def
% 5.49/5.82 thf(fact_9323_Gcd__int__def,axiom,
% 5.49/5.82 ( gcd_Gcd_int
% 5.49/5.82 = ( ^ [K6: set_int] : ( semiri1314217659103216013at_int @ ( gcd_Gcd_nat @ ( image_int_nat @ ( comp_int_nat_int @ nat2 @ abs_abs_int ) @ K6 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Gcd_int_def
% 5.49/5.82 thf(fact_9324_INT__greaterThan__UNIV,axiom,
% 5.49/5.82 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.49/5.82 = bot_bot_set_nat ) ).
% 5.49/5.82
% 5.49/5.82 % INT_greaterThan_UNIV
% 5.49/5.82 thf(fact_9325_Max__divisors__self__int,axiom,
% 5.49/5.82 ! [N2: int] :
% 5.49/5.82 ( ( N2 != zero_zero_int )
% 5.49/5.82 => ( ( lattic8263393255366662781ax_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [D5: int] : ( dvd_dvd_int @ D5 @ N2 ) ) )
% 5.49/5.82 = ( abs_abs_int @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % Max_divisors_self_int
% 5.49/5.82 thf(fact_9326_greaterThan__Suc,axiom,
% 5.49/5.82 ! [K: nat] :
% 5.49/5.82 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.49/5.82 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % greaterThan_Suc
% 5.49/5.82 thf(fact_9327_mono__Suc,axiom,
% 5.49/5.82 order_mono_nat_nat @ suc ).
% 5.49/5.82
% 5.49/5.82 % mono_Suc
% 5.49/5.82 thf(fact_9328_mono__times__nat,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mono_times_nat
% 5.49/5.82 thf(fact_9329_mono__ge2__power__minus__self,axiom,
% 5.49/5.82 ! [K: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.49/5.82 => ( order_mono_nat_nat
% 5.49/5.82 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mono_ge2_power_minus_self
% 5.49/5.82 thf(fact_9330_binomial__def,axiom,
% 5.49/5.82 ( binomial
% 5.49/5.82 = ( ^ [N: nat,K3: nat] :
% 5.49/5.82 ( finite_card_set_nat
% 5.49/5.82 @ ( collect_set_nat
% 5.49/5.82 @ ^ [K6: set_nat] :
% 5.49/5.82 ( ( member_set_nat @ K6 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.49/5.82 & ( ( finite_card_nat @ K6 )
% 5.49/5.82 = K3 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % binomial_def
% 5.49/5.82 thf(fact_9331_upto__aux__rec,axiom,
% 5.49/5.82 ( upto_aux
% 5.49/5.82 = ( ^ [I4: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I4 ) @ Js @ ( upto_aux @ I4 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_aux_rec
% 5.49/5.82 thf(fact_9332_upto_Opsimps,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.49/5.82 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( upto @ I2 @ J )
% 5.49/5.82 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( upto @ I2 @ J )
% 5.49/5.82 = nil_int ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto.psimps
% 5.49/5.82 thf(fact_9333_upto_Opelims,axiom,
% 5.49/5.82 ! [X: int,Xa: int,Y: list_int] :
% 5.49/5.82 ( ( ( upto @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) )
% 5.49/5.82 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.49/5.82 => ( Y = nil_int ) ) )
% 5.49/5.82 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto.pelims
% 5.49/5.82 thf(fact_9334_sort__upto,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( linord1735203802627413978nt_int
% 5.49/5.82 @ ^ [X4: int] : X4
% 5.49/5.82 @ ( upto @ I2 @ J ) )
% 5.49/5.82 = ( upto @ I2 @ J ) ) ).
% 5.49/5.82
% 5.49/5.82 % sort_upto
% 5.49/5.82 thf(fact_9335_upto__Nil,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( ( upto @ I2 @ J )
% 5.49/5.82 = nil_int )
% 5.49/5.82 = ( ord_less_int @ J @ I2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_Nil
% 5.49/5.82 thf(fact_9336_upto__Nil2,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( nil_int
% 5.49/5.82 = ( upto @ I2 @ J ) )
% 5.49/5.82 = ( ord_less_int @ J @ I2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_Nil2
% 5.49/5.82 thf(fact_9337_upto__empty,axiom,
% 5.49/5.82 ! [J: int,I2: int] :
% 5.49/5.82 ( ( ord_less_int @ J @ I2 )
% 5.49/5.82 => ( ( upto @ I2 @ J )
% 5.49/5.82 = nil_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_empty
% 5.49/5.82 thf(fact_9338_nth__upto,axiom,
% 5.49/5.82 ! [I2: int,K: nat,J: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.49/5.82 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.49/5.82 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nth_upto
% 5.49/5.82 thf(fact_9339_upto__rec__numeral_I1_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 = nil_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec_numeral(1)
% 5.49/5.82 thf(fact_9340_upto__rec__numeral_I4_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = nil_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec_numeral(4)
% 5.49/5.82 thf(fact_9341_upto__rec__numeral_I3_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.49/5.82 = nil_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec_numeral(3)
% 5.49/5.82 thf(fact_9342_upto__rec__numeral_I2_J,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.49/5.82 = nil_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec_numeral(2)
% 5.49/5.82 thf(fact_9343_sorted__upto,axiom,
% 5.49/5.82 ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % sorted_upto
% 5.49/5.82 thf(fact_9344_sorted__wrt__upto,axiom,
% 5.49/5.82 ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 5.49/5.82
% 5.49/5.82 % sorted_wrt_upto
% 5.49/5.82 thf(fact_9345_upto__split2,axiom,
% 5.49/5.82 ! [I2: int,J: int,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( ord_less_eq_int @ J @ K )
% 5.49/5.82 => ( ( upto @ I2 @ K )
% 5.49/5.82 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_split2
% 5.49/5.82 thf(fact_9346_upto__split1,axiom,
% 5.49/5.82 ! [I2: int,J: int,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( ord_less_eq_int @ J @ K )
% 5.49/5.82 => ( ( upto @ I2 @ K )
% 5.49/5.82 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_split1
% 5.49/5.82 thf(fact_9347_upto_Oelims,axiom,
% 5.49/5.82 ! [X: int,Xa: int,Y: list_int] :
% 5.49/5.82 ( ( ( upto @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( ord_less_eq_int @ X @ Xa )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_int @ X @ Xa )
% 5.49/5.82 => ( Y = nil_int ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto.elims
% 5.49/5.82 thf(fact_9348_upto_Osimps,axiom,
% 5.49/5.82 ( upto
% 5.49/5.82 = ( ^ [I4: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I4 @ J3 ) @ ( cons_int @ I4 @ ( upto @ ( plus_plus_int @ I4 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto.simps
% 5.49/5.82 thf(fact_9349_upto__rec1,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( upto @ I2 @ J )
% 5.49/5.82 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec1
% 5.49/5.82 thf(fact_9350_upto__rec2,axiom,
% 5.49/5.82 ! [I2: int,J: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( upto @ I2 @ J )
% 5.49/5.82 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_rec2
% 5.49/5.82 thf(fact_9351_upto__split3,axiom,
% 5.49/5.82 ! [I2: int,J: int,K: int] :
% 5.49/5.82 ( ( ord_less_eq_int @ I2 @ J )
% 5.49/5.82 => ( ( ord_less_eq_int @ J @ K )
% 5.49/5.82 => ( ( upto @ I2 @ K )
% 5.49/5.82 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upto_split3
% 5.49/5.82 thf(fact_9352_card__length__sum__list__rec,axiom,
% 5.49/5.82 ! [M: nat,N7: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.49/5.82 => ( ( finite_card_list_nat
% 5.49/5.82 @ ( collect_list_nat
% 5.49/5.82 @ ^ [L2: list_nat] :
% 5.49/5.82 ( ( ( size_size_list_nat @ L2 )
% 5.49/5.82 = M )
% 5.49/5.82 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.49/5.82 = N7 ) ) ) )
% 5.49/5.82 = ( plus_plus_nat
% 5.49/5.82 @ ( finite_card_list_nat
% 5.49/5.82 @ ( collect_list_nat
% 5.49/5.82 @ ^ [L2: list_nat] :
% 5.49/5.82 ( ( ( size_size_list_nat @ L2 )
% 5.49/5.82 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.49/5.82 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.49/5.82 = N7 ) ) ) )
% 5.49/5.82 @ ( finite_card_list_nat
% 5.49/5.82 @ ( collect_list_nat
% 5.49/5.82 @ ^ [L2: list_nat] :
% 5.49/5.82 ( ( ( size_size_list_nat @ L2 )
% 5.49/5.82 = M )
% 5.49/5.82 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.49/5.82 = N7 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_length_sum_list_rec
% 5.49/5.82 thf(fact_9353_card__length__sum__list,axiom,
% 5.49/5.82 ! [M: nat,N7: nat] :
% 5.49/5.82 ( ( finite_card_list_nat
% 5.49/5.82 @ ( collect_list_nat
% 5.49/5.82 @ ^ [L2: list_nat] :
% 5.49/5.82 ( ( ( size_size_list_nat @ L2 )
% 5.49/5.82 = M )
% 5.49/5.82 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.49/5.82 = N7 ) ) ) )
% 5.49/5.82 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N7 @ M ) @ one_one_nat ) @ N7 ) ) ).
% 5.49/5.82
% 5.49/5.82 % card_length_sum_list
% 5.49/5.82 thf(fact_9354_sort__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( linord738340561235409698at_nat
% 5.49/5.82 @ ^ [X4: nat] : X4
% 5.49/5.82 @ ( upt @ M @ N2 ) )
% 5.49/5.82 = ( upt @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % sort_upt
% 5.49/5.82 thf(fact_9355_upt__0__eq__Nil__conv,axiom,
% 5.49/5.82 ! [J: nat] :
% 5.49/5.82 ( ( ( upt @ zero_zero_nat @ J )
% 5.49/5.82 = nil_nat )
% 5.49/5.82 = ( J = zero_zero_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_0_eq_Nil_conv
% 5.49/5.82 thf(fact_9356_hd__upt,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.82 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 5.49/5.82 = I2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % hd_upt
% 5.49/5.82 thf(fact_9357_upt__conv__Nil,axiom,
% 5.49/5.82 ! [J: nat,I2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ J @ I2 )
% 5.49/5.82 => ( ( upt @ I2 @ J )
% 5.49/5.82 = nil_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_conv_Nil
% 5.49/5.82 thf(fact_9358_upt__merge,axiom,
% 5.49/5.82 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.82 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 & ( ord_less_eq_nat @ J @ K ) )
% 5.49/5.82 => ( ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ K ) )
% 5.49/5.82 = ( upt @ I2 @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_merge
% 5.49/5.82 thf(fact_9359_upt__eq__Nil__conv,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ( upt @ I2 @ J )
% 5.49/5.82 = nil_nat )
% 5.49/5.82 = ( ( J = zero_zero_nat )
% 5.49/5.82 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_eq_Nil_conv
% 5.49/5.82 thf(fact_9360_take__upt,axiom,
% 5.49/5.82 ! [I2: nat,M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 5.49/5.82 => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 5.49/5.82 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % take_upt
% 5.49/5.82 thf(fact_9361_upt__rec__numeral,axiom,
% 5.49/5.82 ! [M: num,N2: num] :
% 5.49/5.82 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.49/5.82 = nil_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_rec_numeral
% 5.49/5.82 thf(fact_9362_last__upt,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.82 => ( ( last_nat @ ( upt @ I2 @ J ) )
% 5.49/5.82 = ( minus_minus_nat @ J @ one_one_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % last_upt
% 5.49/5.82 thf(fact_9363_nth__upt,axiom,
% 5.49/5.82 ! [I2: nat,K: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 5.49/5.82 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 5.49/5.82 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nth_upt
% 5.49/5.82 thf(fact_9364_sum__list__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.82 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 5.49/5.82 = ( groups3542108847815614940at_nat
% 5.49/5.82 @ ^ [X4: nat] : X4
% 5.49/5.82 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sum_list_upt
% 5.49/5.82 thf(fact_9365_map__add__upt_H,axiom,
% 5.49/5.82 ! [Ofs: nat,A: nat,B: nat] :
% 5.49/5.82 ( ( map_nat_nat
% 5.49/5.82 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ Ofs )
% 5.49/5.82 @ ( upt @ A @ B ) )
% 5.49/5.82 = ( upt @ ( plus_plus_nat @ A @ Ofs ) @ ( plus_plus_nat @ B @ Ofs ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % map_add_upt'
% 5.49/5.82 thf(fact_9366_upt__eq__append__conv,axiom,
% 5.49/5.82 ! [I2: nat,J: nat,Xs: list_nat,Ys3: list_nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 => ( ( ( upt @ I2 @ J )
% 5.49/5.82 = ( append_nat @ Xs @ Ys3 ) )
% 5.49/5.82 = ( ? [K3: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ I2 @ K3 )
% 5.49/5.82 & ( ord_less_eq_nat @ K3 @ J )
% 5.49/5.82 & ( ( upt @ I2 @ K3 )
% 5.49/5.82 = Xs )
% 5.49/5.82 & ( ( upt @ K3 @ J )
% 5.49/5.82 = Ys3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_eq_append_conv
% 5.49/5.82 thf(fact_9367_upt__append,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.82 => ( ( append_nat @ ( upt @ zero_zero_nat @ I2 ) @ ( upt @ I2 @ J ) )
% 5.49/5.82 = ( upt @ zero_zero_nat @ J ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_append
% 5.49/5.82 thf(fact_9368_upt__rec,axiom,
% 5.49/5.82 ( upt
% 5.49/5.82 = ( ^ [I4: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I4 @ J3 ) @ ( cons_nat @ I4 @ ( upt @ ( suc @ I4 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_rec
% 5.49/5.82 thf(fact_9369_upt__conv__Cons,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_nat @ I2 @ J )
% 5.49/5.82 => ( ( upt @ I2 @ J )
% 5.49/5.82 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_conv_Cons
% 5.49/5.82 thf(fact_9370_upt__Suc,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.49/5.82 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.49/5.82 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.49/5.82 = nil_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_Suc
% 5.49/5.82 thf(fact_9371_upt__Suc__append,axiom,
% 5.49/5.82 ! [I2: nat,J: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.49/5.82 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_Suc_append
% 5.49/5.82 thf(fact_9372_upt__add__eq__append,axiom,
% 5.49/5.82 ! [I2: nat,J: nat,K: nat] :
% 5.49/5.82 ( ( ord_less_eq_nat @ I2 @ J )
% 5.49/5.82 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.49/5.82 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_add_eq_append
% 5.49/5.82 thf(fact_9373_butlast__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( butlast_nat @ ( upt @ M @ N2 ) )
% 5.49/5.82 = ( upt @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % butlast_upt
% 5.49/5.82 thf(fact_9374_sorted__wrt__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % sorted_wrt_upt
% 5.49/5.82 thf(fact_9375_map__add__upt,axiom,
% 5.49/5.82 ! [N2: nat,M: nat] :
% 5.49/5.82 ( ( map_nat_nat
% 5.49/5.82 @ ^ [I4: nat] : ( plus_plus_nat @ I4 @ N2 )
% 5.49/5.82 @ ( upt @ zero_zero_nat @ M ) )
% 5.49/5.82 = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % map_add_upt
% 5.49/5.82 thf(fact_9376_sorted__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % sorted_upt
% 5.49/5.82 thf(fact_9377_upt__eq__lel__conv,axiom,
% 5.49/5.82 ! [L: nat,H: nat,Is1: list_nat,I2: nat,Is2: list_nat] :
% 5.49/5.82 ( ( ( upt @ L @ H )
% 5.49/5.82 = ( append_nat @ Is1 @ ( cons_nat @ I2 @ Is2 ) ) )
% 5.49/5.82 = ( ( Is1
% 5.49/5.82 = ( upt @ L @ I2 ) )
% 5.49/5.82 & ( Is2
% 5.49/5.82 = ( upt @ ( suc @ I2 ) @ H ) )
% 5.49/5.82 & ( ord_less_eq_nat @ L @ I2 )
% 5.49/5.82 & ( ord_less_nat @ I2 @ H ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_eq_lel_conv
% 5.49/5.82 thf(fact_9378_upt__eq__Cons__conv,axiom,
% 5.49/5.82 ! [I2: nat,J: nat,X: nat,Xs: list_nat] :
% 5.49/5.82 ( ( ( upt @ I2 @ J )
% 5.49/5.82 = ( cons_nat @ X @ Xs ) )
% 5.49/5.82 = ( ( ord_less_nat @ I2 @ J )
% 5.49/5.82 & ( I2 = X )
% 5.49/5.82 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 5.49/5.82 = Xs ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_eq_Cons_conv
% 5.49/5.82 thf(fact_9379_upt__filter__extend,axiom,
% 5.49/5.82 ! [U: nat,U3: nat,P: nat > $o] :
% 5.49/5.82 ( ( ord_less_eq_nat @ U @ U3 )
% 5.49/5.82 => ( ! [I3: nat] :
% 5.49/5.82 ( ( ( ord_less_eq_nat @ U @ I3 )
% 5.49/5.82 & ( ord_less_nat @ I3 @ U3 ) )
% 5.49/5.82 => ~ ( P @ I3 ) )
% 5.49/5.82 => ( ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U ) )
% 5.49/5.82 = ( filter_nat2 @ P @ ( upt @ zero_zero_nat @ U3 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % upt_filter_extend
% 5.49/5.82 thf(fact_9380_map__decr__upt,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( map_nat_nat
% 5.49/5.82 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.49/5.82 @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.49/5.82 = ( upt @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % map_decr_upt
% 5.49/5.82 thf(fact_9381_bezw_Oelims,axiom,
% 5.49/5.82 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 5.49/5.82 ( ( ( bezw @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( ( Xa = zero_zero_nat )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.49/5.82 & ( ( Xa != zero_zero_nat )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bezw.elims
% 5.49/5.82 thf(fact_9382_bezw_Osimps,axiom,
% 5.49/5.82 ( bezw
% 5.49/5.82 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bezw.simps
% 5.49/5.82 thf(fact_9383_bezw_Opelims,axiom,
% 5.49/5.82 ! [X: nat,Xa: nat,Y: product_prod_int_int] :
% 5.49/5.82 ( ( ( bezw @ X @ Xa )
% 5.49/5.82 = Y )
% 5.49/5.82 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.49/5.82 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.49/5.82 & ( ( Xa != zero_zero_nat )
% 5.49/5.82 => ( Y
% 5.49/5.82 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa ) ) ) ) ) ) ) )
% 5.49/5.82 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bezw.pelims
% 5.49/5.82 thf(fact_9384_bezw__non__0,axiom,
% 5.49/5.82 ! [Y: nat,X: nat] :
% 5.49/5.82 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.49/5.82 => ( ( bezw @ X @ Y )
% 5.49/5.82 = ( 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 ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % bezw_non_0
% 5.49/5.82 thf(fact_9385_mod__pure,axiom,
% 5.49/5.82 ! [B: $o,H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ ( pure_assn @ B ) @ H )
% 5.49/5.82 = ( ( ( produc8586169260539613262et_nat @ H )
% 5.49/5.82 = bot_bot_set_nat )
% 5.49/5.82 & B ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_pure
% 5.49/5.82 thf(fact_9386_mod__emp,axiom,
% 5.49/5.82 ! [H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ one_one_assn @ H )
% 5.49/5.82 = ( ( produc8586169260539613262et_nat @ H )
% 5.49/5.82 = bot_bot_set_nat ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_emp
% 5.49/5.82 thf(fact_9387_mod__star__trueE_H,axiom,
% 5.49/5.82 ! [P: assn,H: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( rep_assn @ ( times_times_assn @ P @ top_top_assn ) @ H )
% 5.49/5.82 => ~ ! [H5: produc3658429121746597890et_nat] :
% 5.49/5.82 ( ( ( produc1824681642469235216et_nat @ H5 )
% 5.49/5.82 = ( produc1824681642469235216et_nat @ H ) )
% 5.49/5.82 => ( ( ord_less_eq_set_nat @ ( produc8586169260539613262et_nat @ H5 ) @ ( produc8586169260539613262et_nat @ H ) )
% 5.49/5.82 => ~ ( rep_assn @ P @ H5 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % mod_star_trueE'
% 5.49/5.82 thf(fact_9388_natLess__def,axiom,
% 5.49/5.82 ( bNF_Ca8459412986667044542atLess
% 5.49/5.82 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % natLess_def
% 5.49/5.82 thf(fact_9389_less__eq,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.49/5.82 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq
% 5.49/5.82 thf(fact_9390_pred__nat__trancl__eq__le,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.49/5.82 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % pred_nat_trancl_eq_le
% 5.49/5.82 thf(fact_9391_min__0R,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % min_0R
% 5.49/5.82 thf(fact_9392_min__0L,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 = zero_zero_nat ) ).
% 5.49/5.82
% 5.49/5.82 % min_0L
% 5.49/5.82 thf(fact_9393_min__Suc__Suc,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.49/5.82 = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_Suc_Suc
% 5.49/5.82 thf(fact_9394_min__Suc__gt_I2_J,axiom,
% 5.49/5.82 ! [A: nat,B: nat] :
% 5.49/5.82 ( ( ord_less_nat @ A @ B )
% 5.49/5.82 => ( ( ord_min_nat @ B @ ( suc @ A ) )
% 5.49/5.82 = ( suc @ A ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_Suc_gt(2)
% 5.49/5.82 thf(fact_9395_min__Suc__gt_I1_J,axiom,
% 5.49/5.82 ! [A: nat,B: nat] :
% 5.49/5.82 ( ( ord_less_nat @ A @ B )
% 5.49/5.82 => ( ( ord_min_nat @ ( suc @ A ) @ B )
% 5.49/5.82 = ( suc @ A ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_Suc_gt(1)
% 5.49/5.82 thf(fact_9396_nat__mult__min__right,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q6 ) )
% 5.49/5.82 = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_mult_min_right
% 5.49/5.82 thf(fact_9397_nat__mult__min__left,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q6 )
% 5.49/5.82 = ( ord_min_nat @ ( times_times_nat @ M @ Q6 ) @ ( times_times_nat @ N2 @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_mult_min_left
% 5.49/5.82 thf(fact_9398_min__diff,axiom,
% 5.49/5.82 ! [M: nat,I2: nat,N2: nat] :
% 5.49/5.82 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.49/5.82 = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_diff
% 5.49/5.82 thf(fact_9399_inf__nat__def,axiom,
% 5.49/5.82 inf_inf_nat = ord_min_nat ).
% 5.49/5.82
% 5.49/5.82 % inf_nat_def
% 5.49/5.82 thf(fact_9400_min__Suc2,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = ( case_nat_nat @ zero_zero_nat
% 5.49/5.82 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ M7 @ N2 ) )
% 5.49/5.82 @ M ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_Suc2
% 5.49/5.82 thf(fact_9401_min__Suc1,axiom,
% 5.49/5.82 ! [N2: nat,M: nat] :
% 5.49/5.82 ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 5.49/5.82 = ( case_nat_nat @ zero_zero_nat
% 5.49/5.82 @ ^ [M7: nat] : ( suc @ ( ord_min_nat @ N2 @ M7 ) )
% 5.49/5.82 @ M ) ) ).
% 5.49/5.82
% 5.49/5.82 % min_Suc1
% 5.49/5.82 thf(fact_9402_of__nat__eq__id,axiom,
% 5.49/5.82 semiri1316708129612266289at_nat = id_nat ).
% 5.49/5.82
% 5.49/5.82 % of_nat_eq_id
% 5.49/5.82 thf(fact_9403_nat__def,axiom,
% 5.49/5.82 ( nat2
% 5.49/5.82 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_def
% 5.49/5.82 thf(fact_9404_less__int__def,axiom,
% 5.49/5.82 ( ord_less_int
% 5.49/5.82 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.49/5.82 @ ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_int_def
% 5.49/5.82 thf(fact_9405_less__eq__int__def,axiom,
% 5.49/5.82 ( ord_less_eq_int
% 5.49/5.82 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.49/5.82 @ ( produc8739625826339149834_nat_o
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.82 ( produc6081775807080527818_nat_o
% 5.49/5.82 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_int_def
% 5.49/5.82 thf(fact_9406_less__eq__integer__def,axiom,
% 5.49/5.82 ( ord_le3102999989581377725nteger
% 5.49/5.82 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_eq_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_integer_def
% 5.49/5.82 thf(fact_9407_less__integer__def,axiom,
% 5.49/5.82 ( ord_le6747313008572928689nteger
% 5.49/5.82 = ( map_fu2496120808607739376eger_o @ code_int_of_integer @ ( map_fu6957801986076833569nt_o_o @ code_int_of_integer @ id_o ) @ ord_less_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_integer_def
% 5.49/5.82 thf(fact_9408_max__nat_Oeq__neutr__iff,axiom,
% 5.49/5.82 ! [A: nat,B: nat] :
% 5.49/5.82 ( ( ( ord_max_nat @ A @ B )
% 5.49/5.82 = zero_zero_nat )
% 5.49/5.82 = ( ( A = zero_zero_nat )
% 5.49/5.82 & ( B = zero_zero_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_nat.eq_neutr_iff
% 5.49/5.82 thf(fact_9409_max__nat_Oleft__neutral,axiom,
% 5.49/5.82 ! [A: nat] :
% 5.49/5.82 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.49/5.82 = A ) ).
% 5.49/5.82
% 5.49/5.82 % max_nat.left_neutral
% 5.49/5.82 thf(fact_9410_max__nat_Oneutr__eq__iff,axiom,
% 5.49/5.82 ! [A: nat,B: nat] :
% 5.49/5.82 ( ( zero_zero_nat
% 5.49/5.82 = ( ord_max_nat @ A @ B ) )
% 5.49/5.82 = ( ( A = zero_zero_nat )
% 5.49/5.82 & ( B = zero_zero_nat ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_nat.neutr_eq_iff
% 5.49/5.82 thf(fact_9411_max__nat_Oright__neutral,axiom,
% 5.49/5.82 ! [A: nat] :
% 5.49/5.82 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.49/5.82 = A ) ).
% 5.49/5.82
% 5.49/5.82 % max_nat.right_neutral
% 5.49/5.82 thf(fact_9412_max__0L,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 5.49/5.82 = N2 ) ).
% 5.49/5.82
% 5.49/5.82 % max_0L
% 5.49/5.82 thf(fact_9413_max__0R,axiom,
% 5.49/5.82 ! [N2: nat] :
% 5.49/5.82 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 5.49/5.82 = N2 ) ).
% 5.49/5.82
% 5.49/5.82 % max_0R
% 5.49/5.82 thf(fact_9414_max__Suc__Suc,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.49/5.82 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_Suc_Suc
% 5.49/5.82 thf(fact_9415_nat__mult__max__left,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q6 )
% 5.49/5.82 = ( ord_max_nat @ ( times_times_nat @ M @ Q6 ) @ ( times_times_nat @ N2 @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_mult_max_left
% 5.49/5.82 thf(fact_9416_nat__mult__max__right,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q6 ) )
% 5.49/5.82 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_mult_max_right
% 5.49/5.82 thf(fact_9417_nat__add__max__right,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q6 ) )
% 5.49/5.82 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_add_max_right
% 5.49/5.82 thf(fact_9418_nat__add__max__left,axiom,
% 5.49/5.82 ! [M: nat,N2: nat,Q6: nat] :
% 5.49/5.82 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q6 )
% 5.49/5.82 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q6 ) @ ( plus_plus_nat @ N2 @ Q6 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_add_max_left
% 5.49/5.82 thf(fact_9419_nat__minus__add__max,axiom,
% 5.49/5.82 ! [N2: nat,M: nat] :
% 5.49/5.82 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.49/5.82 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.49/5.82
% 5.49/5.82 % nat_minus_add_max
% 5.49/5.82 thf(fact_9420_max__Suc1,axiom,
% 5.49/5.82 ! [N2: nat,M: nat] :
% 5.49/5.82 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.49/5.82 = ( case_nat_nat @ ( suc @ N2 )
% 5.49/5.82 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ N2 @ M7 ) )
% 5.49/5.82 @ M ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_Suc1
% 5.49/5.82 thf(fact_9421_max__Suc2,axiom,
% 5.49/5.82 ! [M: nat,N2: nat] :
% 5.49/5.82 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.49/5.82 = ( case_nat_nat @ ( suc @ N2 )
% 5.49/5.82 @ ^ [M7: nat] : ( suc @ ( ord_max_nat @ M7 @ N2 ) )
% 5.49/5.82 @ M ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_Suc2
% 5.49/5.82 thf(fact_9422_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.49/5.82 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] : ( ord_less_eq_nat @ Y4 @ X4 )
% 5.49/5.82 @ ^ [X4: nat,Y4: nat] : ( ord_less_nat @ Y4 @ X4 ) ) ).
% 5.49/5.82
% 5.49/5.82 % max_nat.semilattice_neutr_order_axioms
% 5.49/5.82 thf(fact_9423_sup__nat__def,axiom,
% 5.49/5.82 sup_sup_nat = ord_max_nat ).
% 5.49/5.82
% 5.49/5.82 % sup_nat_def
% 5.49/5.82 thf(fact_9424_inj__Suc,axiom,
% 5.49/5.82 ! [N7: set_nat] : ( inj_on_nat_nat @ suc @ N7 ) ).
% 5.49/5.82
% 5.49/5.82 % inj_Suc
% 5.49/5.82 thf(fact_9425_inj__on__diff__nat,axiom,
% 5.49/5.82 ! [N7: set_nat,K: nat] :
% 5.49/5.82 ( ! [N5: nat] :
% 5.49/5.82 ( ( member_nat @ N5 @ N7 )
% 5.49/5.82 => ( ord_less_eq_nat @ K @ N5 ) )
% 5.49/5.82 => ( inj_on_nat_nat
% 5.49/5.82 @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 5.49/5.82 @ N7 ) ) ).
% 5.49/5.82
% 5.49/5.82 % inj_on_diff_nat
% 5.49/5.82 thf(fact_9426_floor__rat__def,axiom,
% 5.49/5.82 ( archim3151403230148437115or_rat
% 5.49/5.82 = ( ^ [X4: rat] :
% 5.49/5.82 ( the_int
% 5.49/5.82 @ ^ [Z6: int] :
% 5.49/5.82 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z6 ) @ X4 )
% 5.49/5.82 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z6 @ one_one_int ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % floor_rat_def
% 5.49/5.82 thf(fact_9427_less__eq__rat__def,axiom,
% 5.49/5.82 ( ord_less_eq_rat
% 5.49/5.82 = ( ^ [X4: rat,Y4: rat] :
% 5.49/5.82 ( ( ord_less_rat @ X4 @ Y4 )
% 5.49/5.82 | ( X4 = Y4 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % less_eq_rat_def
% 5.49/5.82 thf(fact_9428_abs__rat__def,axiom,
% 5.49/5.82 ( abs_abs_rat
% 5.49/5.82 = ( ^ [A5: rat] : ( if_rat @ ( ord_less_rat @ A5 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A5 ) @ A5 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % abs_rat_def
% 5.49/5.82 thf(fact_9429_sgn__rat__def,axiom,
% 5.49/5.82 ( sgn_sgn_rat
% 5.49/5.82 = ( ^ [A5: rat] : ( if_rat @ ( A5 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A5 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % sgn_rat_def
% 5.49/5.82 thf(fact_9430_normalize__negative,axiom,
% 5.49/5.82 ! [Q6: int,P3: int] :
% 5.49/5.82 ( ( ord_less_int @ Q6 @ zero_zero_int )
% 5.49/5.82 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.82 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P3 ) @ ( uminus_uminus_int @ Q6 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % normalize_negative
% 5.49/5.82 thf(fact_9431_normalize__denom__zero,axiom,
% 5.49/5.82 ! [P3: int] :
% 5.49/5.82 ( ( normalize @ ( product_Pair_int_int @ P3 @ zero_zero_int ) )
% 5.49/5.82 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % normalize_denom_zero
% 5.49/5.82 thf(fact_9432_normalize__denom__pos,axiom,
% 5.49/5.82 ! [R3: product_prod_int_int,P3: int,Q6: int] :
% 5.49/5.82 ( ( ( normalize @ R3 )
% 5.49/5.82 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.82 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 5.49/5.82
% 5.49/5.82 % normalize_denom_pos
% 5.49/5.82 thf(fact_9433_normalize__crossproduct,axiom,
% 5.49/5.82 ! [Q6: int,S2: int,P3: int,R3: int] :
% 5.49/5.82 ( ( Q6 != zero_zero_int )
% 5.49/5.82 => ( ( S2 != zero_zero_int )
% 5.49/5.82 => ( ( ( normalize @ ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.82 = ( normalize @ ( product_Pair_int_int @ R3 @ S2 ) ) )
% 5.49/5.82 => ( ( times_times_int @ P3 @ S2 )
% 5.49/5.82 = ( times_times_int @ R3 @ Q6 ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % normalize_crossproduct
% 5.49/5.82 thf(fact_9434_normalize__def,axiom,
% 5.49/5.82 ( normalize
% 5.49/5.82 = ( ^ [P7: product_prod_int_int] :
% 5.49/5.82 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P7 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) )
% 5.49/5.82 @ ( if_Pro3027730157355071871nt_int
% 5.49/5.82 @ ( ( product_snd_int_int @ P7 )
% 5.49/5.82 = zero_zero_int )
% 5.49/5.82 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.82 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P7 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P7 ) @ ( product_snd_int_int @ P7 ) ) ) ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % normalize_def
% 5.49/5.82 thf(fact_9435_quotient__of__number_I4_J,axiom,
% 5.49/5.82 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.49/5.82 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_number(4)
% 5.49/5.82 thf(fact_9436_gcd__pos__int,axiom,
% 5.49/5.82 ! [M: int,N2: int] :
% 5.49/5.82 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 5.49/5.82 = ( ( M != zero_zero_int )
% 5.49/5.82 | ( N2 != zero_zero_int ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_pos_int
% 5.49/5.82 thf(fact_9437_quotient__of__number_I3_J,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.49/5.82 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_number(3)
% 5.49/5.82 thf(fact_9438_rat__one__code,axiom,
% 5.49/5.82 ( ( quotient_of @ one_one_rat )
% 5.49/5.82 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % rat_one_code
% 5.49/5.82 thf(fact_9439_rat__zero__code,axiom,
% 5.49/5.82 ( ( quotient_of @ zero_zero_rat )
% 5.49/5.82 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % rat_zero_code
% 5.49/5.82 thf(fact_9440_quotient__of__number_I5_J,axiom,
% 5.49/5.82 ! [K: num] :
% 5.49/5.82 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.49/5.82 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_number(5)
% 5.49/5.82 thf(fact_9441_gcd__ge__0__int,axiom,
% 5.49/5.82 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_ge_0_int
% 5.49/5.82 thf(fact_9442_quotient__of__div,axiom,
% 5.49/5.82 ! [R3: rat,N2: int,D2: int] :
% 5.49/5.82 ( ( ( quotient_of @ R3 )
% 5.49/5.82 = ( product_Pair_int_int @ N2 @ D2 ) )
% 5.49/5.82 => ( R3
% 5.49/5.82 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N2 ) @ ( ring_1_of_int_rat @ D2 ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_div
% 5.49/5.82 thf(fact_9443_gcd__le1__int,axiom,
% 5.49/5.82 ! [A: int,B: int] :
% 5.49/5.82 ( ( ord_less_int @ zero_zero_int @ A )
% 5.49/5.82 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_le1_int
% 5.49/5.82 thf(fact_9444_gcd__le2__int,axiom,
% 5.49/5.82 ! [B: int,A: int] :
% 5.49/5.82 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.82 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_le2_int
% 5.49/5.82 thf(fact_9445_gcd__cases__int,axiom,
% 5.49/5.82 ! [X: int,Y: int,P: int > $o] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 5.49/5.82 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.49/5.82 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.49/5.82 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.49/5.82 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.49/5.82 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 5.49/5.82 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.49/5.82 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.49/5.82 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.49/5.82 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_cases_int
% 5.49/5.82 thf(fact_9446_gcd__unique__int,axiom,
% 5.49/5.82 ! [D2: int,A: int,B: int] :
% 5.49/5.82 ( ( ( ord_less_eq_int @ zero_zero_int @ D2 )
% 5.49/5.82 & ( dvd_dvd_int @ D2 @ A )
% 5.49/5.82 & ( dvd_dvd_int @ D2 @ B )
% 5.49/5.82 & ! [E3: int] :
% 5.49/5.82 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.49/5.82 & ( dvd_dvd_int @ E3 @ B ) )
% 5.49/5.82 => ( dvd_dvd_int @ E3 @ D2 ) ) )
% 5.49/5.82 = ( D2
% 5.49/5.82 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_unique_int
% 5.49/5.82 thf(fact_9447_gcd__non__0__int,axiom,
% 5.49/5.82 ! [Y: int,X: int] :
% 5.49/5.82 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.49/5.82 => ( ( gcd_gcd_int @ X @ Y )
% 5.49/5.82 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % gcd_non_0_int
% 5.49/5.82 thf(fact_9448_quotient__of__denom__pos,axiom,
% 5.49/5.82 ! [R3: rat,P3: int,Q6: int] :
% 5.49/5.82 ( ( ( quotient_of @ R3 )
% 5.49/5.82 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.82 => ( ord_less_int @ zero_zero_int @ Q6 ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_denom_pos
% 5.49/5.82 thf(fact_9449_quotient__of__denom__pos_H,axiom,
% 5.49/5.82 ! [R3: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R3 ) ) ) ).
% 5.49/5.82
% 5.49/5.82 % quotient_of_denom_pos'
% 5.49/5.82 thf(fact_9450_gcd__is__Max__divisors__int,axiom,
% 5.49/5.82 ! [N2: int,M: int] :
% 5.49/5.82 ( ( N2 != zero_zero_int )
% 5.49/5.82 => ( ( gcd_gcd_int @ M @ N2 )
% 5.49/5.82 = ( lattic8263393255366662781ax_int
% 5.49/5.82 @ ( collect_int
% 5.49/5.82 @ ^ [D5: int] :
% 5.49/5.82 ( ( dvd_dvd_int @ D5 @ M )
% 5.49/5.83 & ( dvd_dvd_int @ D5 @ N2 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_is_Max_divisors_int
% 5.49/5.83 thf(fact_9451_rat__uminus__code,axiom,
% 5.49/5.83 ! [P3: rat] :
% 5.49/5.83 ( ( quotient_of @ ( uminus_uminus_rat @ P3 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A5 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_uminus_code
% 5.49/5.83 thf(fact_9452_rat__times__code,axiom,
% 5.49/5.83 ! [P3: rat,Q6: rat] :
% 5.49/5.83 ( ( quotient_of @ ( times_times_rat @ P3 @ Q6 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ B5 ) @ ( times_times_int @ C4 @ D5 ) ) )
% 5.49/5.83 @ ( quotient_of @ Q6 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_times_code
% 5.49/5.83 thf(fact_9453_rat__divide__code,axiom,
% 5.49/5.83 ! [P3: rat,Q6: rat] :
% 5.49/5.83 ( ( quotient_of @ ( divide_divide_rat @ P3 @ Q6 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C4 @ B5 ) ) )
% 5.49/5.83 @ ( quotient_of @ Q6 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_divide_code
% 5.49/5.83 thf(fact_9454_rat__less__code,axiom,
% 5.49/5.83 ( ord_less_rat
% 5.49/5.83 = ( ^ [P7: rat,Q7: rat] :
% 5.49/5.83 ( produc4947309494688390418_int_o
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4947309494688390418_int_o
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( ord_less_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C4 @ B5 ) )
% 5.49/5.83 @ ( quotient_of @ Q7 ) )
% 5.49/5.83 @ ( quotient_of @ P7 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_less_code
% 5.49/5.83 thf(fact_9455_rat__less__eq__code,axiom,
% 5.49/5.83 ( ord_less_eq_rat
% 5.49/5.83 = ( ^ [P7: rat,Q7: rat] :
% 5.49/5.83 ( produc4947309494688390418_int_o
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4947309494688390418_int_o
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( ord_less_eq_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ C4 @ B5 ) )
% 5.49/5.83 @ ( quotient_of @ Q7 ) )
% 5.49/5.83 @ ( quotient_of @ P7 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_less_eq_code
% 5.49/5.83 thf(fact_9456_rat__floor__code,axiom,
% 5.49/5.83 ( archim3151403230148437115or_rat
% 5.49/5.83 = ( ^ [P7: rat] : ( produc8211389475949308722nt_int @ divide_divide_int @ ( quotient_of @ P7 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_floor_code
% 5.49/5.83 thf(fact_9457_rat__abs__code,axiom,
% 5.49/5.83 ! [P3: rat] :
% 5.49/5.83 ( ( quotient_of @ ( abs_abs_rat @ P3 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int] : ( product_Pair_int_int @ ( abs_abs_int @ A5 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_abs_code
% 5.49/5.83 thf(fact_9458_rat__plus__code,axiom,
% 5.49/5.83 ! [P3: rat,Q6: rat] :
% 5.49/5.83 ( ( quotient_of @ ( plus_plus_rat @ P3 @ Q6 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ B5 @ C4 ) ) @ ( times_times_int @ C4 @ D5 ) ) )
% 5.49/5.83 @ ( quotient_of @ Q6 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_plus_code
% 5.49/5.83 thf(fact_9459_rat__minus__code,axiom,
% 5.49/5.83 ! [P3: rat,Q6: rat] :
% 5.49/5.83 ( ( quotient_of @ ( minus_minus_rat @ P3 @ Q6 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int,C4: int] :
% 5.49/5.83 ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [B5: int,D5: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A5 @ D5 ) @ ( times_times_int @ B5 @ C4 ) ) @ ( times_times_int @ C4 @ D5 ) ) )
% 5.49/5.83 @ ( quotient_of @ Q6 ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_minus_code
% 5.49/5.83 thf(fact_9460_rat__sgn__code,axiom,
% 5.49/5.83 ! [P3: rat] :
% 5.49/5.83 ( ( quotient_of @ ( sgn_sgn_rat @ P3 ) )
% 5.49/5.83 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P3 ) ) ) @ one_one_int ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_sgn_code
% 5.49/5.83 thf(fact_9461_quotient__of__int,axiom,
% 5.49/5.83 ! [A: int] :
% 5.49/5.83 ( ( quotient_of @ ( of_int @ A ) )
% 5.49/5.83 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_int
% 5.49/5.83 thf(fact_9462_rat__inverse__code,axiom,
% 5.49/5.83 ! [P3: rat] :
% 5.49/5.83 ( ( quotient_of @ ( inverse_inverse_rat @ P3 ) )
% 5.49/5.83 = ( produc4245557441103728435nt_int
% 5.49/5.83 @ ^ [A5: int,B5: 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 ) @ B5 ) @ ( abs_abs_int @ A5 ) ) )
% 5.49/5.83 @ ( quotient_of @ P3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_inverse_code
% 5.49/5.83 thf(fact_9463_gcd__pos__nat,axiom,
% 5.49/5.83 ! [M: nat,N2: nat] :
% 5.49/5.83 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.49/5.83 = ( ( M != zero_zero_nat )
% 5.49/5.83 | ( N2 != zero_zero_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_pos_nat
% 5.49/5.83 thf(fact_9464_gcd__le1__nat,axiom,
% 5.49/5.83 ! [A: nat,B: nat] :
% 5.49/5.83 ( ( A != zero_zero_nat )
% 5.49/5.83 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_le1_nat
% 5.49/5.83 thf(fact_9465_gcd__le2__nat,axiom,
% 5.49/5.83 ! [B: nat,A: nat] :
% 5.49/5.83 ( ( B != zero_zero_nat )
% 5.49/5.83 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_le2_nat
% 5.49/5.83 thf(fact_9466_gcd__diff1__nat,axiom,
% 5.49/5.83 ! [N2: nat,M: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ N2 @ M )
% 5.49/5.83 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 5.49/5.83 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_diff1_nat
% 5.49/5.83 thf(fact_9467_gcd__diff2__nat,axiom,
% 5.49/5.83 ! [M: nat,N2: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.83 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 5.49/5.83 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_diff2_nat
% 5.49/5.83 thf(fact_9468_Gcd__in,axiom,
% 5.49/5.83 ! [A3: set_nat] :
% 5.49/5.83 ( ! [A4: nat,B4: nat] :
% 5.49/5.83 ( ( member_nat @ A4 @ A3 )
% 5.49/5.83 => ( ( member_nat @ B4 @ A3 )
% 5.49/5.83 => ( member_nat @ ( gcd_gcd_nat @ A4 @ B4 ) @ A3 ) ) )
% 5.49/5.83 => ( ( A3 != bot_bot_set_nat )
% 5.49/5.83 => ( member_nat @ ( gcd_Gcd_nat @ A3 ) @ A3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Gcd_in
% 5.49/5.83 thf(fact_9469_bezout__gcd__nat_H,axiom,
% 5.49/5.83 ! [B: nat,A: nat] :
% 5.49/5.83 ? [X3: nat,Y3: nat] :
% 5.49/5.83 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X3 ) )
% 5.49/5.83 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X3 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.49/5.83 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.49/5.83 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X3 ) )
% 5.49/5.83 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X3 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.49/5.83 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % bezout_gcd_nat'
% 5.49/5.83 thf(fact_9470_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.49/5.83 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.49/5.83 @ ^ [M3: nat,N: nat] :
% 5.49/5.83 ( ( dvd_dvd_nat @ M3 @ N )
% 5.49/5.83 & ( M3 != N ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_nat.semilattice_neutr_order_axioms
% 5.49/5.83 thf(fact_9471_gcd__is__Max__divisors__nat,axiom,
% 5.49/5.83 ! [N2: nat,M: nat] :
% 5.49/5.83 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.83 => ( ( gcd_gcd_nat @ M @ N2 )
% 5.49/5.83 = ( lattic8265883725875713057ax_nat
% 5.49/5.83 @ ( collect_nat
% 5.49/5.83 @ ^ [D5: nat] :
% 5.49/5.83 ( ( dvd_dvd_nat @ D5 @ M )
% 5.49/5.83 & ( dvd_dvd_nat @ D5 @ N2 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_is_Max_divisors_nat
% 5.49/5.83 thf(fact_9472_gcd__nat_Opelims,axiom,
% 5.49/5.83 ! [X: nat,Xa: nat,Y: nat] :
% 5.49/5.83 ( ( ( gcd_gcd_nat @ X @ Xa )
% 5.49/5.83 = Y )
% 5.49/5.83 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) )
% 5.49/5.83 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.49/5.83 => ( Y = X ) )
% 5.49/5.83 & ( ( Xa != zero_zero_nat )
% 5.49/5.83 => ( Y
% 5.49/5.83 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X @ Xa ) ) ) ) )
% 5.49/5.83 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % gcd_nat.pelims
% 5.49/5.83 thf(fact_9473_Frct__code__post_I5_J,axiom,
% 5.49/5.83 ! [K: num] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.49/5.83 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(5)
% 5.49/5.83 thf(fact_9474_Frct__code__post_I2_J,axiom,
% 5.49/5.83 ! [A: int] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.49/5.83 = zero_zero_rat ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(2)
% 5.49/5.83 thf(fact_9475_Frct__code__post_I1_J,axiom,
% 5.49/5.83 ! [A: int] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.49/5.83 = zero_zero_rat ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(1)
% 5.49/5.83 thf(fact_9476_Frct__code__post_I3_J,axiom,
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.49/5.83 = one_one_rat ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(3)
% 5.49/5.83 thf(fact_9477_Frct__code__post_I8_J,axiom,
% 5.49/5.83 ! [A: int,B: int] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.49/5.83 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(8)
% 5.49/5.83 thf(fact_9478_Frct__code__post_I7_J,axiom,
% 5.49/5.83 ! [A: int,B: int] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.49/5.83 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(7)
% 5.49/5.83 thf(fact_9479_Frct__code__post_I4_J,axiom,
% 5.49/5.83 ! [K: num] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.49/5.83 = ( numeral_numeral_rat @ K ) ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(4)
% 5.49/5.83 thf(fact_9480_Frct__code__post_I6_J,axiom,
% 5.49/5.83 ! [K: num,L: num] :
% 5.49/5.83 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L ) ) )
% 5.49/5.83 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Frct_code_post(6)
% 5.49/5.83 thf(fact_9481_rat__floor__lemma,axiom,
% 5.49/5.83 ! [A: int,B: int] :
% 5.49/5.83 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.49/5.83 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % rat_floor_lemma
% 5.49/5.83 thf(fact_9482_less__rat,axiom,
% 5.49/5.83 ! [B: int,D2: int,A: int,C: int] :
% 5.49/5.83 ( ( B != zero_zero_int )
% 5.49/5.83 => ( ( D2 != zero_zero_int )
% 5.49/5.83 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.49/5.83 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_rat
% 5.49/5.83 thf(fact_9483_le__rat,axiom,
% 5.49/5.83 ! [B: int,D2: int,A: int,C: int] :
% 5.49/5.83 ( ( B != zero_zero_int )
% 5.49/5.83 => ( ( D2 != zero_zero_int )
% 5.49/5.83 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D2 ) )
% 5.49/5.83 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D2 ) @ ( times_times_int @ B @ D2 ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D2 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % le_rat
% 5.49/5.83 thf(fact_9484_quotient__of__eq,axiom,
% 5.49/5.83 ! [A: int,B: int,P3: int,Q6: int] :
% 5.49/5.83 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 5.49/5.83 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.83 => ( ( fract @ P3 @ Q6 )
% 5.49/5.83 = ( fract @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_eq
% 5.49/5.83 thf(fact_9485_Rat__induct__pos,axiom,
% 5.49/5.83 ! [P: rat > $o,Q6: rat] :
% 5.49/5.83 ( ! [A4: int,B4: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.49/5.83 => ( P @ ( fract @ A4 @ B4 ) ) )
% 5.49/5.83 => ( P @ Q6 ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rat_induct_pos
% 5.49/5.83 thf(fact_9486_normalize__eq,axiom,
% 5.49/5.83 ! [A: int,B: int,P3: int,Q6: int] :
% 5.49/5.83 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 5.49/5.83 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.83 => ( ( fract @ P3 @ Q6 )
% 5.49/5.83 = ( fract @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % normalize_eq
% 5.49/5.83 thf(fact_9487_quotient__of__Fract,axiom,
% 5.49/5.83 ! [A: int,B: int] :
% 5.49/5.83 ( ( quotient_of @ ( fract @ A @ B ) )
% 5.49/5.83 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_Fract
% 5.49/5.83 thf(fact_9488_Fract__less__zero__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.49/5.83 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract_less_zero_iff
% 5.49/5.83 thf(fact_9489_zero__less__Fract__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.49/5.83 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % zero_less_Fract_iff
% 5.49/5.83 thf(fact_9490_Fract__less__one__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.49/5.83 = ( ord_less_int @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract_less_one_iff
% 5.49/5.83 thf(fact_9491_one__less__Fract__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.49/5.83 = ( ord_less_int @ B @ A ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % one_less_Fract_iff
% 5.49/5.83 thf(fact_9492_zero__le__Fract__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.49/5.83 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % zero_le_Fract_iff
% 5.49/5.83 thf(fact_9493_Fract__le__zero__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.49/5.83 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract_le_zero_iff
% 5.49/5.83 thf(fact_9494_one__le__Fract__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.49/5.83 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % one_le_Fract_iff
% 5.49/5.83 thf(fact_9495_Fract__le__one__iff,axiom,
% 5.49/5.83 ! [B: int,A: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B )
% 5.49/5.83 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.49/5.83 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract_le_one_iff
% 5.49/5.83 thf(fact_9496_positive__rat,axiom,
% 5.49/5.83 ! [A: int,B: int] :
% 5.49/5.83 ( ( positive @ ( fract @ A @ B ) )
% 5.49/5.83 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % positive_rat
% 5.49/5.83 thf(fact_9497_less__rat__def,axiom,
% 5.49/5.83 ( ord_less_rat
% 5.49/5.83 = ( ^ [X4: rat,Y4: rat] : ( positive @ ( minus_minus_rat @ Y4 @ X4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_rat_def
% 5.49/5.83 thf(fact_9498_positive__def,axiom,
% 5.49/5.83 ( positive
% 5.49/5.83 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % positive_def
% 5.49/5.83 thf(fact_9499_positive_Orep__eq,axiom,
% 5.49/5.83 ( positive
% 5.49/5.83 = ( ^ [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 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % positive.rep_eq
% 5.49/5.83 thf(fact_9500_plus__rat__def,axiom,
% 5.49/5.83 ( plus_plus_rat
% 5.49/5.83 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.49/5.83 @ ^ [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 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % plus_rat_def
% 5.49/5.83 thf(fact_9501_inverse__rat__def,axiom,
% 5.49/5.83 ( inverse_inverse_rat
% 5.49/5.83 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.49/5.83 @ ^ [X4: product_prod_int_int] :
% 5.49/5.83 ( if_Pro3027730157355071871nt_int
% 5.49/5.83 @ ( ( product_fst_int_int @ X4 )
% 5.49/5.83 = zero_zero_int )
% 5.49/5.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % inverse_rat_def
% 5.49/5.83 thf(fact_9502_one__rat__def,axiom,
% 5.49/5.83 ( one_one_rat
% 5.49/5.83 = ( abs_Rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % one_rat_def
% 5.49/5.83 thf(fact_9503_Fract_Oabs__eq,axiom,
% 5.49/5.83 ( fract
% 5.49/5.83 = ( ^ [Xa4: int,X4: int] : ( abs_Rat @ ( if_Pro3027730157355071871nt_int @ ( X4 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ Xa4 @ X4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract.abs_eq
% 5.49/5.83 thf(fact_9504_zero__rat__def,axiom,
% 5.49/5.83 ( zero_zero_rat
% 5.49/5.83 = ( abs_Rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % zero_rat_def
% 5.49/5.83 thf(fact_9505_Fract__def,axiom,
% 5.49/5.83 ( fract
% 5.49/5.83 = ( map_fu7831380289885515383nt_rat @ id_int @ ( map_fu3424225382358772769nt_rat @ id_int @ abs_Rat )
% 5.49/5.83 @ ^ [A5: int,B5: int] : ( if_Pro3027730157355071871nt_int @ ( B5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B5 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract_def
% 5.49/5.83 thf(fact_9506_uminus__rat__def,axiom,
% 5.49/5.83 ( uminus_uminus_rat
% 5.49/5.83 = ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_rat_def
% 5.49/5.83 thf(fact_9507_times__rat__def,axiom,
% 5.49/5.83 ( times_times_rat
% 5.49/5.83 = ( map_fu4333342158222067775at_rat @ rep_Rat @ ( map_fu5673905371560938248nt_rat @ rep_Rat @ abs_Rat )
% 5.49/5.83 @ ^ [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 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % times_rat_def
% 5.49/5.83 thf(fact_9508_plus__rat_Oabs__eq,axiom,
% 5.49/5.83 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 5.49/5.83 ( ( ratrel @ Xa @ Xa )
% 5.49/5.83 => ( ( ratrel @ X @ X )
% 5.49/5.83 => ( ( plus_plus_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 5.49/5.83 = ( abs_Rat @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % plus_rat.abs_eq
% 5.49/5.83 thf(fact_9509_one__rat_Orsp,axiom,
% 5.49/5.83 ratrel @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ ( product_Pair_int_int @ one_one_int @ one_one_int ) ).
% 5.49/5.83
% 5.49/5.83 % one_rat.rsp
% 5.49/5.83 thf(fact_9510_zero__rat_Orsp,axiom,
% 5.49/5.83 ratrel @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ).
% 5.49/5.83
% 5.49/5.83 % zero_rat.rsp
% 5.49/5.83 thf(fact_9511_ratrel__def,axiom,
% 5.49/5.83 ( ratrel
% 5.49/5.83 = ( ^ [X4: product_prod_int_int,Y4: product_prod_int_int] :
% 5.49/5.83 ( ( ( product_snd_int_int @ X4 )
% 5.49/5.83 != zero_zero_int )
% 5.49/5.83 & ( ( product_snd_int_int @ Y4 )
% 5.49/5.83 != zero_zero_int )
% 5.49/5.83 & ( ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ Y4 ) )
% 5.49/5.83 = ( times_times_int @ ( product_fst_int_int @ Y4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % ratrel_def
% 5.49/5.83 thf(fact_9512_uminus__rat_Oabs__eq,axiom,
% 5.49/5.83 ! [X: product_prod_int_int] :
% 5.49/5.83 ( ( ratrel @ X @ X )
% 5.49/5.83 => ( ( uminus_uminus_rat @ ( abs_Rat @ X ) )
% 5.49/5.83 = ( abs_Rat @ ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X ) ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_rat.abs_eq
% 5.49/5.83 thf(fact_9513_times__rat_Oabs__eq,axiom,
% 5.49/5.83 ! [Xa: product_prod_int_int,X: product_prod_int_int] :
% 5.49/5.83 ( ( ratrel @ Xa @ Xa )
% 5.49/5.83 => ( ( ratrel @ X @ X )
% 5.49/5.83 => ( ( times_times_rat @ ( abs_Rat @ Xa ) @ ( abs_Rat @ X ) )
% 5.49/5.83 = ( abs_Rat @ ( product_Pair_int_int @ ( times_times_int @ ( product_fst_int_int @ Xa ) @ ( product_fst_int_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ Xa ) @ ( product_snd_int_int @ X ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % times_rat.abs_eq
% 5.49/5.83 thf(fact_9514_positive_Oabs__eq,axiom,
% 5.49/5.83 ! [X: product_prod_int_int] :
% 5.49/5.83 ( ( ratrel @ X @ X )
% 5.49/5.83 => ( ( positive @ ( abs_Rat @ X ) )
% 5.49/5.83 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % positive.abs_eq
% 5.49/5.83 thf(fact_9515_inverse__rat_Oabs__eq,axiom,
% 5.49/5.83 ! [X: product_prod_int_int] :
% 5.49/5.83 ( ( ratrel @ X @ X )
% 5.49/5.83 => ( ( inverse_inverse_rat @ ( abs_Rat @ X ) )
% 5.49/5.83 = ( abs_Rat
% 5.49/5.83 @ ( if_Pro3027730157355071871nt_int
% 5.49/5.83 @ ( ( product_fst_int_int @ X )
% 5.49/5.83 = zero_zero_int )
% 5.49/5.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X ) @ ( product_fst_int_int @ X ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % inverse_rat.abs_eq
% 5.49/5.83 thf(fact_9516_cr__rat__def,axiom,
% 5.49/5.83 ( cr_rat
% 5.49/5.83 = ( ^ [X4: product_prod_int_int,Y4: rat] :
% 5.49/5.83 ( ( ratrel @ X4 @ X4 )
% 5.49/5.83 & ( ( abs_Rat @ X4 )
% 5.49/5.83 = Y4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % cr_rat_def
% 5.49/5.83 thf(fact_9517_Code__Numeral_Odup__def,axiom,
% 5.49/5.83 ( code_dup
% 5.49/5.83 = ( map_fu2599414010547811884nteger @ code_int_of_integer @ code_integer_of_int
% 5.49/5.83 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Code_Numeral.dup_def
% 5.49/5.83 thf(fact_9518_quotient__of__def,axiom,
% 5.49/5.83 ( quotient_of
% 5.49/5.83 = ( ^ [X4: rat] :
% 5.49/5.83 ( the_Pr4378521158711661632nt_int
% 5.49/5.83 @ ^ [Pair: product_prod_int_int] :
% 5.49/5.83 ( ( X4
% 5.49/5.83 = ( fract @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) )
% 5.49/5.83 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Pair ) )
% 5.49/5.83 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Pair ) @ ( product_snd_int_int @ Pair ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_def
% 5.49/5.83 thf(fact_9519_normalize__stable,axiom,
% 5.49/5.83 ! [Q6: int,P3: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ Q6 )
% 5.49/5.83 => ( ( algebr932160517623751201me_int @ P3 @ Q6 )
% 5.49/5.83 => ( ( normalize @ ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.83 = ( product_Pair_int_int @ P3 @ Q6 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % normalize_stable
% 5.49/5.83 thf(fact_9520_quotient__of__coprime,axiom,
% 5.49/5.83 ! [R3: rat,P3: int,Q6: int] :
% 5.49/5.83 ( ( ( quotient_of @ R3 )
% 5.49/5.83 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.83 => ( algebr932160517623751201me_int @ P3 @ Q6 ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_coprime
% 5.49/5.83 thf(fact_9521_normalize__coprime,axiom,
% 5.49/5.83 ! [R3: product_prod_int_int,P3: int,Q6: int] :
% 5.49/5.83 ( ( ( normalize @ R3 )
% 5.49/5.83 = ( product_Pair_int_int @ P3 @ Q6 ) )
% 5.49/5.83 => ( algebr932160517623751201me_int @ P3 @ Q6 ) ) ).
% 5.49/5.83
% 5.49/5.83 % normalize_coprime
% 5.49/5.83 thf(fact_9522_Rat__induct,axiom,
% 5.49/5.83 ! [P: rat > $o,Q6: rat] :
% 5.49/5.83 ( ! [A4: int,B4: int] :
% 5.49/5.83 ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.49/5.83 => ( ( algebr932160517623751201me_int @ A4 @ B4 )
% 5.49/5.83 => ( P @ ( fract @ A4 @ B4 ) ) ) )
% 5.49/5.83 => ( P @ Q6 ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rat_induct
% 5.49/5.83 thf(fact_9523_Rat__cases,axiom,
% 5.49/5.83 ! [Q6: rat] :
% 5.49/5.83 ~ ! [A4: int,B4: int] :
% 5.49/5.83 ( ( Q6
% 5.49/5.83 = ( fract @ A4 @ B4 ) )
% 5.49/5.83 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.49/5.83 => ~ ( algebr932160517623751201me_int @ A4 @ B4 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rat_cases
% 5.49/5.83 thf(fact_9524_Rat__cases__nonzero,axiom,
% 5.49/5.83 ! [Q6: rat] :
% 5.49/5.83 ( ! [A4: int,B4: int] :
% 5.49/5.83 ( ( Q6
% 5.49/5.83 = ( fract @ A4 @ B4 ) )
% 5.49/5.83 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.49/5.83 => ( ( A4 != zero_zero_int )
% 5.49/5.83 => ~ ( algebr932160517623751201me_int @ A4 @ B4 ) ) ) )
% 5.49/5.83 => ( Q6 = zero_zero_rat ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rat_cases_nonzero
% 5.49/5.83 thf(fact_9525_quotient__of__unique,axiom,
% 5.49/5.83 ! [R3: rat] :
% 5.49/5.83 ? [X3: product_prod_int_int] :
% 5.49/5.83 ( ( R3
% 5.49/5.83 = ( fract @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) ) )
% 5.49/5.83 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ X3 ) )
% 5.49/5.83 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ X3 ) @ ( product_snd_int_int @ X3 ) )
% 5.49/5.83 & ! [Y6: product_prod_int_int] :
% 5.49/5.83 ( ( ( R3
% 5.49/5.83 = ( fract @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.49/5.83 & ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ Y6 ) )
% 5.49/5.83 & ( algebr932160517623751201me_int @ ( product_fst_int_int @ Y6 ) @ ( product_snd_int_int @ Y6 ) ) )
% 5.49/5.83 => ( Y6 = X3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % quotient_of_unique
% 5.49/5.83 thf(fact_9526_coprime__diff__one__left__nat,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.83 => ( algebr934650988132801477me_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ N2 ) ) ).
% 5.49/5.83
% 5.49/5.83 % coprime_diff_one_left_nat
% 5.49/5.83 thf(fact_9527_coprime__diff__one__right__nat,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.49/5.83 => ( algebr934650988132801477me_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % coprime_diff_one_right_nat
% 5.49/5.83 thf(fact_9528_positive_Orsp,axiom,
% 5.49/5.83 ( bNF_re8699439704749558557nt_o_o @ ratrel
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % positive.rsp
% 5.49/5.83 thf(fact_9529_sub_Orsp,axiom,
% 5.49/5.83 ( bNF_re8402795839162346335um_int
% 5.49/5.83 @ ^ [Y5: num,Z3: num] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re1822329894187522285nt_int
% 5.49/5.83 @ ^ [Y5: num,Z3: num] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ^ [M3: num,N: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) )
% 5.49/5.83 @ ^ [M3: num,N: num] : ( minus_minus_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % sub.rsp
% 5.49/5.83 thf(fact_9530_Fract_Orsp,axiom,
% 5.49/5.83 ( bNF_re157797125943740599nt_int
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re6250860962936578807nt_int
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ratrel )
% 5.49/5.83 @ ^ [A5: int,B5: int] : ( if_Pro3027730157355071871nt_int @ ( B5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B5 ) )
% 5.49/5.83 @ ^ [A5: int,B5: int] : ( if_Pro3027730157355071871nt_int @ ( B5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B5 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Fract.rsp
% 5.49/5.83 thf(fact_9531_dup_Orsp,axiom,
% 5.49/5.83 ( bNF_re4712519889275205905nt_int
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 )
% 5.49/5.83 @ ^ [K3: int] : ( plus_plus_int @ K3 @ K3 ) ) ).
% 5.49/5.83
% 5.49/5.83 % dup.rsp
% 5.49/5.83 thf(fact_9532_less__eq__integer_Orsp,axiom,
% 5.49/5.83 ( bNF_re3403563459893282935_int_o
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re5089333283451836215nt_o_o
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ord_less_eq_int
% 5.49/5.83 @ ord_less_eq_int ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_integer.rsp
% 5.49/5.83 thf(fact_9533_less__eq__natural_Orsp,axiom,
% 5.49/5.83 ( bNF_re578469030762574527_nat_o
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re4705727531993890431at_o_o
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ord_less_eq_nat
% 5.49/5.83 @ ord_less_eq_nat ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_natural.rsp
% 5.49/5.83 thf(fact_9534_less__natural_Orsp,axiom,
% 5.49/5.83 ( bNF_re578469030762574527_nat_o
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re4705727531993890431at_o_o
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ord_less_nat
% 5.49/5.83 @ ord_less_nat ) ).
% 5.49/5.83
% 5.49/5.83 % less_natural.rsp
% 5.49/5.83 thf(fact_9535_less__integer_Orsp,axiom,
% 5.49/5.83 ( bNF_re3403563459893282935_int_o
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re5089333283451836215nt_o_o
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ord_less_int
% 5.49/5.83 @ ord_less_int ) ).
% 5.49/5.83
% 5.49/5.83 % less_integer.rsp
% 5.49/5.83 thf(fact_9536_times__rat_Orsp,axiom,
% 5.49/5.83 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.49/5.83 @ ^ [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 ) ) )
% 5.49/5.83 @ ^ [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 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % times_rat.rsp
% 5.49/5.83 thf(fact_9537_plus__rat_Orsp,axiom,
% 5.49/5.83 ( bNF_re5228765855967844073nt_int @ ratrel @ ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel )
% 5.49/5.83 @ ^ [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 ) ) )
% 5.49/5.83 @ ^ [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 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % plus_rat.rsp
% 5.49/5.83 thf(fact_9538_uminus__rat_Orsp,axiom,
% 5.49/5.83 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) )
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_rat.rsp
% 5.49/5.83 thf(fact_9539_inverse__rat_Orsp,axiom,
% 5.49/5.83 ( bNF_re7145576690424134365nt_int @ ratrel @ ratrel
% 5.49/5.83 @ ^ [X4: product_prod_int_int] :
% 5.49/5.83 ( if_Pro3027730157355071871nt_int
% 5.49/5.83 @ ( ( product_fst_int_int @ X4 )
% 5.49/5.83 = zero_zero_int )
% 5.49/5.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) )
% 5.49/5.83 @ ^ [X4: product_prod_int_int] :
% 5.49/5.83 ( if_Pro3027730157355071871nt_int
% 5.49/5.83 @ ( ( product_fst_int_int @ X4 )
% 5.49/5.83 = zero_zero_int )
% 5.49/5.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % inverse_rat.rsp
% 5.49/5.83 thf(fact_9540_plus__rat_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.49/5.83 @ ^ [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 ) ) )
% 5.49/5.83 @ plus_plus_rat ) ).
% 5.49/5.83
% 5.49/5.83 % plus_rat.transfer
% 5.49/5.83 thf(fact_9541_one__rat_Otransfer,axiom,
% 5.49/5.83 pcr_rat @ ( product_Pair_int_int @ one_one_int @ one_one_int ) @ one_one_rat ).
% 5.49/5.83
% 5.49/5.83 % one_rat.transfer
% 5.49/5.83 thf(fact_9542_zero__rat_Otransfer,axiom,
% 5.49/5.83 pcr_rat @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ zero_zero_rat ).
% 5.49/5.83
% 5.49/5.83 % zero_rat.transfer
% 5.49/5.83 thf(fact_9543_Fract_Otransfer,axiom,
% 5.49/5.83 ( bNF_re3461391660133120880nt_rat
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ ( bNF_re2214769303045360666nt_rat
% 5.49/5.83 @ ^ [Y5: int,Z3: int] : ( Y5 = Z3 )
% 5.49/5.83 @ pcr_rat )
% 5.49/5.83 @ ^ [A5: int,B5: int] : ( if_Pro3027730157355071871nt_int @ ( B5 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ A5 @ B5 ) )
% 5.49/5.83 @ fract ) ).
% 5.49/5.83
% 5.49/5.83 % Fract.transfer
% 5.49/5.83 thf(fact_9544_uminus__rat_Otransfer,axiom,
% 5.49/5.83 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( product_Pair_int_int @ ( uminus_uminus_int @ ( product_fst_int_int @ X4 ) ) @ ( product_snd_int_int @ X4 ) )
% 5.49/5.83 @ uminus_uminus_rat ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_rat.transfer
% 5.49/5.83 thf(fact_9545_times__rat_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7627151682743391978at_rat @ pcr_rat @ ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat )
% 5.49/5.83 @ ^ [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 ) ) )
% 5.49/5.83 @ times_times_rat ) ).
% 5.49/5.83
% 5.49/5.83 % times_rat.transfer
% 5.49/5.83 thf(fact_9546_positive_Otransfer,axiom,
% 5.49/5.83 ( bNF_re1494630372529172596at_o_o @ pcr_rat
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 )
% 5.49/5.83 @ ^ [X4: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X4 ) @ ( product_snd_int_int @ X4 ) ) )
% 5.49/5.83 @ positive ) ).
% 5.49/5.83
% 5.49/5.83 % positive.transfer
% 5.49/5.83 thf(fact_9547_inverse__rat_Otransfer,axiom,
% 5.49/5.83 ( bNF_re8279943556446156061nt_rat @ pcr_rat @ pcr_rat
% 5.49/5.83 @ ^ [X4: product_prod_int_int] :
% 5.49/5.83 ( if_Pro3027730157355071871nt_int
% 5.49/5.83 @ ( ( product_fst_int_int @ X4 )
% 5.49/5.83 = zero_zero_int )
% 5.49/5.83 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.49/5.83 @ ( product_Pair_int_int @ ( product_snd_int_int @ X4 ) @ ( product_fst_int_int @ X4 ) ) )
% 5.49/5.83 @ inverse_inverse_rat ) ).
% 5.49/5.83
% 5.49/5.83 % inverse_rat.transfer
% 5.49/5.83 thf(fact_9548_times__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 5.49/5.83 @ times_times_int ) ).
% 5.49/5.83
% 5.49/5.83 % times_int.transfer
% 5.49/5.83 thf(fact_9549_zero__int_Otransfer,axiom,
% 5.49/5.83 pcr_int @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ zero_zero_int ).
% 5.49/5.83
% 5.49/5.83 % zero_int.transfer
% 5.49/5.83 thf(fact_9550_int__transfer,axiom,
% 5.49/5.83 ( bNF_re6830278522597306478at_int
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ pcr_int
% 5.49/5.83 @ ^ [N: nat] : ( product_Pair_nat_nat @ N @ zero_zero_nat )
% 5.49/5.83 @ semiri1314217659103216013at_int ) ).
% 5.49/5.83
% 5.49/5.83 % int_transfer
% 5.49/5.83 thf(fact_9551_uminus__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int
% 5.49/5.83 @ ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 5.49/5.83 @ uminus_uminus_int ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_int.transfer
% 5.49/5.83 thf(fact_9552_nat_Otransfer,axiom,
% 5.49/5.83 ( bNF_re4555766996558763186at_nat @ pcr_int
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.49/5.83 @ nat2 ) ).
% 5.49/5.83
% 5.49/5.83 % nat.transfer
% 5.49/5.83 thf(fact_9553_one__int_Otransfer,axiom,
% 5.49/5.83 pcr_int @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ one_one_int ).
% 5.49/5.83
% 5.49/5.83 % one_int.transfer
% 5.49/5.83 thf(fact_9554_less__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.49/5.83 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.49/5.83 @ ord_less_int ) ).
% 5.49/5.83
% 5.49/5.83 % less_int.transfer
% 5.49/5.83 thf(fact_9555_less__eq__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re717283939379294677_int_o @ pcr_int
% 5.49/5.83 @ ( bNF_re6644619430987730960nt_o_o @ pcr_int
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.49/5.83 @ ord_less_eq_int ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_int.transfer
% 5.49/5.83 thf(fact_9556_plus__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) )
% 5.49/5.83 @ plus_plus_int ) ).
% 5.49/5.83
% 5.49/5.83 % plus_int.transfer
% 5.49/5.83 thf(fact_9557_minus__int_Otransfer,axiom,
% 5.49/5.83 ( bNF_re7408651293131936558nt_int @ pcr_int @ ( bNF_re7400052026677387805at_int @ pcr_int @ pcr_int )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 5.49/5.83 @ minus_minus_int ) ).
% 5.49/5.83
% 5.49/5.83 % minus_int.transfer
% 5.49/5.83 thf(fact_9558_Sup__int__def,axiom,
% 5.49/5.83 ( complete_Sup_Sup_int
% 5.49/5.83 = ( ^ [X11: set_int] :
% 5.49/5.83 ( the_int
% 5.49/5.83 @ ^ [X4: int] :
% 5.49/5.83 ( ( member_int @ X4 @ X11 )
% 5.49/5.83 & ! [Y4: int] :
% 5.49/5.83 ( ( member_int @ Y4 @ X11 )
% 5.49/5.83 => ( ord_less_eq_int @ Y4 @ X4 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Sup_int_def
% 5.49/5.83 thf(fact_9559_times__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X4 @ U2 ) @ ( times_times_nat @ Y4 @ V2 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X4 @ V2 ) @ ( times_times_nat @ Y4 @ U2 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % times_int.rsp
% 5.49/5.83 thf(fact_9560_intrel__iff,axiom,
% 5.49/5.83 ! [X: nat,Y: nat,U: nat,V: nat] :
% 5.49/5.83 ( ( intrel @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ U @ V ) )
% 5.49/5.83 = ( ( plus_plus_nat @ X @ V )
% 5.49/5.83 = ( plus_plus_nat @ U @ Y ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % intrel_iff
% 5.49/5.83 thf(fact_9561_zero__int_Orsp,axiom,
% 5.49/5.83 intrel @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.49/5.83
% 5.49/5.83 % zero_int.rsp
% 5.49/5.83 thf(fact_9562_uminus__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re2241393799969408733at_nat @ intrel @ intrel
% 5.49/5.83 @ ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) )
% 5.49/5.83 @ ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] : ( product_Pair_nat_nat @ Y4 @ X4 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_int.rsp
% 5.49/5.83 thf(fact_9563_nat_Orsp,axiom,
% 5.49/5.83 ( bNF_re8246922863344978751at_nat @ intrel
% 5.49/5.83 @ ^ [Y5: nat,Z3: nat] : ( Y5 = Z3 )
% 5.49/5.83 @ ( produc6842872674320459806at_nat @ minus_minus_nat )
% 5.49/5.83 @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % nat.rsp
% 5.49/5.83 thf(fact_9564_one__int_Orsp,axiom,
% 5.49/5.83 intrel @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.49/5.83
% 5.49/5.83 % one_int.rsp
% 5.49/5.83 thf(fact_9565_intrel__def,axiom,
% 5.49/5.83 ( intrel
% 5.49/5.83 = ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] :
% 5.49/5.83 ( ( plus_plus_nat @ X4 @ V2 )
% 5.49/5.83 = ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % intrel_def
% 5.49/5.83 thf(fact_9566_less__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.49/5.83 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_int.rsp
% 5.49/5.83 thf(fact_9567_less__eq__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re4202695980764964119_nat_o @ intrel
% 5.49/5.83 @ ( bNF_re3666534408544137501at_o_o @ intrel
% 5.49/5.83 @ ^ [Y5: $o,Z3: $o] : ( Y5 = Z3 ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) )
% 5.49/5.83 @ ( produc8739625826339149834_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ U2 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_int.rsp
% 5.49/5.83 thf(fact_9568_minus__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ V2 ) @ ( plus_plus_nat @ Y4 @ U2 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % minus_int.rsp
% 5.49/5.83 thf(fact_9569_plus__int_Orsp,axiom,
% 5.49/5.83 ( bNF_re3099431351363272937at_nat @ intrel @ ( bNF_re2241393799969408733at_nat @ intrel @ intrel )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) )
% 5.49/5.83 @ ( produc27273713700761075at_nat
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( produc2626176000494625587at_nat
% 5.49/5.83 @ ^ [U2: nat,V2: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X4 @ U2 ) @ ( plus_plus_nat @ Y4 @ V2 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % plus_int.rsp
% 5.49/5.83 thf(fact_9570_GreatestI__nat,axiom,
% 5.49/5.83 ! [P: nat > $o,K: nat,B: nat] :
% 5.49/5.83 ( ( P @ K )
% 5.49/5.83 => ( ! [Y3: nat] :
% 5.49/5.83 ( ( P @ Y3 )
% 5.49/5.83 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.49/5.83 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % GreatestI_nat
% 5.49/5.83 thf(fact_9571_Greatest__le__nat,axiom,
% 5.49/5.83 ! [P: nat > $o,K: nat,B: nat] :
% 5.49/5.83 ( ( P @ K )
% 5.49/5.83 => ( ! [Y3: nat] :
% 5.49/5.83 ( ( P @ Y3 )
% 5.49/5.83 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.49/5.83 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Greatest_le_nat
% 5.49/5.83 thf(fact_9572_GreatestI__ex__nat,axiom,
% 5.49/5.83 ! [P: nat > $o,B: nat] :
% 5.49/5.83 ( ? [X_12: nat] : ( P @ X_12 )
% 5.49/5.83 => ( ! [Y3: nat] :
% 5.49/5.83 ( ( P @ Y3 )
% 5.49/5.83 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.49/5.83 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % GreatestI_ex_nat
% 5.49/5.83 thf(fact_9573_Field__natLeq__on,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( ( field_nat
% 5.49/5.83 @ ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 5.49/5.83 = ( collect_nat
% 5.49/5.83 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Field_natLeq_on
% 5.49/5.83 thf(fact_9574_wf__less,axiom,
% 5.49/5.83 wf_nat @ ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % wf_less
% 5.49/5.83 thf(fact_9575_less__than__iff,axiom,
% 5.49/5.83 ! [X: nat,Y: nat] :
% 5.49/5.83 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ less_than )
% 5.49/5.83 = ( ord_less_nat @ X @ Y ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_than_iff
% 5.49/5.83 thf(fact_9576_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.49/5.83 ! [N2: nat,J: nat,I2: nat] :
% 5.49/5.83 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.49/5.83 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 5.49/5.83 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % nth_sorted_list_of_set_greaterThanLessThan
% 5.49/5.83 thf(fact_9577_le__enumerate,axiom,
% 5.49/5.83 ! [S: set_nat,N2: nat] :
% 5.49/5.83 ( ~ ( finite_finite_nat @ S )
% 5.49/5.83 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % le_enumerate
% 5.49/5.83 thf(fact_9578_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.49/5.83 ! [I2: nat,J: nat] :
% 5.49/5.83 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.49/5.83 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.49/5.83 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % sorted_list_of_set_greaterThanLessThan
% 5.49/5.83 thf(fact_9579_finite__le__enumerate,axiom,
% 5.49/5.83 ! [S: set_nat,N2: nat] :
% 5.49/5.83 ( ( finite_finite_nat @ S )
% 5.49/5.83 => ( ( ord_less_nat @ N2 @ ( finite_card_nat @ S ) )
% 5.49/5.83 => ( ord_less_eq_nat @ N2 @ ( infini8530281810654367211te_nat @ S @ N2 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % finite_le_enumerate
% 5.49/5.83 thf(fact_9580_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.49/5.83 ! [N2: nat,J: nat,I2: nat] :
% 5.49/5.83 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 5.49/5.83 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 5.49/5.83 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % nth_sorted_list_of_set_greaterThanAtMost
% 5.49/5.83 thf(fact_9581_Least__eq__0,axiom,
% 5.49/5.83 ! [P: nat > $o] :
% 5.49/5.83 ( ( P @ zero_zero_nat )
% 5.49/5.83 => ( ( ord_Least_nat @ P )
% 5.49/5.83 = zero_zero_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % Least_eq_0
% 5.49/5.83 thf(fact_9582_finite__greaterThanLessThan__integer,axiom,
% 5.49/5.83 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 5.49/5.83
% 5.49/5.83 % finite_greaterThanLessThan_integer
% 5.49/5.83 thf(fact_9583_Inf__nat__def,axiom,
% 5.49/5.83 ( complete_Inf_Inf_nat
% 5.49/5.83 = ( ^ [X11: set_nat] :
% 5.49/5.83 ( ord_Least_nat
% 5.49/5.83 @ ^ [N: nat] : ( member_nat @ N @ X11 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Inf_nat_def
% 5.49/5.83 thf(fact_9584_Least__Suc2,axiom,
% 5.49/5.83 ! [P: nat > $o,N2: nat,Q: nat > $o,M: nat] :
% 5.49/5.83 ( ( P @ N2 )
% 5.49/5.83 => ( ( Q @ M )
% 5.49/5.83 => ( ~ ( P @ zero_zero_nat )
% 5.49/5.83 => ( ! [K2: nat] :
% 5.49/5.83 ( ( P @ ( suc @ K2 ) )
% 5.49/5.83 = ( Q @ K2 ) )
% 5.49/5.83 => ( ( ord_Least_nat @ P )
% 5.49/5.83 = ( suc @ ( ord_Least_nat @ Q ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Least_Suc2
% 5.49/5.83 thf(fact_9585_Least__Suc,axiom,
% 5.49/5.83 ! [P: nat > $o,N2: nat] :
% 5.49/5.83 ( ( P @ N2 )
% 5.49/5.83 => ( ~ ( P @ zero_zero_nat )
% 5.49/5.83 => ( ( ord_Least_nat @ P )
% 5.49/5.83 = ( suc
% 5.49/5.83 @ ( ord_Least_nat
% 5.49/5.83 @ ^ [M3: nat] : ( P @ ( suc @ M3 ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Least_Suc
% 5.49/5.83 thf(fact_9586_atLeastPlusOneLessThan__greaterThanLessThan__integer,axiom,
% 5.49/5.83 ! [L: code_integer,U: code_integer] :
% 5.49/5.83 ( ( set_or8404916559141939852nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 5.49/5.83 = ( set_or4266950643985792945nteger @ L @ U ) ) ).
% 5.49/5.83
% 5.49/5.83 % atLeastPlusOneLessThan_greaterThanLessThan_integer
% 5.49/5.83 thf(fact_9587_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.49/5.83 ! [I2: nat,J: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.49/5.83 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.49/5.83 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % sorted_list_of_set_greaterThanAtMost
% 5.49/5.83 thf(fact_9588_finite__greaterThanAtMost__integer,axiom,
% 5.49/5.83 ! [L: code_integer,U: code_integer] : ( finite6017078050557962740nteger @ ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 5.49/5.83
% 5.49/5.83 % finite_greaterThanAtMost_integer
% 5.49/5.83 thf(fact_9589_atLeastPlusOneAtMost__greaterThanAtMost__integer,axiom,
% 5.49/5.83 ! [L: code_integer,U: code_integer] :
% 5.49/5.83 ( ( set_or189985376899183464nteger @ ( plus_p5714425477246183910nteger @ L @ one_one_Code_integer ) @ U )
% 5.49/5.83 = ( set_or2715278749043346189nteger @ L @ U ) ) ).
% 5.49/5.83
% 5.49/5.83 % atLeastPlusOneAtMost_greaterThanAtMost_integer
% 5.49/5.83 thf(fact_9590_atLeast__Suc,axiom,
% 5.49/5.83 ! [K: nat] :
% 5.49/5.83 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.49/5.83 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % atLeast_Suc
% 5.49/5.83 thf(fact_9591_UN__atLeast__UNIV,axiom,
% 5.49/5.83 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.49/5.83 = top_top_set_nat ) ).
% 5.49/5.83
% 5.49/5.83 % UN_atLeast_UNIV
% 5.49/5.83 thf(fact_9592_filterlim__atMost__at__top,axiom,
% 5.49/5.83 filter3212408913953519116et_nat @ set_ord_atMost_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 5.49/5.83
% 5.49/5.83 % filterlim_atMost_at_top
% 5.49/5.83 thf(fact_9593_filterlim__lessThan__at__top,axiom,
% 5.49/5.83 filter3212408913953519116et_nat @ set_ord_lessThan_nat @ ( finite3254316476582989077op_nat @ top_top_set_nat ) @ at_top_nat ).
% 5.49/5.83
% 5.49/5.83 % filterlim_lessThan_at_top
% 5.49/5.83 thf(fact_9594_filterlim__Suc,axiom,
% 5.49/5.83 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.49/5.83
% 5.49/5.83 % filterlim_Suc
% 5.49/5.83 thf(fact_9595_trivial__limit__sequentially,axiom,
% 5.49/5.83 at_top_nat != bot_bot_filter_nat ).
% 5.49/5.83
% 5.49/5.83 % trivial_limit_sequentially
% 5.49/5.83 thf(fact_9596_bij__betw__Suc,axiom,
% 5.49/5.83 ! [M6: set_nat,N7: set_nat] :
% 5.49/5.83 ( ( bij_betw_nat_nat @ suc @ M6 @ N7 )
% 5.49/5.83 = ( ( image_nat_nat @ suc @ M6 )
% 5.49/5.83 = N7 ) ) ).
% 5.49/5.83
% 5.49/5.83 % bij_betw_Suc
% 5.49/5.83 thf(fact_9597_Rep__unit,axiom,
% 5.49/5.83 ! [X: product_unit] : ( member_o @ ( product_Rep_unit @ X ) @ ( insert_o @ $true @ bot_bot_set_o ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rep_unit
% 5.49/5.83 thf(fact_9598_Rep__unit__inject,axiom,
% 5.49/5.83 ! [X: product_unit,Y: product_unit] :
% 5.49/5.83 ( ( ( product_Rep_unit @ X )
% 5.49/5.83 = ( product_Rep_unit @ Y ) )
% 5.49/5.83 = ( X = Y ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rep_unit_inject
% 5.49/5.83 thf(fact_9599_Rep__unit__induct,axiom,
% 5.49/5.83 ! [Y: $o,P: $o > $o] :
% 5.49/5.83 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ( ! [X3: product_unit] : ( P @ ( product_Rep_unit @ X3 ) )
% 5.49/5.83 => ( P @ Y ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rep_unit_induct
% 5.49/5.83 thf(fact_9600_Rep__unit__cases,axiom,
% 5.49/5.83 ! [Y: $o] :
% 5.49/5.83 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ~ ! [X3: product_unit] :
% 5.49/5.83 ( Y
% 5.49/5.83 = ( ~ ( product_Rep_unit @ X3 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Rep_unit_cases
% 5.49/5.83 thf(fact_9601_type__definition__unit,axiom,
% 5.49/5.83 type_d6188575255521822967unit_o @ product_Rep_unit @ product_Abs_unit @ ( insert_o @ $true @ bot_bot_set_o ) ).
% 5.49/5.83
% 5.49/5.83 % type_definition_unit
% 5.49/5.83 thf(fact_9602_Abs__unit__inverse,axiom,
% 5.49/5.83 ! [Y: $o] :
% 5.49/5.83 ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ( ( product_Rep_unit @ ( product_Abs_unit @ Y ) )
% 5.49/5.83 = Y ) ) ).
% 5.49/5.83
% 5.49/5.83 % Abs_unit_inverse
% 5.49/5.83 thf(fact_9603_Rep__unit__inverse,axiom,
% 5.49/5.83 ! [X: product_unit] :
% 5.49/5.83 ( ( product_Abs_unit @ ( product_Rep_unit @ X ) )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 % Rep_unit_inverse
% 5.49/5.83 thf(fact_9604_Abs__unit__cases,axiom,
% 5.49/5.83 ! [X: product_unit] :
% 5.49/5.83 ~ ! [Y3: $o] :
% 5.49/5.83 ( ( X
% 5.49/5.83 = ( product_Abs_unit @ Y3 ) )
% 5.49/5.83 => ~ ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Abs_unit_cases
% 5.49/5.83 thf(fact_9605_Abs__unit__induct,axiom,
% 5.49/5.83 ! [P: product_unit > $o,X: product_unit] :
% 5.49/5.83 ( ! [Y3: $o] :
% 5.49/5.83 ( ( member_o @ Y3 @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ( P @ ( product_Abs_unit @ Y3 ) ) )
% 5.49/5.83 => ( P @ X ) ) ).
% 5.49/5.83
% 5.49/5.83 % Abs_unit_induct
% 5.49/5.83 thf(fact_9606_Abs__unit__inject,axiom,
% 5.49/5.83 ! [X: $o,Y: $o] :
% 5.49/5.83 ( ( member_o @ X @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ( ( member_o @ Y @ ( insert_o @ $true @ bot_bot_set_o ) )
% 5.49/5.83 => ( ( ( product_Abs_unit @ X )
% 5.49/5.83 = ( product_Abs_unit @ Y ) )
% 5.49/5.83 = ( X = Y ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Abs_unit_inject
% 5.49/5.83 thf(fact_9607_eventually__sequentially__Suc,axiom,
% 5.49/5.83 ! [P: nat > $o] :
% 5.49/5.83 ( ( eventually_nat
% 5.49/5.83 @ ^ [I4: nat] : ( P @ ( suc @ I4 ) )
% 5.49/5.83 @ at_top_nat )
% 5.49/5.83 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % eventually_sequentially_Suc
% 5.49/5.83 thf(fact_9608_eventually__sequentially__seg,axiom,
% 5.49/5.83 ! [P: nat > $o,K: nat] :
% 5.49/5.83 ( ( eventually_nat
% 5.49/5.83 @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 5.49/5.83 @ at_top_nat )
% 5.49/5.83 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % eventually_sequentially_seg
% 5.49/5.83 thf(fact_9609_le__sequentially,axiom,
% 5.49/5.83 ! [F4: filter_nat] :
% 5.49/5.83 ( ( ord_le2510731241096832064er_nat @ F4 @ at_top_nat )
% 5.49/5.83 = ( ! [N8: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N8 ) @ F4 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % le_sequentially
% 5.49/5.83 thf(fact_9610_eventually__sequentiallyI,axiom,
% 5.49/5.83 ! [C: nat,P: nat > $o] :
% 5.49/5.83 ( ! [X3: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ C @ X3 )
% 5.49/5.83 => ( P @ X3 ) )
% 5.49/5.83 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % eventually_sequentiallyI
% 5.49/5.83 thf(fact_9611_eventually__sequentially,axiom,
% 5.49/5.83 ! [P: nat > $o] :
% 5.49/5.83 ( ( eventually_nat @ P @ at_top_nat )
% 5.49/5.83 = ( ? [N8: nat] :
% 5.49/5.83 ! [N: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ N8 @ N )
% 5.49/5.83 => ( P @ N ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % eventually_sequentially
% 5.49/5.83 thf(fact_9612_eventually__False__sequentially,axiom,
% 5.49/5.83 ~ ( eventually_nat
% 5.49/5.83 @ ^ [N: nat] : $false
% 5.49/5.83 @ at_top_nat ) ).
% 5.49/5.83
% 5.49/5.83 % eventually_False_sequentially
% 5.49/5.83 thf(fact_9613_natLeq__on__wo__rel,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( bNF_We3818239936649020644el_nat
% 5.49/5.83 @ ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natLeq_on_wo_rel
% 5.49/5.83 thf(fact_9614_UNIV__unit,axiom,
% 5.49/5.83 ( top_to1996260823553986621t_unit
% 5.49/5.83 = ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ).
% 5.49/5.83
% 5.49/5.83 % UNIV_unit
% 5.49/5.83 thf(fact_9615_bot__unit__def,axiom,
% 5.49/5.83 bot_bot_Product_unit = product_Unity ).
% 5.49/5.83
% 5.49/5.83 % bot_unit_def
% 5.49/5.83 thf(fact_9616_Unity__def,axiom,
% 5.49/5.83 ( product_Unity
% 5.49/5.83 = ( product_Abs_unit @ $true ) ) ).
% 5.49/5.83
% 5.49/5.83 % Unity_def
% 5.49/5.83 thf(fact_9617_sup__unit__def,axiom,
% 5.49/5.83 ( sup_sup_Product_unit
% 5.49/5.83 = ( ^ [Uu3: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 5.49/5.83
% 5.49/5.83 % sup_unit_def
% 5.49/5.83 thf(fact_9618_Inf__unit__def,axiom,
% 5.49/5.83 ( comple2584293577114468500t_unit
% 5.49/5.83 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 5.49/5.83
% 5.49/5.83 % Inf_unit_def
% 5.49/5.83 thf(fact_9619_old_Ounit_Oexhaust,axiom,
% 5.49/5.83 ! [Y: product_unit] : ( Y = product_Unity ) ).
% 5.49/5.83
% 5.49/5.83 % old.unit.exhaust
% 5.49/5.83 thf(fact_9620_top__unit__def,axiom,
% 5.49/5.83 top_top_Product_unit = product_Unity ).
% 5.49/5.83
% 5.49/5.83 % top_unit_def
% 5.49/5.83 thf(fact_9621_uminus__unit__def,axiom,
% 5.49/5.83 ( uminus2952777764628376836t_unit
% 5.49/5.83 = ( ^ [Uu3: product_unit] : product_Unity ) ) ).
% 5.49/5.83
% 5.49/5.83 % uminus_unit_def
% 5.49/5.83 thf(fact_9622_Sup__unit__def,axiom,
% 5.49/5.83 ( comple4687483117567863418t_unit
% 5.49/5.83 = ( ^ [Uu3: set_Product_unit] : product_Unity ) ) ).
% 5.49/5.83
% 5.49/5.83 % Sup_unit_def
% 5.49/5.83 thf(fact_9623_inf__unit__def,axiom,
% 5.49/5.83 ( inf_inf_Product_unit
% 5.49/5.83 = ( ^ [Uu3: product_unit,Uv2: product_unit] : product_Unity ) ) ).
% 5.49/5.83
% 5.49/5.83 % inf_unit_def
% 5.49/5.83 thf(fact_9624_wait__def,axiom,
% 5.49/5.83 ( heap_Time_wait
% 5.49/5.83 = ( ^ [N: nat] :
% 5.49/5.83 ( heap_T6183433275982383450t_unit
% 5.49/5.83 @ ^ [H6: heap_e7401611519738050253t_unit] : ( some_P1914260805536162275it_nat @ ( produc7133225469290080770it_nat @ product_Unity @ ( produc584006145561248582it_nat @ H6 @ N ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % wait_def
% 5.49/5.83 thf(fact_9625_default__unit__def,axiom,
% 5.49/5.83 defaul566961228789861419t_unit = product_Unity ).
% 5.49/5.83
% 5.49/5.83 % default_unit_def
% 5.49/5.83 thf(fact_9626_log_Osimps,axiom,
% 5.49/5.83 ( log
% 5.49/5.83 = ( ^ [B5: code_natural,I4: code_natural] :
% 5.49/5.83 ( if_Code_natural
% 5.49/5.83 @ ( ( ord_le1926595141338095240atural @ B5 @ one_one_Code_natural )
% 5.49/5.83 | ( ord_le5570908160329646204atural @ I4 @ B5 ) )
% 5.49/5.83 @ one_one_Code_natural
% 5.49/5.83 @ ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ B5 @ ( divide5121882707175180666atural @ I4 @ B5 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % log.simps
% 5.49/5.83 thf(fact_9627_log_Oelims,axiom,
% 5.49/5.83 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 5.49/5.83 ( ( ( log @ X @ Xa )
% 5.49/5.83 = Y )
% 5.49/5.83 => ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.49/5.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.49/5.83 => ( Y = one_one_Code_natural ) )
% 5.49/5.83 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.49/5.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.49/5.83 => ( Y
% 5.49/5.83 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % log.elims
% 5.49/5.83 thf(fact_9628_log_Opelims,axiom,
% 5.49/5.83 ! [X: code_natural,Xa: code_natural,Y: code_natural] :
% 5.49/5.83 ( ( ( log @ X @ Xa )
% 5.49/5.83 = Y )
% 5.49/5.83 => ( ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) )
% 5.49/5.83 => ~ ( ( ( ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.49/5.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.49/5.83 => ( Y = one_one_Code_natural ) )
% 5.49/5.83 & ( ~ ( ( ord_le1926595141338095240atural @ X @ one_one_Code_natural )
% 5.49/5.83 | ( ord_le5570908160329646204atural @ Xa @ X ) )
% 5.49/5.83 => ( Y
% 5.49/5.83 = ( plus_p4538020629002901425atural @ one_one_Code_natural @ ( log @ X @ ( divide5121882707175180666atural @ Xa @ X ) ) ) ) ) )
% 5.49/5.83 => ~ ( accp_P8126237942716283194atural @ log_rel @ ( produc3574140220909816553atural @ X @ Xa ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % log.pelims
% 5.49/5.83 thf(fact_9629_minus__shift__def,axiom,
% 5.49/5.83 ( minus_shift
% 5.49/5.83 = ( ^ [R4: code_natural,K3: code_natural,L2: code_natural] : ( if_Code_natural @ ( ord_le5570908160329646204atural @ K3 @ L2 ) @ ( minus_7197305767214868737atural @ ( plus_p4538020629002901425atural @ R4 @ K3 ) @ L2 ) @ ( minus_7197305767214868737atural @ K3 @ L2 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % minus_shift_def
% 5.49/5.83 thf(fact_9630_exhaustive__natural_H_Ocases,axiom,
% 5.49/5.83 ! [X: produc8731074985263844745atural] :
% 5.49/5.83 ~ ! [F2: code_natural > option6357759511663192854e_term,D: code_natural,I3: code_natural] :
% 5.49/5.83 ( X
% 5.49/5.83 != ( produc2252593628808123835atural @ F2 @ ( produc3574140220909816553atural @ D @ I3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % exhaustive_natural'.cases
% 5.49/5.83 thf(fact_9631_full__exhaustive__natural_H_Ocases,axiom,
% 5.49/5.83 ! [X: produc989692990947075319atural] :
% 5.49/5.83 ~ ! [F2: produc4972180933644002618e_term > option6357759511663192854e_term,D: code_natural,I3: code_natural] :
% 5.49/5.83 ( X
% 5.49/5.83 != ( produc3831813291587773865atural @ F2 @ ( produc3574140220909816553atural @ D @ I3 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % full_exhaustive_natural'.cases
% 5.49/5.83 thf(fact_9632_log_Ocases,axiom,
% 5.49/5.83 ! [X: produc7822875418678951345atural] :
% 5.49/5.83 ~ ! [B4: code_natural,I3: code_natural] :
% 5.49/5.83 ( X
% 5.49/5.83 != ( produc3574140220909816553atural @ B4 @ I3 ) ) ).
% 5.49/5.83
% 5.49/5.83 % log.cases
% 5.49/5.83 thf(fact_9633_next_Osimps,axiom,
% 5.49/5.83 ! [V: code_natural,W2: code_natural] :
% 5.49/5.83 ( ( next @ ( produc3574140220909816553atural @ V @ W2 ) )
% 5.49/5.83 = ( 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 @ V @ ( 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 @ V @ ( 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 @ V @ ( 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 @ V @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % next.simps
% 5.49/5.83 thf(fact_9634_split__seed__def,axiom,
% 5.49/5.83 ( split_seed
% 5.49/5.83 = ( ^ [S6: produc7822875418678951345atural] :
% 5.49/5.83 ( produc8282080750456430313atural
% 5.49/5.83 @ ^ [V2: code_natural,W3: code_natural] :
% 5.49/5.83 ( produc8282080750456430313atural
% 5.49/5.83 @ ^ [V3: code_natural,W4: code_natural] : ( produc4480994950612372183atural @ ( produc3574140220909816553atural @ ( inc_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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ V2 ) @ W4 ) @ ( produc3574140220909816553atural @ V3 @ ( inc_shift @ ( numera5444537566228673987atural @ ( bit0 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ W3 ) ) )
% 5.49/5.83 @ ( produc6591912806276919810atural @ ( next @ S6 ) ) )
% 5.49/5.83 @ S6 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % split_seed_def
% 5.49/5.83 thf(fact_9635_Random_Orange__def,axiom,
% 5.49/5.83 ( range
% 5.49/5.83 = ( ^ [K3: code_natural] :
% 5.49/5.83 ( produc5538323210962509403atural
% 5.49/5.83 @ ( 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 )
% 5.49/5.83 @ ^ [L2: code_natural] :
% 5.49/5.83 ( produc5538323210962509403atural @ next
% 5.49/5.83 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( plus_p4538020629002901425atural @ V2 @ ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.49/5.83 @ one_one_Code_natural )
% 5.49/5.83 @ ^ [V2: code_natural] : ( produc6639722614265839536atural @ ( modulo8411746178871703098atural @ V2 @ K3 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Random.range_def
% 5.49/5.83 thf(fact_9636_range,axiom,
% 5.49/5.83 ! [K: code_natural,S2: produc7822875418678951345atural] :
% 5.49/5.83 ( ( ord_le5570908160329646204atural @ zero_z2226904508553997617atural @ K )
% 5.49/5.83 => ( ord_le5570908160329646204atural @ ( produc497848011034438852atural @ ( range @ K @ S2 ) ) @ K ) ) ).
% 5.49/5.83
% 5.49/5.83 % range
% 5.49/5.83 thf(fact_9637_less__natural_Oabs__eq,axiom,
% 5.49/5.83 ! [Xa: nat,X: nat] :
% 5.49/5.83 ( ( ord_le5570908160329646204atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 5.49/5.83 = ( ord_less_nat @ Xa @ X ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_natural.abs_eq
% 5.49/5.83 thf(fact_9638_less__eq__natural_Oabs__eq,axiom,
% 5.49/5.83 ! [Xa: nat,X: nat] :
% 5.49/5.83 ( ( ord_le1926595141338095240atural @ ( code_natural_of_nat @ Xa ) @ ( code_natural_of_nat @ X ) )
% 5.49/5.83 = ( ord_less_eq_nat @ Xa @ X ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_natural.abs_eq
% 5.49/5.83 thf(fact_9639_less__eq__natural_Orep__eq,axiom,
% 5.49/5.83 ( ord_le1926595141338095240atural
% 5.49/5.83 = ( ^ [X4: code_natural,Xa4: code_natural] : ( ord_less_eq_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_natural.rep_eq
% 5.49/5.83 thf(fact_9640_less__natural_Orep__eq,axiom,
% 5.49/5.83 ( ord_le5570908160329646204atural
% 5.49/5.83 = ( ^ [X4: code_natural,Xa4: code_natural] : ( ord_less_nat @ ( code_nat_of_natural @ X4 ) @ ( code_nat_of_natural @ Xa4 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_natural.rep_eq
% 5.49/5.83 thf(fact_9641_less__natural__def,axiom,
% 5.49/5.83 ( ord_le5570908160329646204atural
% 5.49/5.83 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_natural_def
% 5.49/5.83 thf(fact_9642_less__eq__natural__def,axiom,
% 5.49/5.83 ( ord_le1926595141338095240atural
% 5.49/5.83 = ( map_fu6256889081107267320ural_o @ code_nat_of_natural @ ( map_fu4892316939951275536at_o_o @ code_nat_of_natural @ id_o ) @ ord_less_eq_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % less_eq_natural_def
% 5.49/5.83 thf(fact_9643_natural__decr,axiom,
% 5.49/5.83 ! [N2: code_natural] :
% 5.49/5.83 ( ( N2 != zero_z2226904508553997617atural )
% 5.49/5.83 => ( ord_less_nat @ ( minus_minus_nat @ ( code_nat_of_natural @ N2 ) @ ( suc @ zero_zero_nat ) ) @ ( code_nat_of_natural @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natural_decr
% 5.49/5.83 thf(fact_9644_bit__concat__bit__iff,axiom,
% 5.49/5.83 ! [M: nat,K: int,L: int,N2: nat] :
% 5.49/5.83 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 5.49/5.83 = ( ( ( ord_less_nat @ N2 @ M )
% 5.49/5.83 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.49/5.83 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.49/5.83 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % bit_concat_bit_iff
% 5.49/5.83 thf(fact_9645_concat__bit__nonnegative__iff,axiom,
% 5.49/5.83 ! [N2: nat,K: int,L: int] :
% 5.49/5.83 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 5.49/5.83 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.49/5.83
% 5.49/5.83 % concat_bit_nonnegative_iff
% 5.49/5.83 thf(fact_9646_concat__bit__negative__iff,axiom,
% 5.49/5.83 ! [N2: nat,K: int,L: int] :
% 5.49/5.83 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 5.49/5.83 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.49/5.83
% 5.49/5.83 % concat_bit_negative_iff
% 5.49/5.83 thf(fact_9647_pair__lessI2,axiom,
% 5.49/5.83 ! [A: nat,B: nat,S2: nat,T5: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.83 => ( ( ord_less_nat @ S2 @ T5 )
% 5.49/5.83 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T5 ) ) @ fun_pair_less ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_lessI2
% 5.49/5.83 thf(fact_9648_total__pair__less,axiom,
% 5.49/5.83 ! [A3: set_Pr1261947904930325089at_nat] : ( total_3592101749530773125at_nat @ A3 @ fun_pair_less ) ).
% 5.49/5.83
% 5.49/5.83 % total_pair_less
% 5.49/5.83 thf(fact_9649_trans__pair__less,axiom,
% 5.49/5.83 trans_4347625901269045472at_nat @ fun_pair_less ).
% 5.49/5.83
% 5.49/5.83 % trans_pair_less
% 5.49/5.83 thf(fact_9650_pair__less__iff1,axiom,
% 5.49/5.83 ! [X: nat,Y: nat,Z: nat] :
% 5.49/5.83 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ X @ Y ) @ ( product_Pair_nat_nat @ X @ Z ) ) @ fun_pair_less )
% 5.49/5.83 = ( ord_less_nat @ Y @ Z ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_less_iff1
% 5.49/5.83 thf(fact_9651_pair__less__def,axiom,
% 5.49/5.83 ( fun_pair_less
% 5.49/5.83 = ( lex_prod_nat_nat @ less_than @ less_than ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_less_def
% 5.49/5.83 thf(fact_9652_wf__pair__less,axiom,
% 5.49/5.83 wf_Pro7803398752247294826at_nat @ fun_pair_less ).
% 5.49/5.83
% 5.49/5.83 % wf_pair_less
% 5.49/5.83 thf(fact_9653_pair__lessI1,axiom,
% 5.49/5.83 ! [A: nat,B: nat,S2: nat,T5: nat] :
% 5.49/5.83 ( ( ord_less_nat @ A @ B )
% 5.49/5.83 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T5 ) ) @ fun_pair_less ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_lessI1
% 5.49/5.83 thf(fact_9654_smin__insertI,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( member8440522571783428010at_nat @ X @ XS )
% 5.49/5.83 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_strict )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_strict ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % smin_insertI
% 5.49/5.83 thf(fact_9655_pair__leqI2,axiom,
% 5.49/5.83 ! [A: nat,B: nat,S2: nat,T5: nat] :
% 5.49/5.83 ( ( ord_less_eq_nat @ A @ B )
% 5.49/5.83 => ( ( ord_less_eq_nat @ S2 @ T5 )
% 5.49/5.83 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T5 ) ) @ fun_pair_leq ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_leqI2
% 5.49/5.83 thf(fact_9656_pair__leq__def,axiom,
% 5.49/5.83 ( fun_pair_leq
% 5.49/5.83 = ( sup_su718114333110466843at_nat @ fun_pair_less @ id_Pro2258643101195443293at_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_leq_def
% 5.49/5.83 thf(fact_9657_smin__emptyI,axiom,
% 5.49/5.83 ! [X6: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( X6 != bot_bo2099793752762293965at_nat )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ bot_bo2099793752762293965at_nat ) @ fun_min_strict ) ) ).
% 5.49/5.83
% 5.49/5.83 % smin_emptyI
% 5.49/5.83 thf(fact_9658_min__strict__def,axiom,
% 5.49/5.83 ( fun_min_strict
% 5.49/5.83 = ( min_ex6901939911449802026at_nat @ fun_pair_less ) ) ).
% 5.49/5.83
% 5.49/5.83 % min_strict_def
% 5.49/5.83 thf(fact_9659_pair__leqI1,axiom,
% 5.49/5.83 ! [A: nat,B: nat,S2: nat,T5: nat] :
% 5.49/5.83 ( ( ord_less_nat @ A @ B )
% 5.49/5.83 => ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ ( product_Pair_nat_nat @ A @ S2 ) @ ( product_Pair_nat_nat @ B @ T5 ) ) @ fun_pair_leq ) ) ).
% 5.49/5.83
% 5.49/5.83 % pair_leqI1
% 5.49/5.83 thf(fact_9660_wmax__insertI,axiom,
% 5.49/5.83 ! [Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( member8440522571783428010at_nat @ Y @ YS )
% 5.49/5.83 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_max_weak )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ XS ) @ YS ) @ fun_max_weak ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % wmax_insertI
% 5.49/5.83 thf(fact_9661_wmin__insertI,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,XS: set_Pr1261947904930325089at_nat,Y: product_prod_nat_nat,YS: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( member8440522571783428010at_nat @ X @ XS )
% 5.49/5.83 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ YS ) @ fun_min_weak )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ XS @ ( insert8211810215607154385at_nat @ Y @ YS ) ) @ fun_min_weak ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % wmin_insertI
% 5.49/5.83 thf(fact_9662_wmax__emptyI,axiom,
% 5.49/5.83 ! [X6: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( finite6177210948735845034at_nat @ X6 )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ X6 ) @ fun_max_weak ) ) ).
% 5.49/5.83
% 5.49/5.83 % wmax_emptyI
% 5.49/5.83 thf(fact_9663_wmin__emptyI,axiom,
% 5.49/5.83 ! [X6: set_Pr1261947904930325089at_nat] : ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ bot_bo2099793752762293965at_nat ) @ fun_min_weak ) ).
% 5.49/5.83
% 5.49/5.83 % wmin_emptyI
% 5.49/5.83 thf(fact_9664_min__rpair__set,axiom,
% 5.49/5.83 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_min_strict @ fun_min_weak ) ).
% 5.49/5.83
% 5.49/5.83 % min_rpair_set
% 5.49/5.83 thf(fact_9665_min__weak__def,axiom,
% 5.49/5.83 ( fun_min_weak
% 5.49/5.83 = ( sup_su5525570899277871387at_nat @ ( min_ex6901939911449802026at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % min_weak_def
% 5.49/5.83 thf(fact_9666_max__weak__def,axiom,
% 5.49/5.83 ( fun_max_weak
% 5.49/5.83 = ( sup_su5525570899277871387at_nat @ ( max_ex8135407076693332796at_nat @ fun_pair_leq ) @ ( insert9069300056098147895at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ bot_bo2099793752762293965at_nat ) @ bot_bo228742789529271731at_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % max_weak_def
% 5.49/5.83 thf(fact_9667_smax__insertI,axiom,
% 5.49/5.83 ! [Y: product_prod_nat_nat,Y7: set_Pr1261947904930325089at_nat,X: product_prod_nat_nat,X6: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( member8440522571783428010at_nat @ Y @ Y7 )
% 5.49/5.83 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_less )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ X6 @ Y7 ) @ fun_max_strict )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( insert8211810215607154385at_nat @ X @ X6 ) @ Y7 ) @ fun_max_strict ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % smax_insertI
% 5.49/5.83 thf(fact_9668_max__strict__def,axiom,
% 5.49/5.83 ( fun_max_strict
% 5.49/5.83 = ( max_ex8135407076693332796at_nat @ fun_pair_less ) ) ).
% 5.49/5.83
% 5.49/5.83 % max_strict_def
% 5.49/5.83 thf(fact_9669_max__rpair__set,axiom,
% 5.49/5.83 fun_re2478310338295953701at_nat @ ( produc9060074326276436823at_nat @ fun_max_strict @ fun_max_weak ) ).
% 5.49/5.83
% 5.49/5.83 % max_rpair_set
% 5.49/5.83 thf(fact_9670_smax__emptyI,axiom,
% 5.49/5.83 ! [Y7: set_Pr1261947904930325089at_nat] :
% 5.49/5.83 ( ( finite6177210948735845034at_nat @ Y7 )
% 5.49/5.83 => ( ( Y7 != bot_bo2099793752762293965at_nat )
% 5.49/5.83 => ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ bot_bo2099793752762293965at_nat @ Y7 ) @ fun_max_strict ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % smax_emptyI
% 5.49/5.83 thf(fact_9671_division__segment__int__def,axiom,
% 5.49/5.83 ( euclid3395696857347342551nt_int
% 5.49/5.83 = ( ^ [K3: int] : ( if_int @ ( ord_less_eq_int @ zero_zero_int @ K3 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % division_segment_int_def
% 5.49/5.83 thf(fact_9672_wmsI,axiom,
% 5.49/5.83 ! [A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat,Z4: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A3 ) @ ( set_ms8126754132646256062at_nat @ B3 ) ) @ fun_max_strict )
% 5.49/5.83 | ( ( A3 = zero_z1048942125864253310at_nat )
% 5.49/5.83 & ( B3 = zero_z1048942125864253310at_nat ) ) )
% 5.49/5.83 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z4 @ A3 ) @ ( plus_p7104986032573967614at_nat @ Z4 @ B3 ) ) @ ms_weak ) ) ).
% 5.49/5.83
% 5.49/5.83 % wmsI
% 5.49/5.83 thf(fact_9673_smsI,axiom,
% 5.49/5.83 ! [A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat,Z4: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A3 ) @ ( set_ms8126754132646256062at_nat @ B3 ) ) @ fun_max_strict )
% 5.49/5.83 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z4 @ A3 ) @ ( plus_p7104986032573967614at_nat @ Z4 @ B3 ) ) @ ms_strict ) ) ).
% 5.49/5.83
% 5.49/5.83 % smsI
% 5.49/5.83 thf(fact_9674_ms__reduction__pair,axiom,
% 5.49/5.83 fun_re7357418987779152907at_nat @ ( produc5245064249948416855at_nat @ ms_strict @ ms_weak ) ).
% 5.49/5.83
% 5.49/5.83 % ms_reduction_pair
% 5.49/5.83 thf(fact_9675_ms__weak__def,axiom,
% 5.49/5.83 ( ms_weak
% 5.49/5.83 = ( sup_su3035147773818789531at_nat @ ms_strict @ id_mul2649389997224486051at_nat ) ) ).
% 5.49/5.83
% 5.49/5.83 % ms_weak_def
% 5.49/5.83 thf(fact_9676_ms__strictI,axiom,
% 5.49/5.83 ! [Z4: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( pw_leq @ Z4 @ Z9 )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A3 ) @ ( set_ms8126754132646256062at_nat @ B3 ) ) @ fun_max_strict )
% 5.49/5.83 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z4 @ A3 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B3 ) ) @ ms_strict ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % ms_strictI
% 5.49/5.83 thf(fact_9677_ms__weakI1,axiom,
% 5.49/5.83 ! [Z4: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat,A3: multis2468970476368604999at_nat,B3: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( pw_leq @ Z4 @ Z9 )
% 5.49/5.83 => ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A3 ) @ ( set_ms8126754132646256062at_nat @ B3 ) ) @ fun_max_strict )
% 5.49/5.83 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z4 @ A3 ) @ ( plus_p7104986032573967614at_nat @ Z9 @ B3 ) ) @ ms_weak ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % ms_weakI1
% 5.49/5.83 thf(fact_9678_pw__leq__lstep,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.49/5.83 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 5.49/5.83 => ( pw_leq @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pw_leq_lstep
% 5.49/5.83 thf(fact_9679_pw__leq__step,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat,X6: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X @ Y ) @ fun_pair_leq )
% 5.49/5.83 => ( ( pw_leq @ X6 @ Y7 )
% 5.49/5.83 => ( pw_leq @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X @ zero_z1048942125864253310at_nat ) @ X6 ) @ ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y @ zero_z1048942125864253310at_nat ) @ Y7 ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pw_leq_step
% 5.49/5.83 thf(fact_9680_pw__leq_Osimps,axiom,
% 5.49/5.83 ( pw_leq
% 5.49/5.83 = ( ^ [A12: multis2468970476368604999at_nat,A22: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( ( A12 = zero_z1048942125864253310at_nat )
% 5.49/5.83 & ( A22 = zero_z1048942125864253310at_nat ) )
% 5.49/5.83 | ? [X4: product_prod_nat_nat,Y4: product_prod_nat_nat,X11: multis2468970476368604999at_nat,Y8: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( A12
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X4 @ zero_z1048942125864253310at_nat ) @ X11 ) )
% 5.49/5.83 & ( A22
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y4 @ zero_z1048942125864253310at_nat ) @ Y8 ) )
% 5.49/5.83 & ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X4 @ Y4 ) @ fun_pair_leq )
% 5.49/5.83 & ( pw_leq @ X11 @ Y8 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pw_leq.simps
% 5.49/5.83 thf(fact_9681_pw__leq_Ocases,axiom,
% 5.49/5.83 ! [A1: multis2468970476368604999at_nat,A23: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( pw_leq @ A1 @ A23 )
% 5.49/5.83 => ( ( ( A1 = zero_z1048942125864253310at_nat )
% 5.49/5.83 => ( A23 != zero_z1048942125864253310at_nat ) )
% 5.49/5.83 => ~ ! [X3: product_prod_nat_nat,Y3: product_prod_nat_nat,X14: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( A1
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ X3 @ zero_z1048942125864253310at_nat ) @ X14 ) )
% 5.49/5.83 => ! [Y9: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( A23
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ ( add_ms2612439473150266591at_nat @ Y3 @ zero_z1048942125864253310at_nat ) @ Y9 ) )
% 5.49/5.83 => ( ( member8206827879206165904at_nat @ ( produc6161850002892822231at_nat @ X3 @ Y3 ) @ fun_pair_leq )
% 5.49/5.83 => ~ ( pw_leq @ X14 @ Y9 ) ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pw_leq.cases
% 5.49/5.83 thf(fact_9682_ms__weakI2,axiom,
% 5.49/5.83 ! [Z4: multis2468970476368604999at_nat,Z9: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( pw_leq @ Z4 @ Z9 )
% 5.49/5.83 => ( member6689249552917799696at_nat @ ( produc4348348721325984599at_nat @ ( plus_p7104986032573967614at_nat @ Z4 @ zero_z1048942125864253310at_nat ) @ ( plus_p7104986032573967614at_nat @ Z9 @ zero_z1048942125864253310at_nat ) ) @ ms_weak ) ) ).
% 5.49/5.83
% 5.49/5.83 % ms_weakI2
% 5.49/5.83 thf(fact_9683_pw__leq__split,axiom,
% 5.49/5.83 ! [X6: multis2468970476368604999at_nat,Y7: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( pw_leq @ X6 @ Y7 )
% 5.49/5.83 => ? [A8: multis2468970476368604999at_nat,B10: multis2468970476368604999at_nat,Z10: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( X6
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ A8 @ Z10 ) )
% 5.49/5.83 & ( Y7
% 5.49/5.83 = ( plus_p7104986032573967614at_nat @ B10 @ Z10 ) )
% 5.49/5.83 & ( ( member8757157785044589968at_nat @ ( produc2922128104949294807at_nat @ ( set_ms8126754132646256062at_nat @ A8 ) @ ( set_ms8126754132646256062at_nat @ B10 ) ) @ fun_max_strict )
% 5.49/5.83 | ( ( B10 = zero_z1048942125864253310at_nat )
% 5.49/5.83 & ( A8 = zero_z1048942125864253310at_nat ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % pw_leq_split
% 5.49/5.83 thf(fact_9684_natLeq__on__well__order__on,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( order_2888998067076097458on_nat
% 5.49/5.83 @ ( collect_nat
% 5.49/5.83 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 5.49/5.83 @ ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natLeq_on_well_order_on
% 5.49/5.83 thf(fact_9685_natLeq__on__Well__order,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( order_2888998067076097458on_nat
% 5.49/5.83 @ ( field_nat
% 5.49/5.83 @ ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) )
% 5.49/5.83 @ ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natLeq_on_Well_order
% 5.49/5.83 thf(fact_9686_cone__def,axiom,
% 5.49/5.83 ( bNF_Cardinal_cone
% 5.49/5.83 = ( bNF_Ca7083678892733797993t_unit @ ( insert_Product_unit @ product_Unity @ bot_bo3957492148770167129t_unit ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % cone_def
% 5.49/5.83 thf(fact_9687_ctwo__Cnotzero,axiom,
% 5.49/5.83 ( ~ ( member444158400953824016od_o_o @ ( produc763777882069021527od_o_o @ bNF_Cardinal_ctwo @ bNF_Cardinal_czero_o ) @ bNF_We2654380646378065620so_o_o )
% 5.49/5.83 & ( bNF_Ca8331644756375544342r_on_o @ ( field_o @ bNF_Cardinal_ctwo ) @ bNF_Cardinal_ctwo ) ) ).
% 5.49/5.83
% 5.49/5.83 % ctwo_Cnotzero
% 5.49/5.83 thf(fact_9688_ctwo__ordLess__natLeq,axiom,
% 5.49/5.83 member4095101504841534314at_nat @ ( produc8517790099723286449at_nat @ bNF_Cardinal_ctwo @ bNF_Ca8665028551170535155natLeq ) @ bNF_We8182288985678559134_o_nat ).
% 5.49/5.83
% 5.49/5.83 % ctwo_ordLess_natLeq
% 5.49/5.83 thf(fact_9689_natLeq__def,axiom,
% 5.49/5.83 ( bNF_Ca8665028551170535155natLeq
% 5.49/5.83 = ( collec3392354462482085612at_nat @ ( produc6081775807080527818_nat_o @ ord_less_eq_nat ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natLeq_def
% 5.49/5.83 thf(fact_9690_natLeq__underS__less,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( ( order_underS_nat @ bNF_Ca8665028551170535155natLeq @ N2 )
% 5.49/5.83 = ( collect_nat
% 5.49/5.83 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % natLeq_underS_less
% 5.49/5.83 thf(fact_9691_Restr__natLeq,axiom,
% 5.49/5.83 ! [N2: nat] :
% 5.49/5.83 ( ( inf_in2572325071724192079at_nat @ bNF_Ca8665028551170535155natLeq
% 5.49/5.83 @ ( produc457027306803732586at_nat
% 5.49/5.83 @ ( collect_nat
% 5.49/5.83 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) )
% 5.49/5.83 @ ^ [Uu2: nat] :
% 5.49/5.83 ( collect_nat
% 5.49/5.83 @ ^ [X4: nat] : ( ord_less_nat @ X4 @ N2 ) ) ) )
% 5.49/5.83 = ( collec3392354462482085612at_nat
% 5.49/5.83 @ ( produc6081775807080527818_nat_o
% 5.49/5.83 @ ^ [X4: nat,Y4: nat] :
% 5.49/5.83 ( ( ord_less_nat @ X4 @ N2 )
% 5.49/5.83 & ( ord_less_nat @ Y4 @ N2 )
% 5.49/5.83 & ( ord_less_eq_nat @ X4 @ Y4 ) ) ) ) ) ).
% 5.49/5.83
% 5.49/5.83 % Restr_natLeq
% 5.49/5.83
% 5.49/5.83 % Helper facts (51)
% 5.49/5.83 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.49/5.83 ! [X: int,Y: int] :
% 5.49/5.83 ( ( if_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.49/5.83 ! [X: int,Y: int] :
% 5.49/5.83 ( ( if_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.49/5.83 ! [X: nat,Y: nat] :
% 5.49/5.83 ( ( if_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.49/5.83 ! [X: nat,Y: nat] :
% 5.49/5.83 ( ( if_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.49/5.83 ! [X: num,Y: num] :
% 5.49/5.83 ( ( if_num @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.49/5.83 ! [X: num,Y: num] :
% 5.49/5.83 ( ( if_num @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.49/5.83 ! [X: rat,Y: rat] :
% 5.49/5.83 ( ( if_rat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.49/5.83 ! [X: rat,Y: rat] :
% 5.49/5.83 ( ( if_rat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Assertions__Oassn_T,axiom,
% 5.49/5.83 ! [X: assn,Y: assn] :
% 5.49/5.83 ( ( if_assn @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Assertions__Oassn_T,axiom,
% 5.49/5.83 ! [X: assn,Y: assn] :
% 5.49/5.83 ( ( if_assn @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.49/5.83 ! [X: code_integer,Y: code_integer] :
% 5.49/5.83 ( ( if_Code_integer @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.49/5.83 ! [X: code_integer,Y: code_integer] :
% 5.49/5.83 ( ( if_Code_integer @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 5.49/5.83 ! [X: code_natural,Y: code_natural] :
% 5.49/5.83 ( ( if_Code_natural @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Code____Numeral__Onatural_T,axiom,
% 5.49/5.83 ! [X: code_natural,Y: code_natural] :
% 5.49/5.83 ( ( if_Code_natural @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: set_int,Y: set_int] :
% 5.49/5.83 ( ( if_set_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: set_int,Y: set_int] :
% 5.49/5.83 ( ( if_set_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: set_nat,Y: set_nat] :
% 5.49/5.83 ( ( if_set_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Set__Oset_It__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: set_nat,Y: set_nat] :
% 5.49/5.83 ( ( if_set_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: list_int,Y: list_int] :
% 5.49/5.83 ( ( if_list_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: list_int,Y: list_int] :
% 5.49/5.83 ( ( if_list_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: list_nat,Y: list_nat] :
% 5.49/5.83 ( ( if_list_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: list_nat,Y: list_nat] :
% 5.49/5.83 ( ( if_list_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: int > int,Y: int > int] :
% 5.49/5.83 ( ( if_int_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: int > int,Y: int > int] :
% 5.49/5.83 ( ( if_int_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.49/5.83 ! [X: option_num,Y: option_num] :
% 5.49/5.83 ( ( if_option_num @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.49/5.83 ! [X: option_num,Y: option_num] :
% 5.49/5.83 ( ( if_option_num @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_o,Y: option_set_o] :
% 5.49/5.83 ( ( if_option_set_o @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_I_Eo_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_o,Y: option_set_o] :
% 5.49/5.83 ( ( if_option_set_o @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_int,Y: option_set_int] :
% 5.49/5.83 ( ( if_option_set_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Int__Oint_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_int,Y: option_set_int] :
% 5.49/5.83 ( ( if_option_set_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_nat,Y: option_set_nat] :
% 5.49/5.83 ( ( if_option_set_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Nat__Onat_J_J_T,axiom,
% 5.49/5.83 ! [X: option_set_nat,Y: option_set_nat] :
% 5.49/5.83 ( ( if_option_set_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.49/5.83 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.49/5.83 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.49/5.83 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.49/5.83 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.49/5.83 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.49/5.83 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.49/5.83 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.49/5.83 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.49/5.83 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.49/5.83 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.49/5.83 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( if_mul8430962117462786573at_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Multiset__Omultiset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 5.49/5.83 ! [X: multis2468970476368604999at_nat,Y: multis2468970476368604999at_nat] :
% 5.49/5.83 ( ( if_mul8430962117462786573at_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.49/5.83 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.49/5.83 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.49/5.83 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 5.49/5.83 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 5.49/5.83 ( ( if_opt7704869406773131885at_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Set__Oset_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option8963830502488799655at_nat,Y: option8963830502488799655at_nat] :
% 5.49/5.83 ( ( if_opt7704869406773131885at_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_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_T,axiom,
% 5.49/5.83 ! [X: produc859450856879609959at_nat,Y: produc859450856879609959at_nat] :
% 5.49/5.83 ( ( if_Pro4507677147265585453at_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_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_T,axiom,
% 5.49/5.83 ! [X: produc859450856879609959at_nat,Y: produc859450856879609959at_nat] :
% 5.49/5.83 ( ( if_Pro4507677147265585453at_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 5.49/5.83 ( ( if_opt6883606601682554499it_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_Itf__a_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option3562590408128118217it_nat,Y: option3562590408128118217it_nat] :
% 5.49/5.83 ( ( if_opt6883606601682554499it_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_3_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [P: $o] :
% 5.49/5.83 ( ( P = $true )
% 5.49/5.83 | ( P = $false ) ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_2_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 5.49/5.83 ( ( if_opt1729522071442692626it_nat @ $false @ X @ Y )
% 5.49/5.83 = Y ) ).
% 5.49/5.83
% 5.49/5.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Product____Type__Oprod_It__Product____Type__Ounit_Mt__Product____Type__Oprod_It__Heap__Oheap__Oheap____ext_It__Product____Type__Ounit_J_Mt__Nat__Onat_J_J_J_T,axiom,
% 5.49/5.83 ! [X: option8956607266484857688it_nat,Y: option8956607266484857688it_nat] :
% 5.49/5.83 ( ( if_opt1729522071442692626it_nat @ $true @ X @ Y )
% 5.49/5.83 = X ) ).
% 5.49/5.83
% 5.49/5.83 % Conjectures (1)
% 6.70/7.10 thf(conj_0,conjecture,
% 6.70/7.10 rep_assn @ ( times_times_assn @ ( q @ r2 ) @ r ) @ ( produc7507926704131184380et_nat @ h @ ( hoare_new_addrs @ h2 @ as @ h ) ) ).
% 6.70/7.10
% 6.70/7.10 %------------------------------------------------------------------------------
% 6.70/7.10 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.gAObnEuf7e/cvc5---1.0.5_12658.p...
% 6.70/7.10 (declare-sort $$unsorted 0)
% 6.70/7.10 (declare-sort tptp.option2860828798490689354et_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr8536935166611901872et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc4193628355235574503at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc2732055786443039994et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc1319942482725812455at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc989692990947075319atural 0)
% 6.70/7.10 (declare-sort tptp.produc1908205239877642774nteger 0)
% 6.70/7.10 (declare-sort tptp.option7541221861074943443nt_int 0)
% 6.70/7.10 (declare-sort tptp.set_Pr9222295170931077689nt_int 0)
% 6.70/7.10 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 6.70/7.10 (declare-sort tptp.option5190343406534369742et_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr3286484037609594932et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc3925858234332021118et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc8731074985263844745atural 0)
% 6.70/7.10 (declare-sort tptp.produc8763457246119570046nteger 0)
% 6.70/7.10 (declare-sort tptp.produc6576344331059438605e_term 0)
% 6.70/7.10 (declare-sort tptp.option4256020574406277085nt_int 0)
% 6.70/7.10 (declare-sort tptp.option2498585697089621389at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr1872883991513573699nt_int 0)
% 6.70/7.10 (declare-sort tptp.produc3911288613690379145it_nat 0)
% 6.70/7.10 (declare-sort tptp.option1583680563626158861at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 6.70/7.10 (declare-sort tptp.set_Pr8551490117392284871at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc6756470014200349799atural 0)
% 6.70/7.10 (declare-sort tptp.produc4453839368661128058it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_op239864471688321678it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc4166570645942440679at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr4329608150637261639at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.70/7.10 (declare-sort tptp.option2158460348403737357at_nat 0)
% 6.70/7.10 (declare-sort tptp.option8956607266484857688it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_op4617111635268443007it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc3843707927480180839at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr1354866905816374718it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr457366540195662369at_nat 0)
% 6.70/7.10 (declare-sort tptp.option3562590408128118217it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr8693737435421807431at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc8664842809031399944it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc732395585841259969at_nat 0)
% 6.70/7.10 (declare-sort tptp.list_P6935614879863011209it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr1932065953672099015od_o_o 0)
% 6.70/7.10 (declare-sort tptp.set_Pr7098220151150636591it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc6197004810343482825et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc5835291356934675326atural 0)
% 6.70/7.10 (declare-sort tptp.produc859450856879609959at_nat 0)
% 6.70/7.10 (declare-sort tptp.option936205604648967762et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc2934264451710624999od_o_o 0)
% 6.70/7.10 (declare-sort tptp.produc3260487557148687353it_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr7577011563204128103nteger 0)
% 6.70/7.10 (declare-sort tptp.produc4972180933644002618e_term 0)
% 6.70/7.10 (declare-sort tptp.produc6241069584506657477e_term 0)
% 6.70/7.10 (declare-sort tptp.option233860712434008220it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc6491284506569428743nteger 0)
% 6.70/7.10 (declare-sort tptp.list_P131111800688179804it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc3658429121746597890et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc8551481072490612790e_term 0)
% 6.70/7.10 (declare-sort tptp.set_Pr5488025237498180813et_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr2522554150109002629et_int 0)
% 6.70/7.10 (declare-sort tptp.option6357759511663192854e_term 0)
% 6.70/7.10 (declare-sort tptp.produc6653097349344004940it_nat 0)
% 6.70/7.10 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr5094982260447487303t_unit 0)
% 6.70/7.10 (declare-sort tptp.set_mu2057375006010111271at_nat 0)
% 6.70/7.10 (declare-sort tptp.option8963830502488799655at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_se7855581050983116737at_nat 0)
% 6.70/7.10 (declare-sort tptp.produc7819656566062154093et_nat 0)
% 6.70/7.10 (declare-sort tptp.produc2115011035271226405et_int 0)
% 6.70/7.10 (declare-sort tptp.produc7822875418678951345atural 0)
% 6.70/7.10 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.70/7.10 (declare-sort tptp.multis2468970476368604999at_nat 0)
% 6.70/7.10 (declare-sort tptp.option4624381673175914239nt_int 0)
% 6.70/7.10 (declare-sort tptp.set_He475150555083384525t_unit 0)
% 6.70/7.10 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.70/7.10 (declare-sort tptp.list_P3521021558325789923at_int 0)
% 6.70/7.10 (declare-sort tptp.list_P8198026277950538467nt_nat 0)
% 6.70/7.10 (declare-sort tptp.list_P5707943133018811711nt_int 0)
% 6.70/7.10 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.70/7.10 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.70/7.10 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.70/7.10 (declare-sort tptp.list_P5087981734274514673_int_o 0)
% 6.70/7.10 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.70/7.10 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.70/7.10 (declare-sort tptp.set_set_list_nat 0)
% 6.70/7.10 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.70/7.10 (declare-sort tptp.set_set_set_nat 0)
% 6.70/7.10 (declare-sort tptp.set_set_Code_integer 0)
% 6.70/7.10 (declare-sort tptp.heap_T5738788834812785303t_unit 0)
% 6.70/7.10 (declare-sort tptp.heap_e7401611519738050253t_unit 0)
% 6.70/7.10 (declare-sort tptp.product_prod_num_num 0)
% 6.70/7.10 (declare-sort tptp.product_prod_nat_num 0)
% 6.70/7.10 (declare-sort tptp.product_prod_nat_nat 0)
% 6.70/7.10 (declare-sort tptp.product_prod_nat_int 0)
% 6.70/7.10 (declare-sort tptp.product_prod_int_nat 0)
% 6.70/7.10 (declare-sort tptp.product_prod_int_int 0)
% 6.70/7.10 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.70/7.10 (declare-sort tptp.set_Product_prod_o_o 0)
% 6.70/7.10 (declare-sort tptp.set_option_num 0)
% 6.70/7.10 (declare-sort tptp.option_set_nat 0)
% 6.70/7.10 (declare-sort tptp.option_set_int 0)
% 6.70/7.10 (declare-sort tptp.filter_set_nat 0)
% 6.70/7.10 (declare-sort tptp.option_Product_unit 0)
% 6.70/7.10 (declare-sort tptp.set_list_nat 0)
% 6.70/7.10 (declare-sort tptp.product_prod_nat_o 0)
% 6.70/7.10 (declare-sort tptp.product_prod_int_o 0)
% 6.70/7.10 (declare-sort tptp.product_prod_o_nat 0)
% 6.70/7.10 (declare-sort tptp.product_prod_o_int 0)
% 6.70/7.10 (declare-sort tptp.set_set_nat 0)
% 6.70/7.10 (declare-sort tptp.set_set_int 0)
% 6.70/7.10 (declare-sort tptp.set_Code_integer 0)
% 6.70/7.10 (declare-sort tptp.option_assn 0)
% 6.70/7.10 (declare-sort tptp.set_Product_unit 0)
% 6.70/7.10 (declare-sort tptp.option_set_o 0)
% 6.70/7.10 (declare-sort tptp.heap_Time_Heap_a 0)
% 6.70/7.10 (declare-sort tptp.set_list_o 0)
% 6.70/7.10 (declare-sort tptp.product_prod_o_o 0)
% 6.70/7.10 (declare-sort tptp.set_assn 0)
% 6.70/7.10 (declare-sort tptp.option_rat 0)
% 6.70/7.10 (declare-sort tptp.option_num 0)
% 6.70/7.10 (declare-sort tptp.option_nat 0)
% 6.70/7.10 (declare-sort tptp.option_int 0)
% 6.70/7.10 (declare-sort tptp.list_char 0)
% 6.70/7.10 (declare-sort tptp.filter_nat 0)
% 6.70/7.10 (declare-sort tptp.list_rat 0)
% 6.70/7.10 (declare-sort tptp.list_num 0)
% 6.70/7.10 (declare-sort tptp.list_nat 0)
% 6.70/7.10 (declare-sort tptp.list_int 0)
% 6.70/7.10 (declare-sort tptp.set_rat 0)
% 6.70/7.10 (declare-sort tptp.set_num 0)
% 6.70/7.10 (declare-sort tptp.set_nat 0)
% 6.70/7.10 (declare-sort tptp.set_int 0)
% 6.70/7.10 (declare-sort tptp.code_natural 0)
% 6.70/7.10 (declare-sort tptp.code_integer 0)
% 6.70/7.10 (declare-sort tptp.product_unit 0)
% 6.70/7.10 (declare-sort tptp.list_a 0)
% 6.70/7.10 (declare-sort tptp.list_o 0)
% 6.70/7.10 (declare-sort tptp.assn 0)
% 6.70/7.10 (declare-sort tptp.set_o 0)
% 6.70/7.10 (declare-sort tptp.rat 0)
% 6.70/7.10 (declare-sort tptp.num 0)
% 6.70/7.10 (declare-sort tptp.nat 0)
% 6.70/7.10 (declare-sort tptp.int 0)
% 6.70/7.10 (declare-sort tptp.a 0)
% 6.70/7.10 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.70/7.10 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.70/7.10 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.70/7.10 (declare-fun tptp.abs_assn ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.assn)
% 6.70/7.10 (declare-fun tptp.rep_assn (tptp.assn tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.entails (tptp.assn tptp.assn) Bool)
% 6.70/7.10 (declare-fun tptp.in_range (tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.in_range_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.one_assn_raw (tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.one_assn_raw_rel (tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.pure_assn (Bool) tptp.assn)
% 6.70/7.10 (declare-fun tptp.pure_a825153325127701367it_nat (Bool tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.pure_a6022498039421069578it_nat (tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.relH (tptp.set_nat tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 6.70/7.10 (declare-fun tptp.times_assn_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.times_assn_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.wand_assn (tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.wand_raw ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.wand_raw_rel (tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_Cardinal_cone () tptp.set_Pr5094982260447487303t_unit)
% 6.70/7.10 (declare-fun tptp.bNF_Cardinal_ctwo () tptp.set_Product_prod_o_o)
% 6.70/7.10 (declare-fun tptp.bNF_Cardinal_czero_o () tptp.set_Product_prod_o_o)
% 6.70/7.10 (declare-fun tptp.bNF_Ca7083678892733797993t_unit (tptp.set_Product_unit) tptp.set_Pr5094982260447487303t_unit)
% 6.70/7.10 (declare-fun tptp.bNF_Ca8331644756375544342r_on_o (tptp.set_o tptp.set_Product_prod_o_o) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_Ca8665028551170535155natLeq () tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.bNF_Ca8459412986667044542atLess () tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.bNF_re3403563459893282935_int_o ((-> tptp.int tptp.int Bool) (-> (-> tptp.int Bool) (-> tptp.int Bool) Bool) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_re157797125943740599nt_int ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.product_prod_int_int)) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_re3461391660133120880nt_rat ((-> tptp.int tptp.int Bool) (-> (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat) Bool) (-> tptp.int tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.int tptp.rat)) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_re5089333283451836215nt_o_o ((-> tptp.int tptp.int Bool) (-> Bool Bool Bool) (-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_re6250860962936578807nt_int ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.product_prod_int_int)) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_re2214769303045360666nt_rat ((-> tptp.int tptp.int Bool) (-> tptp.product_prod_int_int tptp.rat Bool) (-> tptp.int tptp.product_prod_int_int) (-> tptp.int tptp.rat)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_re4705727531993890431at_o_o ((-> tptp.nat tptp.nat Bool) (-> Bool Bool Bool) (-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_re8402795839162346335um_int ((-> tptp.num tptp.num Bool) (-> (-> tptp.num tptp.int) (-> tptp.num tptp.int) Bool) (-> tptp.num tptp.num tptp.int) (-> tptp.num tptp.num tptp.int)) Bool)
% 6.70/7.10 (declare-fun tptp.bNF_re1822329894187522285nt_int ((-> tptp.num tptp.num Bool) (-> tptp.int tptp.int Bool) (-> tptp.num tptp.int) (-> tptp.num tptp.int)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_re4555766996558763186at_nat ((-> tptp.product_prod_nat_nat tptp.int Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.int tptp.nat)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_re8246922863344978751at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.nat tptp.nat Bool) (-> tptp.product_prod_nat_nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat)) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.bNF_We2654380646378065620so_o_o () tptp.set_Pr1932065953672099015od_o_o)
% 6.70/7.10 (declare-fun tptp.bNF_We8182288985678559134_o_nat () tptp.set_Pr457366540195662369at_nat)
% 6.70/7.10 (declare-fun tptp.bNF_We3818239936649020644el_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.gbinom8545251970709558553nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.gbinom7368847122466276068atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.70/7.10 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se168947363167071951atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se943457434206027407atural (tptp.nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se1617098188084679374atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se569199155075624693atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se7083795435491715335atural (tptp.nat tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.bit_se2046307713759805098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.70/7.10 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.70/7.10 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.70/7.10 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.70/7.10 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.70/7.10 (declare-fun tptp.code_dup (tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.70/7.10 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.70/7.10 (declare-fun tptp.code_nat_of_natural (tptp.code_natural) tptp.nat)
% 6.70/7.10 (declare-fun tptp.code_natural_of_nat (tptp.nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.70/7.10 (declare-fun tptp.complete_Inf_Inf_nat (tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.comple2584293577114468500t_unit (tptp.set_Product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.comple4687483117567863418t_unit (tptp.set_Product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.70/7.10 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.70/7.10 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.70/7.10 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.euclid3395696857347342551nt_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.semiri2447717529341329178atural (tptp.nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.70/7.10 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.70/7.10 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.70/7.10 (declare-fun tptp.filter3212408913953519116et_nat ((-> tptp.nat tptp.set_nat) tptp.filter_set_nat tptp.filter_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite3254316476582989077op_nat (tptp.set_nat) tptp.filter_set_nat)
% 6.70/7.10 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite4902975817058060853nteger (tptp.set_Code_integer) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite7007076676225009423at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite711546835091564841at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite1207074278014112911at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite3771342082235030671at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite1340570857867686763nteger (tptp.set_set_Code_integer) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_card_set_int (tptp.set_set_int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite2364142230527598318st_nat (tptp.set_set_list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite4356350796350151305at_nat (tptp.set_se7855581050983116737at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite1149291290879098388et_nat (tptp.set_set_set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_assn (tptp.set_assn) Bool)
% 6.70/7.10 (declare-fun tptp.finite6017078050557962740nteger (tptp.set_Code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.70/7.10 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.70/7.10 (declare-fun tptp.finite2998713641127702882nt_int (tptp.set_Pr958786334691620121nt_int) Bool)
% 6.70/7.10 (declare-fun tptp.finite1918287321285529104at_nat (tptp.set_Pr8551490117392284871at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite6177210948735845034at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite4392333629123659920at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite4343798906461161616at_nat (tptp.set_Pr4329608150637261639at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.70/7.10 (declare-fun tptp.finite6931041176100689706nteger (tptp.set_set_Code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 6.70/7.10 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.finite9047747110432174090at_nat (tptp.set_se7855581050983116737at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.comp_int_nat_int ((-> tptp.int tptp.nat) (-> tptp.int tptp.int) tptp.int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.id_o (Bool) Bool)
% 6.70/7.10 (declare-fun tptp.id_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.map_fu2496120808607739376eger_o ((-> tptp.code_integer tptp.int) (-> (-> tptp.int Bool) tptp.code_integer Bool) (-> tptp.int tptp.int Bool) tptp.code_integer tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.map_fu6957801986076833569nt_o_o ((-> tptp.code_integer tptp.int) (-> Bool Bool) (-> tptp.int Bool) tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.map_fu2599414010547811884nteger ((-> tptp.code_integer tptp.int) (-> tptp.int tptp.code_integer) (-> tptp.int tptp.int) tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.map_fu6256889081107267320ural_o ((-> tptp.code_natural tptp.nat) (-> (-> tptp.nat Bool) tptp.code_natural Bool) (-> tptp.nat tptp.nat Bool) tptp.code_natural tptp.code_natural) Bool)
% 6.70/7.10 (declare-fun tptp.map_fu4892316939951275536at_o_o ((-> tptp.code_natural tptp.nat) (-> Bool Bool) (-> tptp.nat Bool) tptp.code_natural) Bool)
% 6.70/7.10 (declare-fun tptp.map_fu7831380289885515383nt_rat ((-> tptp.int tptp.int) (-> (-> tptp.int tptp.product_prod_int_int) tptp.int tptp.rat) (-> tptp.int tptp.int tptp.product_prod_int_int) tptp.int tptp.int) tptp.rat)
% 6.70/7.10 (declare-fun tptp.map_fu3424225382358772769nt_rat ((-> tptp.int tptp.int) (-> tptp.product_prod_int_int tptp.rat) (-> tptp.int tptp.product_prod_int_int) tptp.int) tptp.rat)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.map_fu2345160673673942751at_nat ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.nat tptp.nat) (-> tptp.product_prod_nat_nat tptp.nat) tptp.int) tptp.nat)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (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)
% 6.70/7.10 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.fun_max_strict () tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.fun_max_weak () tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.fun_min_strict () tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.fun_min_weak () tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.fun_pair_leq () tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.fun_pair_less () tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.fun_re7357418987779152907at_nat (tptp.produc4193628355235574503at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.fun_re2478310338295953701at_nat (tptp.produc1319942482725812455at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.minus_minus_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 6.70/7.10 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.minus_1139252259498527702_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.minus_711738161318947805_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.minus_2270307095948843157_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.minus_minus_assn (tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.minus_7197305767214868737atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.minus_4286766774447292334at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 6.70/7.10 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.minus_3524152463667985524t_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.minus_minus_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 6.70/7.10 (declare-fun tptp.minus_2355218937544613996nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 6.70/7.10 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.70/7.10 (declare-fun tptp.minus_7954133019191499631st_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.70/7.10 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.minus_minus_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 6.70/7.10 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.minus_5060654252129873198at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 6.70/7.10 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.minus_8321449233255521966at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.minus_3314409938677909166at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.minus_minus_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 6.70/7.10 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.70/7.10 (declare-fun tptp.one_one_assn () tptp.assn)
% 6.70/7.10 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.one_one_Code_natural () tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.one_one_int () tptp.int)
% 6.70/7.10 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.70/7.10 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.70/7.10 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.plus_p4538020629002901425atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.plus_p7104986032573967614at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 6.70/7.10 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.70/7.10 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.times_times_assn (tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.times_2397367101498566445atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.70/7.10 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_o_o ((-> Bool Bool) Bool) Bool)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_int_o ((-> tptp.int Bool) tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.uminus5770388063884162150_nat_o ((-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_nat_o ((-> tptp.nat Bool) tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.uminus7117520113953359693_int_o ((-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.uminus8676089048583255045_nat_o ((-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.uminus6401447641752708672_nat_o ((-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_assn (tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.uminus2952777764628376836t_unit (tptp.product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.uminus_uminus_set_o (tptp.set_o) tptp.set_o)
% 6.70/7.10 (declare-fun tptp.uminus804700908173204444nteger (tptp.set_Code_integer) tptp.set_Code_integer)
% 6.70/7.10 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.70/7.10 (declare-fun tptp.uminus3195874150345416415st_nat (tptp.set_list_nat) tptp.set_list_nat)
% 6.70/7.10 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.uminus6221592323253981072nt_int (tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.uminus2330091110623919550at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 6.70/7.10 (declare-fun tptp.uminus6524753893492686040at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.uminus4384627049435823934at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.uminus935396558254630718at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.uminus2201863774496077783et_rat (tptp.set_rat) tptp.set_rat)
% 6.70/7.10 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.70/7.10 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.zero_z2226904508553997617atural () tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.70/7.10 (declare-fun tptp.zero_z1048942125864253310at_nat () tptp.multis2468970476368604999at_nat)
% 6.70/7.10 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.70/7.10 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups4406642042086082107nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups8505340233167759370_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups8507830703676809646_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups7872700643590313910_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups879477027807139574nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups8926444216418632897atural ((-> tptp.code_integer tptp.code_natural) tptp.set_Code_integer) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.groups7234854612051535045er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups7237345082560585321er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups6602215022474089585er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups6697149243333190288atural ((-> tptp.int tptp.code_natural) tptp.set_int) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups4393565826250045896at_int ((-> tptp.list_nat tptp.int) tptp.set_list_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups4396056296759096172at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups3760926236672600436at_rat ((-> tptp.list_nat tptp.rat) tptp.set_list_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups6325495683096345652atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups6857163185585827899at_nat ((-> tptp.nat tptp.multis2468970476368604999at_nat) tptp.set_nat) tptp.multis2468970476368604999at_nat)
% 6.70/7.10 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups7059897769266147197at_nat ((-> tptp.produc4166570645942440679at_nat tptp.nat) tptp.set_Pr8551490117392284871at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups975429370522433651at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups342789780944988191at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups1898227913876290649at_int ((-> tptp.produc859450856879609959at_nat tptp.int) tptp.set_Pr8693737435421807431at_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups1900718384385340925at_nat ((-> tptp.produc859450856879609959at_nat tptp.nat) tptp.set_Pr8693737435421807431at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups1265588324298845189at_rat ((-> tptp.produc859450856879609959at_nat tptp.rat) tptp.set_Pr8693737435421807431at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups3860910324918113789at_nat ((-> tptp.produc3843707927480180839at_nat tptp.nat) tptp.set_Pr4329608150637261639at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups9190459664516455967nteger ((-> tptp.set_nat tptp.code_integer) tptp.set_set_nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups8292507037921071086at_int ((-> tptp.set_nat tptp.int) tptp.set_set_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups7659867448343625626at_rat ((-> tptp.set_nat tptp.rat) tptp.set_set_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups5301882518646026715o_assn ((-> Bool tptp.assn) tptp.set_o) tptp.assn)
% 6.70/7.10 (declare-fun tptp.groups7694694392188491536nteger ((-> Bool tptp.code_integer) tptp.set_o) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups3502327434004483295_o_int ((-> Bool tptp.int) tptp.set_o) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups3504817904513533571_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups2869687844427037835_o_rat ((-> Bool tptp.rat) tptp.set_o) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups1304777262505850412r_assn ((-> tptp.code_integer tptp.assn) tptp.set_Code_integer) tptp.assn)
% 6.70/7.10 (declare-fun tptp.groups3674199335183972705nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups3188404863801439024er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups3190895334310489300er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups2555765274223993564er_rat ((-> tptp.code_integer tptp.rat) tptp.set_Code_integer) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups7882442080178216443t_assn ((-> tptp.int tptp.assn) tptp.set_int) tptp.assn)
% 6.70/7.10 (declare-fun tptp.groups3827104343326376752nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups1707563613775114915nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups1072433553688619179nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups2905156660866384563at_int ((-> tptp.list_nat tptp.int) tptp.set_list_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups2907647131375434839at_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups6906906614972039071t_assn ((-> tptp.nat tptp.assn) tptp.set_nat) tptp.assn)
% 6.70/7.10 (declare-fun tptp.groups3455450783089532116nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups2279045934846249631atural ((-> tptp.nat tptp.code_natural) tptp.set_nat) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups5938585286922990810at_rat ((-> tptp.produc4166570645942440679at_nat tptp.rat) tptp.set_Pr8551490117392284871at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups4075276357253098568at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups4077766827762148844at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups3442636767675653108at_rat ((-> tptp.product_prod_nat_nat tptp.rat) tptp.set_Pr1261947904930325089at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups7136053025338371162at_rat ((-> tptp.produc859450856879609959at_nat tptp.rat) tptp.set_Pr8693737435421807431at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups8874911130973611098at_rat ((-> tptp.produc3843707927480180839at_nat tptp.rat) tptp.set_Pr4329608150637261639at_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups4246057289670975065at_int ((-> tptp.set_nat tptp.int) tptp.set_set_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups4248547760180025341at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups3417619833198082522nteger ((-> Bool tptp.code_integer) tptp.code_integer tptp.list_o) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups8483887719401441109_o_rat ((-> Bool tptp.rat) tptp.rat tptp.list_o) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups8594936613892548326nteger ((-> tptp.int tptp.code_integer) tptp.code_integer tptp.list_int) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups8485231416243008693nt_int ((-> tptp.int tptp.int) tptp.int tptp.list_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups8487721886752058969nt_nat ((-> tptp.int tptp.nat) tptp.nat tptp.list_int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups7852591826665563233nt_rat ((-> tptp.int tptp.rat) tptp.rat tptp.list_int) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups8223283053655703690nteger ((-> tptp.nat tptp.code_integer) tptp.code_integer tptp.list_nat) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.groups7485877704341954137at_int ((-> tptp.nat tptp.int) tptp.int tptp.list_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.groups7488368174851004413at_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.groups6853238114764508677at_rat ((-> tptp.nat tptp.rat) tptp.rat tptp.list_nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.nO_MAT8252062027627875367nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MAT8427913294028938742er_int (tptp.code_integer tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MAT7795273704451493282er_rat (tptp.code_integer tptp.rat) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MAT9066612773553876470nteger (tptp.int tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_int_int (tptp.int tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_int_nat (tptp.int tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_int_rat (tptp.int tptp.rat) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MAT8694959213317031834nteger (tptp.nat tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_nat_int (tptp.nat tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_nat_nat (tptp.nat tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_nat_rat (tptp.nat tptp.rat) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MAT243659986023775650nteger (tptp.rat tptp.code_integer) Bool)
% 6.70/7.10 (declare-fun tptp.nO_MATCH_rat_rat (tptp.rat tptp.rat) Bool)
% 6.70/7.10 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.70/7.10 (declare-fun tptp.the_Pr4378521158711661632nt_int ((-> tptp.product_prod_int_int Bool)) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.defaul566961228789861419t_unit () tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.lim_Product_unit (tptp.heap_e7401611519738050253t_unit) tptp.nat)
% 6.70/7.10 (declare-fun tptp.heap_T6183433275982383450t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat)) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_Heap_a2 ((-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat)) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T4436805183663264329t_unit (tptp.set_He475150555083384525t_unit) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_T4208721593536448476t_unit ((-> tptp.product_unit Bool) tptp.product_unit) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_assert_a ((-> tptp.a Bool) tptp.a) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T2633723481742716231t_unit (tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_T757603679106148408unit_a (tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.heap_Time_Heap_a)) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T8685611227969916822t_unit (tptp.heap_Time_Heap_a (-> tptp.a tptp.heap_T5738788834812785303t_unit)) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_bind_a_a (tptp.heap_Time_Heap_a (-> tptp.a tptp.heap_Time_Heap_a)) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T6553295506729943825t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.product_unit tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.heap_Time_effect_a (tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit tptp.heap_e7401611519738050253t_unit tptp.a tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.heap_T875086893843062177t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit) tptp.option8956607266484857688it_nat)
% 6.70/7.10 (declare-fun tptp.heap_Time_execute_a (tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit) tptp.option3562590408128118217it_nat)
% 6.70/7.10 (declare-fun tptp.heap_T8440541562793052209t_unit ((-> tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat)) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_guard_a ((-> tptp.heap_e7401611519738050253t_unit Bool) (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat)) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T2927564422264180874t_unit (tptp.list_char) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_raise_a (tptp.list_char) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T584514906347983379t_unit (tptp.heap_T5738788834812785303t_unit tptp.heap_e7401611519738050253t_unit) Bool)
% 6.70/7.10 (declare-fun tptp.heap_Time_success_a (tptp.heap_Time_Heap_a tptp.heap_e7401611519738050253t_unit) Bool)
% 6.70/7.10 (declare-fun tptp.heap_T560649228465745139t_unit ((-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.heap_Time_tap_a ((-> tptp.heap_e7401611519738050253t_unit tptp.a)) tptp.heap_Time_Heap_a)
% 6.70/7.10 (declare-fun tptp.heap_T3616969660504097270t_unit (tptp.nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 6.70/7.10 (declare-fun tptp.heap_T7616092557645711335rame_a (tptp.nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 6.70/7.10 (declare-fun tptp.heap_T996182799752388649t_unit (tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat) Bool)
% 6.70/7.10 (declare-fun tptp.heap_T8132184524487034138_rel_a (tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat) Bool)
% 6.70/7.10 (declare-fun tptp.heap_Time_wait (tptp.nat) tptp.heap_T5738788834812785303t_unit)
% 6.70/7.10 (declare-fun tptp.hoare_8945653483474564448t_unit (tptp.assn tptp.heap_T5738788834812785303t_unit (-> tptp.product_unit tptp.assn)) Bool)
% 6.70/7.10 (declare-fun tptp.hoare_hoare_triple_a (tptp.assn tptp.heap_Time_Heap_a (-> tptp.a tptp.assn)) Bool)
% 6.70/7.10 (declare-fun tptp.hoare_new_addrs (tptp.heap_e7401611519738050253t_unit tptp.set_nat tptp.heap_e7401611519738050253t_unit) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.if_assn (Bool tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.if_Code_natural (Bool tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.70/7.10 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.if_mul8430962117462786573at_nat (Bool tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 6.70/7.10 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.70/7.10 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.if_opt1729522071442692626it_nat (Bool tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 6.70/7.10 (declare-fun tptp.if_opt6883606601682554499it_nat (Bool tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 6.70/7.10 (declare-fun tptp.if_option_set_o (Bool tptp.option_set_o tptp.option_set_o) tptp.option_set_o)
% 6.70/7.10 (declare-fun tptp.if_option_set_int (Bool tptp.option_set_int tptp.option_set_int) tptp.option_set_int)
% 6.70/7.10 (declare-fun tptp.if_option_set_nat (Bool tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 6.70/7.10 (declare-fun tptp.if_opt7704869406773131885at_nat (Bool tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 6.70/7.10 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.70/7.10 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.70/7.10 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.if_Pro4507677147265585453at_nat (Bool tptp.produc859450856879609959at_nat tptp.produc859450856879609959at_nat) tptp.produc859450856879609959at_nat)
% 6.70/7.10 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.70/7.10 (declare-fun tptp.if_set_nat (Bool tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.infini8530281810654367211te_nat (tptp.set_nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.intrel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.70/7.10 (declare-fun tptp.pcr_int (tptp.product_prod_nat_nat tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 6.70/7.10 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 6.70/7.10 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 6.70/7.10 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.70/7.10 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.70/7.10 (declare-fun tptp.inf_in8201999774870019094_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in2641120393918057659_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in3295504058751909687_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in8045883074377559328_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in3604695632404883862_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in5163264567034779214_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_in8051596381320575356_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) (-> tptp.a tptp.produc6653097349344004940it_nat Bool) tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 6.70/7.10 (declare-fun tptp.inf_inf_assn (tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.inf_inf_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.inf_inf_option_assn (tptp.option_assn tptp.option_assn) tptp.option_assn)
% 6.70/7.10 (declare-fun tptp.inf_inf_option_nat (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.70/7.10 (declare-fun tptp.inf_in5800606384722953409t_unit (tptp.option_Product_unit tptp.option_Product_unit) tptp.option_Product_unit)
% 6.70/7.10 (declare-fun tptp.inf_in7812914138253463912et_nat (tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 6.70/7.10 (declare-fun tptp.inf_in777885744494410645at_nat (tptp.option8963830502488799655at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 6.70/7.10 (declare-fun tptp.inf_inf_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.inf_inf_rat (tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 6.70/7.10 (declare-fun tptp.inf_in1364745209274528805nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.inf_in8806012763027673301nt_int (tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int) tptp.set_Pr1872883991513573699nt_int)
% 6.70/7.10 (declare-fun tptp.inf_in3088352823822785602et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 6.70/7.10 (declare-fun tptp.inf_in1768905781608824518et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 6.70/7.10 (declare-fun tptp.inf_in2576786181675586251nt_int (tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int) tptp.set_Pr9222295170931077689nt_int)
% 6.70/7.10 (declare-fun tptp.inf_in2269163501485487111nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.inf_in1697001100524423349at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 6.70/7.10 (declare-fun tptp.inf_in2572325071724192079at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.inf_in4302113700860409141at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.inf_in7913087082777306421at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.inf_in3493107508024165057it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) tptp.set_Pr7098220151150636591it_nat)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 6.70/7.10 (declare-fun tptp.inf_inf_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.70/7.10 (declare-fun tptp.semila8603258263270017530r_assn ((-> tptp.assn tptp.assn tptp.assn) tptp.assn (-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila2554085542299052326_set_o ((-> tptp.set_o tptp.set_o tptp.set_o) tptp.set_o (-> tptp.set_o tptp.set_o Bool) (-> tptp.set_o tptp.set_o Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila6712789903965657268et_int ((-> tptp.set_int tptp.set_int tptp.set_int) tptp.set_int (-> tptp.set_int tptp.set_int Bool) (-> tptp.set_int tptp.set_int Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila1667268886620078168et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) tptp.set_nat (-> tptp.set_nat tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila5207306265035627125at_nat ((-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat (-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool) (-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila4918476307565957903at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila1307241728879085301at_nat ((-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat Bool) (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.semila6534579987270727413at_nat ((-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool) (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su600977994968626096_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su6535292691877529429_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su1630790145277462993_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su4182031696650224058_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_o_o ((-> Bool Bool) (-> Bool Bool) Bool) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_list_nat_o ((-> tptp.list_nat Bool) (-> tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su2200014604384089602_nat_o ((-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool) (-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat Bool) tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_nat_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su8463660629351352368_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su6256023009775730178_nat_o ((-> tptp.produc4166570645942440679at_nat Bool) (-> tptp.produc4166570645942440679at_nat Bool) tptp.produc4166570645942440679at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su362511073950362882_nat_o ((-> 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) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su798857527126471912_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su8986005896011022210_nat_o ((-> tptp.produc859450856879609959at_nat Bool) (-> tptp.produc859450856879609959at_nat Bool) tptp.produc859450856879609959at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su2080679670758317954_nat_o ((-> tptp.produc3843707927480180839at_nat Bool) (-> tptp.produc3843707927480180839at_nat Bool) tptp.produc3843707927480180839at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su7519161239522478338_nat_o ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_su2191776239474528790_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) (-> tptp.a tptp.produc6653097349344004940it_nat Bool) tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sup_sup_assn (tptp.assn tptp.assn) tptp.assn)
% 6.70/7.10 (declare-fun tptp.sup_sup_int (tptp.int tptp.int) tptp.int)
% 6.70/7.10 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.sup_sup_option_nat (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.70/7.10 (declare-fun tptp.sup_su3598758113090618626et_nat (tptp.option_set_nat tptp.option_set_nat) tptp.option_set_nat)
% 6.70/7.10 (declare-fun tptp.sup_su5873096292857799009at_nat (tptp.option2498585697089621389at_nat tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su1419176701018045153at_nat (tptp.option2158460348403737357at_nat tptp.option2158460348403737357at_nat) tptp.option2158460348403737357at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su2273273666271716065at_nat (tptp.option1583680563626158861at_nat tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat)
% 6.70/7.10 (declare-fun tptp.sup_sup_Product_unit (tptp.product_unit tptp.product_unit) tptp.product_unit)
% 6.70/7.10 (declare-fun tptp.sup_sup_rat (tptp.rat tptp.rat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_o (tptp.set_o tptp.set_o) tptp.set_o)
% 6.70/7.10 (declare-fun tptp.sup_su848401254843788991nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.set_Code_integer)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_list_nat (tptp.set_list_nat tptp.set_list_nat) tptp.set_list_nat)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_num (tptp.set_num tptp.set_num) tptp.set_num)
% 6.70/7.10 (declare-fun tptp.sup_su3298353300217089135nt_int (tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int) tptp.set_Pr1872883991513573699nt_int)
% 6.70/7.10 (declare-fun tptp.sup_su8975264963432250076et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) tptp.set_Pr8536935166611901872et_nat)
% 6.70/7.10 (declare-fun tptp.sup_su7128418612487073120et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) tptp.set_Pr3286484037609594932et_nat)
% 6.70/7.10 (declare-fun tptp.sup_su3382966977382714213nt_int (tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int) tptp.set_Pr9222295170931077689nt_int)
% 6.70/7.10 (declare-fun tptp.sup_su6024340866399070445nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.sup_su3035147773818789531at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.set_Pr8551490117392284871at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su6327502436637775413at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su718114333110466843at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su5525570899277871387at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.70/7.10 (declare-fun tptp.sup_su3211442154794319707it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) tptp.set_Pr7098220151150636591it_nat)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_rat (tptp.set_rat tptp.set_rat) tptp.set_rat)
% 6.70/7.10 (declare-fun tptp.sup_sup_set_set_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.70/7.10 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.70/7.10 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.lattic5623431474481994958t_assn ((-> tptp.assn tptp.assn tptp.assn) (-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic6006661108824415698et_int ((-> tptp.int tptp.int tptp.int) (-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic6009151579333465974et_nat ((-> tptp.nat tptp.nat tptp.nat) (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic5111740090977526247t_unit ((-> tptp.product_unit tptp.product_unit tptp.product_unit) (-> tptp.product_unit tptp.product_unit Bool) (-> tptp.product_unit tptp.product_unit Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic5374021519246970238et_rat ((-> tptp.rat tptp.rat tptp.rat) (-> tptp.rat tptp.rat Bool) (-> tptp.rat tptp.rat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic8154731777541915528et_int ((-> tptp.set_int tptp.set_int tptp.set_int) (-> tptp.set_int tptp.set_int Bool) (-> tptp.set_int tptp.set_int Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic3109210760196336428et_nat ((-> tptp.set_nat tptp.set_nat tptp.set_nat) (-> tptp.set_nat tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic5174734335190411425at_nat ((-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) (-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool) (-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic6529551498584149819at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic5672175589177086241at_nat ((-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat Bool) (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.lattic6976360593897529633at_nat ((-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool) (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat Bool)) Bool)
% 6.70/7.10 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.butlast_nat (tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.enumerate_o (tptp.nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.70/7.10 (declare-fun tptp.enumerate_int (tptp.nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 6.70/7.10 (declare-fun tptp.enumerate_nat (tptp.nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.70/7.10 (declare-fun tptp.filter_nat2 ((-> tptp.nat Bool) tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.last_nat (tptp.list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.nil_int () tptp.list_int)
% 6.70/7.10 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.70/7.10 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.70/7.10 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.70/7.10 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.70/7.10 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.70/7.10 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.70/7.10 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.70/7.10 (declare-fun tptp.nth_Pr4561283279332054789it_nat (tptp.list_P131111800688179804it_nat tptp.nat) tptp.produc6653097349344004940it_nat)
% 6.70/7.10 (declare-fun tptp.nth_Pr7514405829937366042_int_o (tptp.list_P5087981734274514673_int_o tptp.nat) tptp.product_prod_int_o)
% 6.70/7.10 (declare-fun tptp.nth_Pr4439495888332055232nt_int (tptp.list_P5707943133018811711nt_int tptp.nat) tptp.product_prod_int_int)
% 6.70/7.10 (declare-fun tptp.nth_Pr8617346907841251940nt_nat (tptp.list_P8198026277950538467nt_nat tptp.nat) tptp.product_prod_int_nat)
% 6.70/7.10 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.70/7.10 (declare-fun tptp.nth_Pr3440142176431000676at_int (tptp.list_P3521021558325789923at_int tptp.nat) tptp.product_prod_nat_int)
% 6.70/7.10 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.70/7.10 (declare-fun tptp.nth_Pr8687047199098054322it_nat (tptp.list_P6935614879863011209it_nat tptp.nat) tptp.produc3260487557148687353it_nat)
% 6.70/7.10 (declare-fun tptp.nth_rat (tptp.list_rat tptp.nat) tptp.rat)
% 6.70/7.10 (declare-fun tptp.nth_a (tptp.list_a tptp.nat) tptp.a)
% 6.70/7.10 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.70/7.10 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.70/7.10 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.70/7.10 (declare-fun tptp.product_int_o (tptp.list_int tptp.list_o) tptp.list_P5087981734274514673_int_o)
% 6.70/7.10 (declare-fun tptp.product_int_int (tptp.list_int tptp.list_int) tptp.list_P5707943133018811711nt_int)
% 6.70/7.10 (declare-fun tptp.product_int_nat (tptp.list_int tptp.list_nat) tptp.list_P8198026277950538467nt_nat)
% 6.70/7.10 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.70/7.10 (declare-fun tptp.product_nat_int (tptp.list_nat tptp.list_int) tptp.list_P3521021558325789923at_int)
% 6.70/7.10 (declare-fun tptp.product_nat_nat (tptp.list_nat tptp.list_nat) tptp.list_P6011104703257516679at_nat)
% 6.70/7.10 (declare-fun tptp.produc6966004487978991557it_nat (tptp.list_a tptp.list_P131111800688179804it_nat) tptp.list_P6935614879863011209it_nat)
% 6.70/7.10 (declare-fun tptp.rotate1_o (tptp.list_o) tptp.list_o)
% 6.70/7.10 (declare-fun tptp.rotate1_int (tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.rotate1_nat (tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.sorted_wrt_o ((-> Bool Bool Bool) tptp.list_o) Bool)
% 6.70/7.10 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.70/7.10 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.70/7.10 (declare-fun tptp.sorted_wrt_num ((-> tptp.num tptp.num Bool) tptp.list_num) Bool)
% 6.70/7.10 (declare-fun tptp.sorted_wrt_rat ((-> tptp.rat tptp.rat Bool) tptp.list_rat) Bool)
% 6.70/7.10 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.70/7.10 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.70/7.10 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.70/7.10 (declare-fun tptp.eps_Opt_nat ((-> tptp.nat Bool)) tptp.option_nat)
% 6.70/7.10 (declare-fun tptp.eps_Opt_num ((-> tptp.num Bool)) tptp.option_num)
% 6.70/7.10 (declare-fun tptp.eps_Op6423059015816587746et_nat ((-> tptp.produc3925858234332021118et_nat Bool)) tptp.option5190343406534369742et_nat)
% 6.70/7.10 (declare-fun tptp.eps_Op8301357815426737072it_nat ((-> tptp.produc6653097349344004940it_nat Bool)) tptp.option233860712434008220it_nat)
% 6.70/7.10 (declare-fun tptp.eps_Op2013419657081471078et_nat ((-> tptp.produc3658429121746597890et_nat Bool)) tptp.option936205604648967762et_nat)
% 6.70/7.10 (declare-fun tptp.eps_Op2446201859369042517nt_int ((-> tptp.product_prod_int_int Bool)) tptp.option4624381673175914239nt_int)
% 6.70/7.10 (declare-fun tptp.eps_Op3393321821070424684it_nat ((-> tptp.produc8664842809031399944it_nat Bool)) tptp.option8956607266484857688it_nat)
% 6.70/7.10 (declare-fun tptp.eps_Op1741419982095519837it_nat ((-> tptp.produc3260487557148687353it_nat Bool)) tptp.option3562590408128118217it_nat)
% 6.70/7.10 (declare-fun tptp.biject576505603616484041nt_int (tptp.set_Pr1872883991513573699nt_int) Bool)
% 6.70/7.10 (declare-fun tptp.biject1468766312547416318et_nat (tptp.set_Pr8536935166611901872et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.biject2615096655818420098et_nat (tptp.set_Pr3286484037609594932et_nat) Bool)
% 6.70/7.10 (declare-fun tptp.biject383251550997737151nt_int (tptp.set_Pr9222295170931077689nt_int) Bool)
% 6.70/7.10 (declare-fun tptp.bijective_nat_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.70/7.10 (declare-fun tptp.biject8592306251674886141it_nat (tptp.set_Pr7098220151150636591it_nat) Bool)
% 6.70/7.10 (declare-fun tptp.dflt_None_set_o (tptp.set_o) tptp.option_set_o)
% 6.70/7.10 (declare-fun tptp.dflt_None_set_int (tptp.set_int) tptp.option_set_int)
% 6.70/7.10 (declare-fun tptp.dflt_None_set_nat (tptp.set_nat) tptp.option_set_nat)
% 6.70/7.10 (declare-fun tptp.dflt_N6592383573632408824at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.option8963830502488799655at_nat)
% 6.70/7.10 (declare-fun tptp.map_to_set_int_int ((-> tptp.int tptp.option_int)) tptp.set_Pr958786334691620121nt_int)
% 6.70/7.10 (declare-fun tptp.map_to_set_nat_nat ((-> tptp.nat tptp.option_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.70/7.10 (declare-fun tptp.pairse3534876335208825186e_term ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc6576344331059438605e_term)
% 6.70/7.10 (declare-fun tptp.pairse6848479906795794847e_term (tptp.produc7773217078559923341nt_int tptp.produc7773217078559923341nt_int) Bool)
% 6.70/7.10 (declare-fun tptp.rel_of5543720577181062686nt_int ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.option4624381673175914239nt_int) (-> tptp.produc7773217078559923341nt_int Bool)) tptp.set_Pr1872883991513573699nt_int)
% 6.70/7.10 (declare-fun tptp.rel_of7774016450764239315et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option5190343406534369742et_nat) (-> tptp.produc2732055786443039994et_nat Bool)) tptp.set_Pr8536935166611901872et_nat)
% 6.75/7.10 (declare-fun tptp.rel_of4838799251197538391et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option936205604648967762et_nat) (-> tptp.produc3925858234332021118et_nat Bool)) tptp.set_Pr3286484037609594932et_nat)
% 6.75/7.10 (declare-fun tptp.rel_of8306664904814525588nt_int ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.option4624381673175914239nt_int) (-> tptp.produc2285326912895808259nt_int Bool)) tptp.set_Pr9222295170931077689nt_int)
% 6.75/7.10 (declare-fun tptp.rel_of_int_int ((-> tptp.int tptp.option_int) (-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.10 (declare-fun tptp.rel_of_nat_nat ((-> tptp.nat tptp.option_nat) (-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.rel_of2761222537318653906it_nat ((-> tptp.a tptp.option233860712434008220it_nat) (-> tptp.produc3260487557148687353it_nat Bool)) tptp.set_Pr7098220151150636591it_nat)
% 6.75/7.10 (declare-fun tptp.set_to1653371902132773855nt_int (tptp.set_Pr1872883991513573699nt_int (-> tptp.int tptp.option6357759511663192854e_term)) tptp.option4624381673175914239nt_int)
% 6.75/7.10 (declare-fun tptp.set_to2047380710992656148et_nat (tptp.set_Pr8536935166611901872et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.option5190343406534369742et_nat)
% 6.75/7.10 (declare-fun tptp.set_to6040779677306527128et_nat (tptp.set_Pr3286484037609594932et_nat (-> tptp.produc3658429121746597890et_nat Bool)) tptp.option936205604648967762et_nat)
% 6.75/7.10 (declare-fun tptp.set_to6585427216324510421nt_int (tptp.set_Pr9222295170931077689nt_int (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) tptp.option4624381673175914239nt_int)
% 6.75/7.10 (declare-fun tptp.set_to_map_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.option_nat)
% 6.75/7.10 (declare-fun tptp.set_to2008915276733485075it_nat (tptp.set_Pr7098220151150636591it_nat tptp.a) tptp.option233860712434008220it_nat)
% 6.75/7.10 (declare-fun tptp.slice_o (tptp.nat tptp.nat tptp.list_o) tptp.list_o)
% 6.75/7.10 (declare-fun tptp.slice_int (tptp.nat tptp.nat tptp.list_int) tptp.list_int)
% 6.75/7.10 (declare-fun tptp.slice_nat (tptp.nat tptp.nat tptp.list_nat) tptp.list_nat)
% 6.75/7.10 (declare-fun tptp.the_default_num (tptp.num tptp.option_num) tptp.num)
% 6.75/7.10 (declare-fun tptp.the_de2487931475039285041it_nat (tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) tptp.produc8664842809031399944it_nat)
% 6.75/7.10 (declare-fun tptp.the_de542837501814275618it_nat (tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) tptp.produc3260487557148687353it_nat)
% 6.75/7.10 (declare-fun tptp.the_default_set_o (tptp.set_o tptp.option_set_o) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.the_default_set_int (tptp.set_int tptp.option_set_int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.the_default_set_nat (tptp.set_nat tptp.option_set_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.the_de3668382347305825784at_nat (tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.uncurry_int_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.uncurry_int_int_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.75/7.10 (declare-fun tptp.uncurr7650761721940715016nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.uncurr7511940902602773877_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.uncurr8011562610307062878at_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)
% 6.75/7.10 (declare-fun tptp.add_ms2612439473150266591at_nat (tptp.product_prod_nat_nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 6.75/7.10 (declare-fun tptp.ms_strict () tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.ms_weak () tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.pw_leq (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.set_ms8126754132646256062at_nat (tptp.multis2468970476368604999at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.semiri3763490453095760265atural (tptp.nat) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.75/7.10 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.75/7.10 (declare-fun tptp.semiri4055485073559036834nteger ((-> tptp.code_integer tptp.code_integer) tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.75/7.10 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.75/7.10 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_s341701280123345136it_nat (tptp.list_P131111800688179804it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_list_rat (tptp.list_rat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_list_a (tptp.list_a) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_s8510653225128441779at_nat (tptp.multis2468970476368604999at_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_s8766407808098229740it_nat (tptp.option8956607266484857688it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_s2363601347547812957it_nat (tptp.option3562590408128118217it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.10 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.75/7.10 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.75/7.10 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.75/7.10 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.75/7.10 (declare-fun tptp.one () tptp.num)
% 6.75/7.10 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.75/7.10 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.numera5444537566228673987atural (tptp.num) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.75/7.10 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.75/7.10 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.combine_options_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.combin4318129983670048329it_nat ((-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat) tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.combin5819755802923621690it_nat ((-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.none_assn () tptp.option_assn)
% 6.75/7.10 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.75/7.10 (declare-fun tptp.none_num () tptp.option_num)
% 6.75/7.10 (declare-fun tptp.none_P3773570700014501484nt_int () tptp.option4256020574406277085nt_int)
% 6.75/7.10 (declare-fun tptp.none_P199884684680593241et_nat () tptp.option2860828798490689354et_nat)
% 6.75/7.10 (declare-fun tptp.none_P4972525538344268765et_nat () tptp.option5190343406534369742et_nat)
% 6.75/7.10 (declare-fun tptp.none_P1286213070022356066nt_int () tptp.option7541221861074943443nt_int)
% 6.75/7.10 (declare-fun tptp.none_P9117596204409417319it_nat () tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.none_P2651198173097904984it_nat () tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.none_Product_unit () tptp.option_Product_unit)
% 6.75/7.10 (declare-fun tptp.none_set_o () tptp.option_set_o)
% 6.75/7.10 (declare-fun tptp.none_set_int () tptp.option_set_int)
% 6.75/7.10 (declare-fun tptp.none_set_nat () tptp.option_set_nat)
% 6.75/7.10 (declare-fun tptp.none_s625347054029921090at_nat () tptp.option8963830502488799655at_nat)
% 6.75/7.10 (declare-fun tptp.some_assn (tptp.assn) tptp.option_assn)
% 6.75/7.10 (declare-fun tptp.some_int (tptp.int) tptp.option_int)
% 6.75/7.10 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.75/7.10 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.some_P7455497367792166888nt_int (tptp.produc7773217078559923341nt_int) tptp.option4256020574406277085nt_int)
% 6.75/7.10 (declare-fun tptp.some_P1630309045189364437et_nat (tptp.produc2732055786443039994et_nat) tptp.option2860828798490689354et_nat)
% 6.75/7.10 (declare-fun tptp.some_P750831030444334937et_nat (tptp.produc3925858234332021118et_nat) tptp.option5190343406534369742et_nat)
% 6.75/7.10 (declare-fun tptp.some_P2355398578364412894nt_int (tptp.produc2285326912895808259nt_int) tptp.option7541221861074943443nt_int)
% 6.75/7.10 (declare-fun tptp.some_P1054239925786823975it_nat (tptp.produc6653097349344004940it_nat) tptp.option233860712434008220it_nat)
% 6.75/7.10 (declare-fun tptp.some_P624177172695371229et_nat (tptp.produc3658429121746597890et_nat) tptp.option936205604648967762et_nat)
% 6.75/7.10 (declare-fun tptp.some_P4184893108420464158nt_int (tptp.product_prod_int_int) tptp.option4624381673175914239nt_int)
% 6.75/7.10 (declare-fun tptp.some_P1914260805536162275it_nat (tptp.produc8664842809031399944it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.some_P7913643980934408916it_nat (tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.some_Product_unit (tptp.product_unit) tptp.option_Product_unit)
% 6.75/7.10 (declare-fun tptp.some_rat (tptp.rat) tptp.option_rat)
% 6.75/7.10 (declare-fun tptp.some_set_o (tptp.set_o) tptp.option_set_o)
% 6.75/7.10 (declare-fun tptp.some_set_int (tptp.set_int) tptp.option_set_int)
% 6.75/7.10 (declare-fun tptp.some_set_nat (tptp.set_nat) tptp.option_set_nat)
% 6.75/7.10 (declare-fun tptp.some_s287724117700012716at_nat (tptp.set_Pr8551490117392284871at_nat) tptp.option2498585697089621389at_nat)
% 6.75/7.10 (declare-fun tptp.some_s147305329494351046at_nat (tptp.set_Pr1261947904930325089at_nat) tptp.option8963830502488799655at_nat)
% 6.75/7.10 (declare-fun tptp.some_s579751585967276588at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.option2158460348403737357at_nat)
% 6.75/7.10 (declare-fun tptp.some_s5890477192898017836at_nat (tptp.set_Pr4329608150637261639at_nat) tptp.option1583680563626158861at_nat)
% 6.75/7.10 (declare-fun tptp.case_option_o_assn (Bool (-> tptp.assn Bool) tptp.option_assn) Bool)
% 6.75/7.10 (declare-fun tptp.case_option_o_int (Bool (-> tptp.int Bool) tptp.option_int) Bool)
% 6.75/7.10 (declare-fun tptp.case_option_o_nat (Bool (-> tptp.nat Bool) tptp.option_nat) Bool)
% 6.75/7.10 (declare-fun tptp.case_option_o_num (Bool (-> tptp.num Bool) tptp.option_num) Bool)
% 6.75/7.10 (declare-fun tptp.case_o2686588417244861013it_nat (Bool (-> tptp.produc8664842809031399944it_nat Bool) tptp.option8956607266484857688it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.case_o3267218206291580230it_nat (Bool (-> tptp.produc3260487557148687353it_nat Bool) tptp.option3562590408128118217it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.case_option_o_rat (Bool (-> tptp.rat Bool) tptp.option_rat) Bool)
% 6.75/7.10 (declare-fun tptp.case_o223999843215110191et_int (Bool (-> tptp.set_int Bool) tptp.option_set_int) Bool)
% 6.75/7.10 (declare-fun tptp.case_o356765784539232260er_num (tptp.code_integer (-> tptp.num tptp.code_integer) tptp.option_num) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.case_o5621594795226839503al_num (tptp.code_natural (-> tptp.num tptp.code_natural) tptp.option_num) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.75/7.10 (declare-fun tptp.case_option_nat_num (tptp.nat (-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.75/7.10 (declare-fun tptp.case_o4484465799723439917n_assn (tptp.option_assn (-> tptp.assn tptp.option_assn) tptp.option_assn) tptp.option_assn)
% 6.75/7.10 (declare-fun tptp.case_o7429725398727453821at_nat (tptp.option_nat (-> tptp.nat tptp.option_nat) tptp.option_nat) tptp.option_nat)
% 6.75/7.10 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.case_o2963978774867076333it_nat (tptp.option8956607266484857688it_nat (-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.case_o7727800614283616222it_nat (tptp.option8956607266484857688it_nat (-> tptp.produc3260487557148687353it_nat tptp.option8956607266484857688it_nat) tptp.option3562590408128118217it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.case_o6061097939050036047it_nat (tptp.option3562590408128118217it_nat (-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat) tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.case_o2985186191577459077t_unit (tptp.option_Product_unit (-> tptp.product_unit tptp.option_Product_unit) tptp.option_Product_unit) tptp.option_Product_unit)
% 6.75/7.10 (declare-fun tptp.case_o4054078431260844265et_nat (tptp.option_set_nat (-> tptp.set_nat tptp.option_set_nat) tptp.option_set_nat) tptp.option_set_nat)
% 6.75/7.10 (declare-fun tptp.case_o8757249484648823045at_nat (tptp.option2498585697089621389at_nat (-> tptp.set_Pr8551490117392284871at_nat tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat) tptp.option2498585697089621389at_nat)
% 6.75/7.10 (declare-fun tptp.case_o311359030874850053at_nat (tptp.option8963830502488799655at_nat (-> tptp.set_Pr1261947904930325089at_nat tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat) tptp.option8963830502488799655at_nat)
% 6.75/7.10 (declare-fun tptp.case_o7467001542679133189at_nat (tptp.option2158460348403737357at_nat (-> tptp.set_Pr8693737435421807431at_nat tptp.option2158460348403737357at_nat) tptp.option2158460348403737357at_nat) tptp.option2158460348403737357at_nat)
% 6.75/7.10 (declare-fun tptp.case_o9080059180780454917at_nat (tptp.option1583680563626158861at_nat (-> tptp.set_Pr4329608150637261639at_nat tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat) tptp.option1583680563626158861at_nat)
% 6.75/7.10 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_o29782932136985253it_nat ((-> tptp.produc8664842809031399944it_nat tptp.nat) tptp.option8956607266484857688it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.size_o1731029420616209814it_nat ((-> tptp.produc3260487557148687353it_nat tptp.nat) tptp.option3562590408128118217it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.order_underS_nat (tptp.set_Pr1261947904930325089at_nat tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.order_2888998067076097458on_nat (tptp.set_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo1403522918969695512_int_o ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo3790638025767943357_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo5580076615179976505_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo8662317086119403298_int_o ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_o_o (Bool) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_int_o (tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_list_nat_o (tptp.list_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_nat_nat_o (tptp.nat tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_nat_o (tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo8147686125503663512_int_o (tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo482883023278783056_nat_o (tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_nat_o (tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bo3200480807726169982_nat_o (tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_o () Bool)
% 6.75/7.10 (declare-fun tptp.bot_bot_assn () tptp.assn)
% 6.75/7.10 (declare-fun tptp.bot_bot_filter_nat () tptp.filter_nat)
% 6.75/7.10 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.75/7.10 (declare-fun tptp.bot_bot_option_num () tptp.option_num)
% 6.75/7.10 (declare-fun tptp.bot_bot_Product_unit () tptp.product_unit)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_o () tptp.set_o)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_assn () tptp.set_assn)
% 6.75/7.10 (declare-fun tptp.bot_bo3990330152332043303nteger () tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.bot_bo8105976889876132193t_unit () tptp.set_He475150555083384525t_unit)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_list_nat () tptp.set_list_nat)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.75/7.10 (declare-fun tptp.bot_bo4508923176915781079nt_int () tptp.set_Pr1872883991513573699nt_int)
% 6.75/7.10 (declare-fun tptp.bot_bo5635537948650799172et_nat () tptp.set_Pr8536935166611901872et_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo1481135142794719944et_nat () tptp.set_Pr3286484037609594932et_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo572930865798478029nt_int () tptp.set_Pr9222295170931077689nt_int)
% 6.75/7.10 (declare-fun tptp.bot_bo1796632182523588997nt_int () tptp.set_Pr958786334691620121nt_int)
% 6.75/7.10 (declare-fun tptp.bot_bo8422036546324065075at_nat () tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo2099793752762293965at_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo5327735625951526323at_nat () tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo228742789529271731at_nat () tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo8480459777671986371it_nat () tptp.set_Pr7098220151150636591it_nat)
% 6.75/7.10 (declare-fun tptp.bot_bo3957492148770167129t_unit () tptp.set_Product_unit)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 6.75/7.10 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.ord_Least_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.75/7.10 (declare-fun tptp.ord_less_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le549003669493604880_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_o (Bool Bool) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_assn (tptp.assn tptp.assn) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le5570908160329646204atural (tptp.code_natural tptp.code_natural) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_option_assn (tptp.option_assn tptp.option_assn) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_option_int (tptp.option_int tptp.option_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_option_nat (tptp.option_nat tptp.option_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_option_num (tptp.option_num tptp.option_num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_option_rat (tptp.option_rat tptp.option_rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le361264281704409273t_unit (tptp.product_unit tptp.product_unit) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_o (tptp.set_o tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_assn (tptp.set_assn tptp.set_assn) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1190675801316882794st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le7642048601412989811at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6428140832669894131at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2604355607129572851at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2124322318746777828_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6753239538765779593_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le8000401564054156549_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le5643404153117327598_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_o_o ((-> Bool Bool) (-> Bool Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2646555220125990790_nat_o ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le7226304311989208114_nat_o ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1658592502415435381_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc2732055786443039994et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3355651325779393058_nat_o ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le729326519192465773_nat_o ((-> tptp.produc3658429121746597890et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1598226405681992910_int_o ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le8369615600986905444_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le5604493270027003598_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2556027599737686990_num_o ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2239182809043710856_num_o ((-> tptp.product_prod_num_num Bool) (-> tptp.product_prod_num_num Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le7992815620007647562_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_o (Bool Bool) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_assn (tptp.assn tptp.assn) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1926595141338095240atural (tptp.code_natural tptp.code_natural) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1736525451366464988on_int (tptp.option_int tptp.option_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le5914376470875661696on_nat (tptp.option_nat tptp.option_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6622620407824499402on_num (tptp.option_num tptp.option_num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2406147912482264968on_rat (tptp.option_rat tptp.option_rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le353528952715127954et_int (tptp.option_set_int tptp.option_set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3221252021190050221t_unit (tptp.product_unit tptp.product_unit) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_assn (tptp.set_assn tptp.set_assn) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le135402666524580259nt_int (tptp.set_Pr1872883991513573699nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le4763372923235995152et_nat (tptp.set_Pr8536935166611901872et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le5966269811547037844et_nat (tptp.set_Pr3286484037609594932et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le8725513860283290265nt_int (tptp.set_Pr9222295170931077689nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le8081472938463900775at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le3000389064537975527at_nat (tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le1268244103169919719at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le4478181985103859343it_nat (tptp.set_Pr7098220151150636591it_nat tptp.set_Pr7098220151150636591it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.75/7.10 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.75/7.10 (declare-fun tptp.ordering_top_assn ((-> tptp.assn tptp.assn Bool) (-> tptp.assn tptp.assn Bool) tptp.assn) Bool)
% 6.75/7.10 (declare-fun tptp.ordering_top_nat ((-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.ordering_top_set_o ((-> tptp.set_o tptp.set_o Bool) (-> tptp.set_o tptp.set_o Bool) tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.ordering_top_set_int ((-> tptp.set_int tptp.set_int Bool) (-> tptp.set_int tptp.set_int Bool) tptp.set_int) Bool)
% 6.75/7.10 (declare-fun tptp.ordering_top_set_nat ((-> tptp.set_nat tptp.set_nat Bool) (-> tptp.set_nat tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.orderi2172309028950807442at_nat ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) (-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.top_top_assn () tptp.assn)
% 6.75/7.10 (declare-fun tptp.top_top_Product_unit () tptp.product_unit)
% 6.75/7.10 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.75/7.10 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.75/7.10 (declare-fun tptp.power_power_assn (tptp.assn tptp.nat) tptp.assn)
% 6.75/7.10 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.power_7079662738309270450atural (tptp.code_natural tptp.nat) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.75/7.10 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.75/7.10 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 6.75/7.10 (declare-fun tptp.produc2252593628808123835atural ((-> tptp.code_natural tptp.option6357759511663192854e_term) tptp.produc7822875418678951345atural) tptp.produc8731074985263844745atural)
% 6.75/7.10 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 6.75/7.10 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.75/7.10 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 6.75/7.10 (declare-fun tptp.produc3831813291587773865atural ((-> tptp.produc4972180933644002618e_term tptp.option6357759511663192854e_term) tptp.produc7822875418678951345atural) tptp.produc989692990947075319atural)
% 6.75/7.10 (declare-fun tptp.produc2245416461498447860et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) tptp.produc2732055786443039994et_nat)
% 6.75/7.10 (declare-fun tptp.produc5001842942810119800et_nat ((-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) tptp.produc3925858234332021118et_nat)
% 6.75/7.10 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 6.75/7.10 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.75/7.10 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.75/7.10 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.75/7.10 (declare-fun tptp.produc3762353314782720579et_nat (Bool tptp.produc3658429121746597890et_nat) tptp.produc6197004810343482825et_nat)
% 6.75/7.10 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.75/7.10 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.75/7.10 (declare-fun tptp.produc3574140220909816553atural (tptp.code_natural tptp.code_natural) tptp.produc7822875418678951345atural)
% 6.75/7.10 (declare-fun tptp.produc6639722614265839536atural (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.75/7.10 (declare-fun tptp.produc584006145561248582it_nat (tptp.heap_e7401611519738050253t_unit tptp.nat) tptp.produc6653097349344004940it_nat)
% 6.75/7.10 (declare-fun tptp.produc7507926704131184380et_nat (tptp.heap_e7401611519738050253t_unit tptp.set_nat) tptp.produc3658429121746597890et_nat)
% 6.75/7.10 (declare-fun tptp.product_Pair_int_o (tptp.int Bool) tptp.product_prod_int_o)
% 6.75/7.10 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.product_Pair_int_nat (tptp.int tptp.nat) tptp.product_prod_int_nat)
% 6.75/7.10 (declare-fun tptp.produc4348348721325984599at_nat (tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.produc4166570645942440679at_nat)
% 6.75/7.10 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.75/7.10 (declare-fun tptp.product_Pair_nat_int (tptp.nat tptp.int) tptp.product_prod_nat_int)
% 6.75/7.10 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.75/7.10 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.75/7.10 (declare-fun tptp.produc638857205735767105it_nat (tptp.nat tptp.option8956607266484857688it_nat) tptp.produc3911288613690379145it_nat)
% 6.75/7.10 (declare-fun tptp.produc4111269673004989362it_nat (tptp.nat tptp.option3562590408128118217it_nat) tptp.produc4453839368661128058it_nat)
% 6.75/7.10 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.75/7.10 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.75/7.10 (declare-fun tptp.produc5950683997804057413e_term (tptp.option6357759511663192854e_term tptp.option6357759511663192854e_term) tptp.produc6576344331059438605e_term)
% 6.75/7.10 (declare-fun tptp.produc4480994950612372183atural (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 6.75/7.10 (declare-fun tptp.produc6161850002892822231at_nat (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc859450856879609959at_nat)
% 6.75/7.10 (declare-fun tptp.produc7133225469290080770it_nat (tptp.product_unit tptp.produc6653097349344004940it_nat) tptp.produc8664842809031399944it_nat)
% 6.75/7.10 (declare-fun tptp.produc7443773368509356479nteger (tptp.set_Code_integer tptp.set_Code_integer) tptp.produc6491284506569428743nteger)
% 6.75/7.10 (declare-fun tptp.produc6363374080413544029et_int (tptp.set_int tptp.set_int) tptp.produc2115011035271226405et_int)
% 6.75/7.10 (declare-fun tptp.produc4532415448927165861et_nat (tptp.set_nat tptp.set_nat) tptp.produc7819656566062154093et_nat)
% 6.75/7.10 (declare-fun tptp.produc763777882069021527od_o_o (tptp.set_Product_prod_o_o tptp.set_Product_prod_o_o) tptp.produc2934264451710624999od_o_o)
% 6.75/7.10 (declare-fun tptp.produc8517790099723286449at_nat (tptp.set_Product_prod_o_o tptp.set_Pr1261947904930325089at_nat) tptp.produc732395585841259969at_nat)
% 6.75/7.10 (declare-fun tptp.produc5245064249948416855at_nat (tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat) tptp.produc4193628355235574503at_nat)
% 6.75/7.10 (declare-fun tptp.produc2922128104949294807at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3843707927480180839at_nat)
% 6.75/7.10 (declare-fun tptp.produc9060074326276436823at_nat (tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat) tptp.produc1319942482725812455at_nat)
% 6.75/7.10 (declare-fun tptp.produc9178034014595674355it_nat (tptp.a tptp.produc6653097349344004940it_nat) tptp.produc3260487557148687353it_nat)
% 6.75/7.10 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.product_Unity () tptp.product_unit)
% 6.75/7.10 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.10 (declare-fun tptp.produc9098658269643458507_int_o ((-> tptp.produc7773217078559923341nt_int Bool) (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc5101573711933517782_nat_o ((-> tptp.produc2732055786443039994et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc6216949301066131538_nat_o ((-> tptp.produc3925858234332021118et_nat Bool) (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc730925184835016917_int_o ((-> tptp.produc2285326912895808259nt_int Bool) (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc175634133007206835_int_o ((-> tptp.product_prod_int_int Bool) tptp.int tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.produc1016772743285680337nt_int ((-> tptp.product_prod_int_int tptp.int) tptp.int tptp.int) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc8249235968001453780nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.int tptp.int) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.produc3704529784387675049_nat_o ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.nat tptp.nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc3610074571335452306at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.10 (declare-fun tptp.produc3709033845735585303_nat_o ((-> tptp.produc3260487557148687353it_nat Bool) tptp.a tptp.produc6653097349344004940it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc8005341501107743676_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc7926200574084438792nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc297006045350968285nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.produc4780622933104268256_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc1854806715440696265at_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)
% 6.75/7.10 (declare-fun tptp.produc2558449545302689196_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc7773217078559923341nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc5122537100556696953nt_int ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.produc7773217078559923341nt_int) tptp.produc7773217078559923341nt_int) tptp.produc7773217078559923341nt_int)
% 6.75/7.10 (declare-fun tptp.produc8646739037753556108_set_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_o) tptp.produc7773217078559923341nt_int) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.produc4111701587417901774et_int ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_int) tptp.produc7773217078559923341nt_int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.produc8289552606927098482et_nat ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat) tptp.produc7773217078559923341nt_int) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.produc3577156405726439208et_nat ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_set_nat) tptp.produc7773217078559923341nt_int) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.produc838355143741117751_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc2377985495875741467et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat) tptp.produc2732055786443039994et_nat)
% 6.75/7.10 (declare-fun tptp.produc1437786849005270451_nat_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc4058941399401191971et_nat ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat) tptp.produc3925858234332021118et_nat)
% 6.75/7.10 (declare-fun tptp.produc7715693535893868691_set_o ((-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.set_o) tptp.produc3925858234332021118et_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.produc1573362020775583542_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc2285326912895808259nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc8492565224438309093nt_int ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.produc2285326912895808259nt_int) tptp.produc2285326912895808259nt_int) tptp.produc2285326912895808259nt_int)
% 6.75/7.10 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.75/7.10 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.75/7.10 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.75/7.10 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.75/7.10 (declare-fun tptp.produc8282080750456430313atural ((-> tptp.code_natural tptp.code_natural tptp.produc6756470014200349799atural) tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 6.75/7.10 (declare-fun tptp.produc7488178964372371019it_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option8956607266484857688it_nat) tptp.produc6653097349344004940it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.produc5645566021302314940it_nat ((-> tptp.heap_e7401611519738050253t_unit tptp.nat tptp.option3562590408128118217it_nat) tptp.produc6653097349344004940it_nat) tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.10 (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)
% 6.75/7.10 (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)
% 6.75/7.10 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.75/7.10 (declare-fun tptp.produc6189476227299908564et_nat ((-> tptp.nat tptp.nat tptp.set_nat) tptp.product_prod_nat_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.75/7.10 (declare-fun tptp.produc1658495936642081476eger_o ((-> tptp.set_Code_integer tptp.set_Code_integer Bool) tptp.produc6491284506569428743nteger) Bool)
% 6.75/7.10 (declare-fun tptp.produc4109468873575309990_int_o ((-> tptp.set_int tptp.set_int Bool) tptp.produc2115011035271226405et_int) Bool)
% 6.75/7.10 (declare-fun tptp.produc6247414631856714078_nat_o ((-> tptp.set_nat tptp.set_nat Bool) tptp.produc7819656566062154093et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc410239310623530412_nat_o ((-> tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat Bool) tptp.produc3843707927480180839at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc8860486935419594360_nat_o ((-> tptp.a tptp.produc6653097349344004940it_nat Bool) tptp.produc3260487557148687353it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.produc7727125748877983984at_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.nat) tptp.produc3260487557148687353it_nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.produc5648861294512138360it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.option8956607266484857688it_nat) tptp.produc3260487557148687353it_nat) tptp.option8956607266484857688it_nat)
% 6.75/7.10 (declare-fun tptp.produc7850007024774191849it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.option3562590408128118217it_nat) tptp.produc3260487557148687353it_nat) tptp.option3562590408128118217it_nat)
% 6.75/7.10 (declare-fun tptp.produc2183267410226956569it_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.produc3260487557148687353it_nat) tptp.produc3260487557148687353it_nat) tptp.produc3260487557148687353it_nat)
% 6.75/7.10 (declare-fun tptp.produc5350075035600711000_set_o ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o) tptp.produc3260487557148687353it_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.produc3137162363284112642et_int ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_int) tptp.produc3260487557148687353it_nat) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.produc7315013382793309350et_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat) tptp.produc3260487557148687353it_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.produc8253449849199807809at_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_Pr1261947904930325089at_nat) tptp.produc3260487557148687353it_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.produc8632796428668088668et_nat ((-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_set_nat) tptp.produc3260487557148687353it_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.produc497848011034438852atural (tptp.produc5835291356934675326atural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.produc1824681642469235216et_nat (tptp.produc3658429121746597890et_nat) tptp.heap_e7401611519738050253t_unit)
% 6.75/7.10 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc6591912806276919810atural (tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural)
% 6.75/7.10 (declare-fun tptp.produc8586169260539613262et_nat (tptp.produc3658429121746597890et_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.75/7.10 (declare-fun tptp.produc5538323210962509403atural ((-> tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.75/7.10 (declare-fun tptp.product_Abs_unit (Bool) tptp.product_unit)
% 6.75/7.10 (declare-fun tptp.product_Rep_unit (tptp.product_unit) Bool)
% 6.75/7.10 (declare-fun tptp.inc_shift (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.iterat8892046348760725948atural (tptp.code_natural (-> tptp.code_natural tptp.produc7822875418678951345atural tptp.produc5835291356934675326atural) tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.75/7.10 (declare-fun tptp.log (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.log_rel (tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural) Bool)
% 6.75/7.10 (declare-fun tptp.minus_shift (tptp.code_natural tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.next (tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.75/7.10 (declare-fun tptp.range (tptp.code_natural tptp.produc7822875418678951345atural) tptp.produc5835291356934675326atural)
% 6.75/7.10 (declare-fun tptp.split_seed (tptp.produc7822875418678951345atural) tptp.produc6756470014200349799atural)
% 6.75/7.10 (declare-fun tptp.abs_Rat (tptp.product_prod_int_int) tptp.rat)
% 6.75/7.10 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.75/7.10 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.75/7.10 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.cr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.75/7.10 (declare-fun tptp.pcr_rat (tptp.product_prod_int_int tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.75/7.10 (declare-fun tptp.ratrel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.field_o (tptp.set_Product_prod_o_o) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.field_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.id_mul2649389997224486051at_nat () tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.id_Pro2258643101195443293at_nat () tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.total_3592101749530773125at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.trans_4347625901269045472at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.algebr932160517623751201me_int (tptp.int tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.algebr934650988132801477me_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.divide5121882707175180666atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.75/7.10 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_assn (tptp.assn tptp.assn) Bool)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_Code_natural (tptp.code_natural tptp.code_natural) Bool)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.75/7.10 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.75/7.10 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.modulo8411746178871703098atural (tptp.code_natural tptp.code_natural) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.75/7.10 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.zero_n8403883297036319079atural (Bool) tptp.code_natural)
% 6.75/7.10 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.75/7.10 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.75/7.10 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.75/7.10 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.collect_assn ((-> tptp.assn Bool)) tptp.set_assn)
% 6.75/7.10 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.75/7.10 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.75/7.10 (declare-fun tptp.collec506566255779805410nt_int ((-> tptp.produc7773217078559923341nt_int Bool)) tptp.set_Pr1872883991513573699nt_int)
% 6.75/7.10 (declare-fun tptp.collec5543584681430388431et_nat ((-> tptp.produc2732055786443039994et_nat Bool)) tptp.set_Pr8536935166611901872et_nat)
% 6.75/7.10 (declare-fun tptp.collec1402215087704437587et_nat ((-> tptp.produc3925858234332021118et_nat Bool)) tptp.set_Pr3286484037609594932et_nat)
% 6.75/7.10 (declare-fun tptp.collec1790188477890212312nt_int ((-> tptp.produc2285326912895808259nt_int Bool)) tptp.set_Pr9222295170931077689nt_int)
% 6.75/7.10 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.10 (declare-fun tptp.collec5204685387357076818at_nat ((-> tptp.produc4166570645942440679at_nat Bool)) tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.collec7088162979684241874at_nat ((-> tptp.produc859450856879609959at_nat Bool)) tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.collec2770208431294612722nteger ((-> tptp.produc6491284506569428743nteger Bool)) tptp.set_Pr7577011563204128103nteger)
% 6.75/7.10 (declare-fun tptp.collec957716948307931664et_int ((-> tptp.produc2115011035271226405et_int Bool)) tptp.set_Pr2522554150109002629et_int)
% 6.75/7.10 (declare-fun tptp.collec6662362479098859352et_nat ((-> tptp.produc7819656566062154093et_nat Bool)) tptp.set_Pr5488025237498180813et_nat)
% 6.75/7.10 (declare-fun tptp.collec6321179662152712658at_nat ((-> tptp.produc3843707927480180839at_nat Bool)) tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.collec4148678073425210574it_nat ((-> tptp.produc3260487557148687353it_nat Bool)) tptp.set_Pr7098220151150636591it_nat)
% 6.75/7.10 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.collec574505750873337192nteger ((-> tptp.set_Code_integer Bool)) tptp.set_set_Code_integer)
% 6.75/7.10 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.75/7.10 (declare-fun tptp.collect_set_list_nat ((-> tptp.set_list_nat Bool)) tptp.set_set_list_nat)
% 6.75/7.10 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.collec5514110066124741708at_nat ((-> tptp.set_Pr1261947904930325089at_nat Bool)) tptp.set_se7855581050983116737at_nat)
% 6.75/7.10 (declare-fun tptp.collect_set_set_nat ((-> tptp.set_set_nat Bool)) tptp.set_set_set_nat)
% 6.75/7.10 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.image_o_o ((-> Bool Bool) tptp.set_o) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_o_Code_integer ((-> Bool tptp.code_integer) tptp.set_o) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.image_o_int ((-> Bool tptp.int) tptp.set_o) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_o_nat ((-> Bool tptp.nat) tptp.set_o) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_o_set_nat ((-> Bool tptp.set_nat) tptp.set_o) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.image_4470545334726330049nteger ((-> tptp.code_integer tptp.code_integer) tptp.set_Code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.image_948535463418740880er_int ((-> tptp.code_integer tptp.int) tptp.set_Code_integer) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_951025933927791156er_nat ((-> tptp.code_integer tptp.nat) tptp.set_Code_integer) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_int_o ((-> tptp.int Bool) tptp.set_int) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_1587234942943678608nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_int_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_6031046145702598900at_nat ((-> tptp.int tptp.produc859450856879609959at_nat) tptp.set_int) tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.image_int_set_nat ((-> tptp.int tptp.set_nat) tptp.set_int) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.image_list_nat_o ((-> tptp.list_nat Bool) tptp.set_list_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_list_nat_nat ((-> tptp.list_nat tptp.nat) tptp.set_list_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_2516384619306764229at_nat ((-> tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.set_mu2057375006010111271at_nat) tptp.set_mu2057375006010111271at_nat)
% 6.75/7.10 (declare-fun tptp.image_nat_o ((-> tptp.nat Bool) tptp.set_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_1215581382706833972nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_nat_list_nat ((-> tptp.nat tptp.list_nat) tptp.set_nat) tptp.set_list_nat)
% 6.75/7.10 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_5319605298250079696at_nat ((-> tptp.nat tptp.produc4166570645942440679at_nat) tptp.set_nat) tptp.set_Pr8551490117392284871at_nat)
% 6.75/7.10 (declare-fun tptp.image_5846123807819985514at_nat ((-> tptp.nat tptp.product_prod_nat_nat) tptp.set_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.image_3276603626957510736at_nat ((-> tptp.nat tptp.produc859450856879609959at_nat) tptp.set_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.image_num_option_num ((-> tptp.num tptp.option_num) tptp.set_num) tptp.set_option_num)
% 6.75/7.10 (declare-fun tptp.image_2135063354759101220_int_o ((-> tptp.product_prod_int_int Bool) tptp.set_Pr958786334691620121nt_int) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_5042161079198086560nt_int ((-> tptp.product_prod_int_int tptp.int) tptp.set_Pr958786334691620121nt_int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_5044651549707136836nt_nat ((-> tptp.product_prod_int_int tptp.nat) tptp.set_Pr958786334691620121nt_int) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_2653370878348428101nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.10 (declare-fun tptp.image_6009382790362589554at_nat ((-> tptp.produc4166570645942440679at_nat tptp.nat) tptp.set_Pr8551490117392284871at_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_3693632289388996572_nat_o ((-> tptp.product_prod_nat_nat Bool) tptp.set_Pr1261947904930325089at_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_2483585944268220136at_int ((-> tptp.product_prod_nat_nat tptp.int) tptp.set_Pr1261947904930325089at_nat) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_2486076414777270412at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_5168914502847457605at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.image_15824709712370754et_nat ((-> tptp.product_prod_nat_nat tptp.set_nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.image_6160980552072806642at_nat ((-> tptp.produc859450856879609959at_nat tptp.nat) tptp.set_Pr8693737435421807431at_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_3455408117458022631it_nat ((-> tptp.produc8664842809031399944it_nat tptp.option8956607266484857688it_nat) tptp.set_Pr1354866905816374718it_nat) tptp.set_op239864471688321678it_nat)
% 6.75/7.10 (declare-fun tptp.image_3198525501578754290at_nat ((-> tptp.produc3843707927480180839at_nat tptp.nat) tptp.set_Pr4329608150637261639at_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_1991556864075471768_nat_o ((-> tptp.produc3260487557148687353it_nat Bool) tptp.set_Pr7098220151150636591it_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_1030127162643715024at_nat ((-> tptp.produc3260487557148687353it_nat tptp.nat) tptp.set_Pr7098220151150636591it_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.image_2003495143432273353it_nat ((-> tptp.produc3260487557148687353it_nat tptp.option3562590408128118217it_nat) tptp.set_Pr7098220151150636591it_nat) tptp.set_op4617111635268443007it_nat)
% 6.75/7.10 (declare-fun tptp.image_rat_rat ((-> tptp.rat tptp.rat) tptp.set_rat) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.image_set_nat_o ((-> tptp.set_nat Bool) tptp.set_set_nat) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.image_set_nat_int ((-> tptp.set_nat tptp.int) tptp.set_set_nat) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.image_set_nat_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.insert_o (Bool tptp.set_o) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.insert8211810215607154385at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.insert9069300056098147895at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.insert_Product_unit (tptp.product_unit tptp.set_Product_unit) tptp.set_Product_unit)
% 6.75/7.10 (declare-fun tptp.is_empty_o (tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.is_empty_int (tptp.set_int) Bool)
% 6.75/7.10 (declare-fun tptp.is_empty_nat (tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.is_emp1662574758705540307at_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.set_fo1959793692361082170t_assn ((-> tptp.nat tptp.assn tptp.assn) tptp.nat tptp.nat tptp.assn) tptp.assn)
% 6.75/7.10 (declare-fun tptp.set_fo1084959871951514735nteger ((-> tptp.nat tptp.code_integer tptp.code_integer) tptp.nat tptp.nat tptp.code_integer) tptp.code_integer)
% 6.75/7.10 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.75/7.10 (declare-fun tptp.set_fo4497565046347964853at_nat ((-> tptp.nat tptp.multis2468970476368604999at_nat tptp.multis2468970476368604999at_nat) tptp.nat tptp.nat tptp.multis2468970476368604999at_nat) tptp.multis2468970476368604999at_nat)
% 6.75/7.10 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.75/7.10 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.75/7.10 (declare-fun tptp.set_fo3699595496184130361el_nat (tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.set_or8904488021354931149Most_o (Bool Bool) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.set_or7959216805967363635t_assn (tptp.assn tptp.assn) tptp.set_assn)
% 6.75/7.10 (declare-fun tptp.set_or189985376899183464nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.75/7.10 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.75/7.10 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.set_or7139685690850216873Than_o (Bool Bool) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.set_or5523502641901747543n_assn (tptp.assn tptp.assn) tptp.set_assn)
% 6.75/7.10 (declare-fun tptp.set_or8404916559141939852nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_or1222409239386451017an_num (tptp.num tptp.num) tptp.set_num)
% 6.75/7.10 (declare-fun tptp.set_or4029947393144176647an_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.set_or8585797421378605585et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.75/7.10 (declare-fun tptp.set_or3540276404033026485et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_ord_atMost_o (Bool) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.set_or9101266186257409494nteger (tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.75/7.10 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 6.75/7.10 (declare-fun tptp.set_or4236626031148496127et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.set_or2715278749043346189nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_or4266950643985792945nteger (tptp.code_integer tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_ord_lessThan_o (Bool) tptp.set_o)
% 6.75/7.10 (declare-fun tptp.set_or7637083652282234053n_assn (tptp.assn) tptp.set_assn)
% 6.75/7.10 (declare-fun tptp.set_or5754767410780653050nteger (tptp.code_integer) tptp.set_Code_integer)
% 6.75/7.10 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.75/7.10 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.75/7.10 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.75/7.10 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.75/7.10 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.type_d6188575255521822967unit_o ((-> tptp.product_unit Bool) (-> Bool tptp.product_unit) tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P8928870874622223812nt_int ((-> tptp.produc7773217078559923341nt_int tptp.produc7773217078559923341nt_int Bool) tptp.produc7773217078559923341nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P6019419558468335806at_nat ((-> tptp.produc4471711990508489141at_nat tptp.produc4471711990508489141at_nat Bool) tptp.produc4471711990508489141at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P1862375125659990705et_nat ((-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool) tptp.produc2732055786443039994et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P8458817951426537472et_nat ((-> tptp.produc6197004810343482825et_nat tptp.produc6197004810343482825et_nat Bool) tptp.produc6197004810343482825et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P8126237942716283194atural ((-> tptp.produc7822875418678951345atural tptp.produc7822875418678951345atural Bool) tptp.produc7822875418678951345atural) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P5801069581201407417et_nat ((-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P414730952086964626it_nat ((-> tptp.produc3911288613690379145it_nat tptp.produc3911288613690379145it_nat Bool) tptp.produc3911288613690379145it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P6263092265436569219it_nat ((-> tptp.produc4453839368661128058it_nat tptp.produc4453839368661128058it_nat Bool) tptp.produc4453839368661128058it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.75/7.10 (declare-fun tptp.finite2416775604798480986nteger () tptp.set_Pr7577011563204128103nteger)
% 6.75/7.10 (declare-fun tptp.finite_psubset_int () tptp.set_Pr2522554150109002629et_int)
% 6.75/7.10 (declare-fun tptp.finite_psubset_nat () tptp.set_Pr5488025237498180813et_nat)
% 6.75/7.10 (declare-fun tptp.finite469560695537375940at_nat () tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.less_than () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.lex_prod_nat_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr8693737435421807431at_nat)
% 6.75/7.10 (declare-fun tptp.max_ex8135407076693332796at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.measure_nat ((-> tptp.nat tptp.nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.min_ex6901939911449802026at_nat (tptp.set_Pr8693737435421807431at_nat) tptp.set_Pr4329608150637261639at_nat)
% 6.75/7.10 (declare-fun tptp.mlex_prod_int ((-> tptp.int tptp.nat) tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.75/7.10 (declare-fun tptp.mlex_prod_nat ((-> tptp.nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.75/7.10 (declare-fun tptp.wf_nat (tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.wf_Pro7803398752247294826at_nat (tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.75/7.10 (declare-fun tptp.member_assn (tptp.assn tptp.set_assn) Bool)
% 6.75/7.10 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.75/7.10 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.75/7.10 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.75/7.10 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.75/7.10 (declare-fun tptp.member_option_num (tptp.option_num tptp.set_option_num) Bool)
% 6.75/7.10 (declare-fun tptp.member5596548051065438575it_nat (tptp.option8956607266484857688it_nat tptp.set_op239864471688321678it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member1310632352865511136it_nat (tptp.option3562590408128118217it_nat tptp.set_op4617111635268443007it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member7034335876925520548nt_int (tptp.produc7773217078559923341nt_int tptp.set_Pr1872883991513573699nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.member6124377750444531601et_nat (tptp.produc2732055786443039994et_nat tptp.set_Pr8536935166611901872et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member1996754912294343701et_nat (tptp.produc3925858234332021118et_nat tptp.set_Pr3286484037609594932et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member7618704894036264090nt_int (tptp.produc2285326912895808259nt_int tptp.set_Pr9222295170931077689nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.75/7.10 (declare-fun tptp.member6689249552917799696at_nat (tptp.produc4166570645942440679at_nat tptp.set_Pr8551490117392284871at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member8206827879206165904at_nat (tptp.produc859450856879609959at_nat tptp.set_Pr8693737435421807431at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member4307123515891402160nteger (tptp.produc6491284506569428743nteger tptp.set_Pr7577011563204128103nteger) Bool)
% 6.75/7.10 (declare-fun tptp.member2572552093476627150et_int (tptp.produc2115011035271226405et_int tptp.set_Pr2522554150109002629et_int) Bool)
% 6.75/7.10 (declare-fun tptp.member8277197624267554838et_nat (tptp.produc7819656566062154093et_nat tptp.set_Pr5488025237498180813et_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member444158400953824016od_o_o (tptp.produc2934264451710624999od_o_o tptp.set_Pr1932065953672099015od_o_o) Bool)
% 6.75/7.10 (declare-fun tptp.member4095101504841534314at_nat (tptp.produc732395585841259969at_nat tptp.set_Pr457366540195662369at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member8757157785044589968at_nat (tptp.produc3843707927480180839at_nat tptp.set_Pr4329608150637261639at_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member4554412811331277712it_nat (tptp.produc3260487557148687353it_nat tptp.set_Pr7098220151150636591it_nat) Bool)
% 6.75/7.10 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.75/7.10 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.75/7.10 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.75/7.10 (declare-fun tptp.p () tptp.assn)
% 6.75/7.10 (declare-fun tptp.q (tptp.a) tptp.assn)
% 6.75/7.10 (declare-fun tptp.r () tptp.assn)
% 6.75/7.10 (declare-fun tptp.as1 () tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.as2 () tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.as () tptp.set_nat)
% 6.75/7.10 (declare-fun tptp.c () tptp.heap_Time_Heap_a)
% 6.75/7.10 (declare-fun tptp.h () tptp.heap_e7401611519738050253t_unit)
% 6.75/7.10 (declare-fun tptp.h2 () tptp.heap_e7401611519738050253t_unit)
% 6.75/7.10 (declare-fun tptp.r2 () tptp.a)
% 6.75/7.10 (declare-fun tptp.t () tptp.nat)
% 6.75/7.10 (assert (= (@ (@ tptp.inf_inf_set_nat tptp.as1) tptp.as2) tptp.bot_bot_set_nat))
% 6.75/7.10 (assert (@ (@ tptp.rep_assn tptp.r) (@ (@ tptp.produc7507926704131184380et_nat tptp.h) tptp.as2)))
% 6.75/7.10 (assert (@ (@ tptp.rep_assn tptp.r) (@ (@ tptp.produc7507926704131184380et_nat tptp.h2) tptp.as2)))
% 6.75/7.10 (assert (= (@ (@ tptp.inf_inf_set_nat (@ (@ (@ tptp.hoare_new_addrs tptp.h2) tptp.as1) tptp.h)) tptp.as2) tptp.bot_bot_set_nat))
% 6.75/7.10 (assert (let ((_let_1 (@ tptp.hoare_new_addrs tptp.h2))) (= (@ (@ _let_1 tptp.as) tptp.h) (@ (@ tptp.sup_sup_set_nat (@ (@ _let_1 tptp.as1) tptp.h)) tptp.as2))))
% 6.75/7.10 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ (@ tptp.hoare_new_addrs H) As) H) As)))
% 6.75/7.10 (assert (@ (@ tptp.rep_assn tptp.p) (@ (@ tptp.produc7507926704131184380et_nat tptp.h2) tptp.as1)))
% 6.75/7.10 (assert (@ (@ tptp.rep_assn (@ tptp.q tptp.r2)) (@ (@ tptp.produc7507926704131184380et_nat tptp.h) (@ (@ (@ tptp.hoare_new_addrs tptp.h2) tptp.as1) tptp.h))))
% 6.75/7.10 (assert (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn tptp.p) tptp.r)) (@ (@ tptp.produc7507926704131184380et_nat tptp.h2) tptp.as)))
% 6.75/7.10 (assert (not (forall ((As1 tptp.set_nat) (As2 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat tptp.h2))) (=> (= tptp.as (@ (@ tptp.sup_sup_set_nat As1) As2)) (=> (= (@ (@ tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (=> (@ (@ tptp.rep_assn tptp.p) (@ _let_1 As1)) (not (@ (@ tptp.rep_assn tptp.r) (@ _let_1 As2))))))))))
% 6.75/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.rep_assn X) (@ tptp.rep_assn Y)) (= X Y))))
% 6.75/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 6.75/7.10 (assert (@ (@ (@ tptp.relH tptp.as2) tptp.h2) tptp.h))
% 6.75/7.10 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X2 tptp.produc3658429121746597890et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat X1) X2) (@ (@ tptp.produc5001842942810119800et_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.75/7.10 (assert (forall ((X1 (-> tptp.produc3658429121746597890et_nat Bool)) (X2 tptp.produc3925858234332021118et_nat) (Y1 (-> tptp.produc3658429121746597890et_nat Bool)) (Y2 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat X1) X2) (@ (@ tptp.produc2245416461498447860et_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.75/7.10 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X2 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X2) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.75/7.10 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X2 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X2) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.75/7.10 (assert (forall ((X1 tptp.a) (X2 tptp.produc6653097349344004940it_nat) (Y1 tptp.a) (Y2 tptp.produc6653097349344004940it_nat)) (= (= (@ (@ tptp.produc9178034014595674355it_nat X1) X2) (@ (@ tptp.produc9178034014595674355it_nat Y1) Y2)) (and (= X1 Y1) (= X2 Y2)))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (= (= (@ (@ tptp.produc5001842942810119800et_nat A) B) (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (= (= (@ (@ tptp.produc2245416461498447860et_nat A) B) (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) (and (= A A2) (= B B2)))))
% 6.75/7.10 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A2) B2)) (and (= A A2) (= B B2)))))
% 6.75/7.10 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A2 tptp.a) (B2 tptp.produc6653097349344004940it_nat)) (= (= (@ (@ tptp.produc9178034014595674355it_nat A) B) (@ (@ tptp.produc9178034014595674355it_nat A2) B2)) (and (= A A2) (= B B2)))))
% 6.75/7.10 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A3) B3)) H) (exists ((H1 tptp.produc3658429121746597890et_nat) (H2 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn A3) H1) (@ (@ tptp.rep_assn B3) H2))))))
% 6.75/7.10 (assert (forall ((A tptp.assn) (B tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A) B)) H) (not (=> (exists ((X_1 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.rep_assn A) X_1)) (forall ((H_2 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn B) H_2))))))))
% 6.75/7.10 (assert (@ (@ (@ tptp.hoare_hoare_triple_a tptp.p) tptp.c) tptp.q))
% 6.75/7.10 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h2)) (@ tptp.lim_Product_unit tptp.h)))
% 6.75/7.10 (assert (= tptp.as (@ (@ tptp.sup_sup_set_nat tptp.as1) tptp.as2)))
% 6.75/7.10 (assert (forall ((P tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.rep_assn P))) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) tptp.bot_bot_set_nat))))))
% 6.75/7.10 (assert (forall ((As tptp.set_nat) (As3 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ (@ tptp.relH (@ (@ tptp.sup_sup_set_nat As) As3)) H) H3) (and (@ (@ (@ tptp.relH As) H) H3) (@ (@ (@ tptp.relH As3) H) H3)))))
% 6.75/7.10 (assert (forall ((X tptp.produc2732055786443039994et_nat)) (not (forall ((P2 (-> tptp.produc3658429121746597890et_nat Bool)) (Q2 (-> tptp.produc3658429121746597890et_nat Bool)) (H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (not (= X (@ (@ tptp.produc2245416461498447860et_nat P2) (@ (@ tptp.produc5001842942810119800et_nat Q2) (@ (@ tptp.produc7507926704131184380et_nat H4) As4)))))))))
% 6.75/7.10 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As))) (=> (@ (@ _let_1 H) H3) (@ (@ _let_1 H3) H)))))
% 6.75/7.10 (assert (forall ((As tptp.set_nat) (H12 tptp.heap_e7401611519738050253t_unit) (H22 tptp.heap_e7401611519738050253t_unit) (H32 tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.relH As))) (let ((_let_2 (@ _let_1 H12))) (=> (@ _let_2 H22) (=> (@ (@ _let_1 H22) H32) (@ _let_2 H32)))))))
% 6.75/7.10 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (P tptp.assn)) (let ((_let_1 (@ tptp.rep_assn P))) (=> (@ (@ (@ tptp.relH As) H) H3) (= (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ _let_1 (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))))
% 6.75/7.10 (assert (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q (-> tptp.a tptp.assn))) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H4) (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q))) (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q))))
% 6.75/7.10 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn A3) B3)) H) (exists ((Hr tptp.heap_e7401611519738050253t_unit) (As12 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat Hr))) (and (= H (@ _let_1 (@ (@ tptp.sup_sup_set_nat As12) As22))) (= (@ (@ tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn A3) (@ _let_1 As12)) (@ (@ tptp.rep_assn B3) (@ _let_1 As22))))))))
% 6.75/7.10 (assert (forall ((P tptp.assn) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q tptp.assn) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (=> (@ (@ tptp.rep_assn P) (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As3)) (=> (= (@ (@ tptp.inf_inf_set_nat As) As3) tptp.bot_bot_set_nat) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) Q)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As3)))))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) (@ (@ tptp.produc7507926704131184380et_nat C2) D))))) (@ P X))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (X tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B4) C2)))) (@ P X))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) C2)))) (@ P X))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C2)))) (@ P X))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C2)))) (@ P X))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.nat)) (@ P (@ (@ tptp.produc9178034014595674355it_nat A4) (@ (@ tptp.produc584006145561248582it_nat B4) C2)))) (@ P X))))
% 6.75/7.10 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.heap_e7401611519738050253t_unit) (D tptp.set_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) (@ (@ tptp.produc7507926704131184380et_nat C2) D)))))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.set_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) (@ (@ tptp.produc7507926704131184380et_nat B4) C2))))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 (-> tptp.produc3658429121746597890et_nat Bool)) (C2 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) (@ (@ tptp.produc5001842942810119800et_nat B4) C2))))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.int) (C2 tptp.int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C2))))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.int) (C2 tptp.int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A4) (@ (@ tptp.product_Pair_int_int B4) C2))))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A4 tptp.a) (B4 tptp.heap_e7401611519738050253t_unit) (C2 tptp.nat)) (not (= Y (@ (@ tptp.produc9178034014595674355it_nat A4) (@ (@ tptp.produc584006145561248582it_nat B4) C2))))))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3658429121746597890et_nat)) (=> (= (@ (@ tptp.produc5001842942810119800et_nat A) B) (@ (@ tptp.produc5001842942810119800et_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (A2 (-> tptp.produc3658429121746597890et_nat Bool)) (B2 tptp.produc3925858234332021118et_nat)) (=> (= (@ (@ tptp.produc2245416461498447860et_nat A) B) (@ (@ tptp.produc2245416461498447860et_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.75/7.10 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.75/7.10 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A2 (-> tptp.int tptp.option6357759511663192854e_term)) (B2 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.75/7.10 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A2 tptp.a) (B2 tptp.produc6653097349344004940it_nat)) (=> (= (@ (@ tptp.produc9178034014595674355it_nat A) B) (@ (@ tptp.produc9178034014595674355it_nat A2) B2)) (not (=> (= A A2) (not (= B B2)))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc3925858234332021118et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (@ P (@ (@ tptp.produc5001842942810119800et_nat A4) B4))) (@ P P3))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc2732055786443039994et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (@ P (@ (@ tptp.produc2245416461498447860et_nat A4) B4))) (@ P P3))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P3 tptp.produc2285326912895808259nt_int)) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A4) B4))) (@ P P3))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P3 tptp.produc7773217078559923341nt_int)) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A4) B4))) (@ P P3))))
% 6.75/7.10 (assert (forall ((P (-> tptp.produc3260487557148687353it_nat Bool)) (P3 tptp.produc3260487557148687353it_nat)) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (@ P (@ (@ tptp.produc9178034014595674355it_nat A4) B4))) (@ P P3))))
% 6.75/7.10 (assert (forall ((P3 tptp.produc3925858234332021118et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)))))
% 6.75/7.10 (assert (forall ((P3 tptp.produc2732055786443039994et_nat)) (exists ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)))))
% 6.75/7.10 (assert (forall ((P3 tptp.produc2285326912895808259nt_int)) (exists ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P3 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)))))
% 6.75/7.10 (assert (forall ((P3 tptp.produc7773217078559923341nt_int)) (exists ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)))))
% 6.75/7.10 (assert (forall ((P3 tptp.produc3260487557148687353it_nat)) (exists ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)))))
% 6.75/7.10 (assert (forall ((A tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.member8440522571783428010at_nat A) (@ tptp.collec3392354462482085612at_nat P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A Bool) (P (-> Bool Bool))) (= (@ (@ tptp.member_o A) (@ tptp.collect_o P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.member5262025264175285858nt_int A) (@ tptp.collec213857154873943460nt_int P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_o)) (= (@ tptp.collect_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A3))) A3)))
% 6.75/7.10 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.product_prod_int_int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collec213857154873943460nt_int P) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.75/7.10 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_list_nat P) (@ tptp.collect_list_nat Q)))))
% 6.75/7.10 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.75/7.10 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.75/7.10 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (= (@ P X3) (@ Q X3))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.75/7.10 (assert (forall ((Y tptp.produc3925858234332021118et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (not (= Y (@ (@ tptp.produc5001842942810119800et_nat A4) B4)))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc2732055786443039994et_nat)) (not (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (not (= Y (@ (@ tptp.produc2245416461498447860et_nat A4) B4)))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A4) B4)))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A4) B4)))))))
% 6.75/7.10 (assert (forall ((Y tptp.produc3260487557148687353it_nat)) (not (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (not (= Y (@ (@ tptp.produc9178034014595674355it_nat A4) B4)))))))
% 6.75/7.10 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (not (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)))))))
% 6.75/7.10 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn P))) (= (@ (@ tptp.times_times_assn (@ _let_1 Q)) R) (@ _let_1 (@ (@ tptp.times_times_assn Q) R))))))
% 6.75/7.10 (assert (= tptp.times_times_assn (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (@ (@ tptp.times_times_assn Q3) P4))))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat T) (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat T) (@ (@ tptp.inf_in4302113700860409141at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat T) (@ (@ tptp.inf_in1697001100524423349at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat T) (@ (@ tptp.inf_in7913087082777306421at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat T) (@ (@ tptp.inf_inf_set_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat S) (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat S) (@ (@ tptp.inf_in4302113700860409141at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat S) (@ (@ tptp.inf_in1697001100524423349at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat S) (@ (@ tptp.inf_in7913087082777306421at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat S) (@ (@ tptp.inf_inf_set_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat T) (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat T) (@ (@ tptp.sup_su718114333110466843at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat T) (@ (@ tptp.sup_su3035147773818789531at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat T) (@ (@ tptp.sup_su5525570899277871387at_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((T tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat T) (@ (@ tptp.sup_sup_set_nat S) T)) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat S) (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat S) (@ (@ tptp.sup_su718114333110466843at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat S) (@ (@ tptp.sup_su3035147773818789531at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat S) (@ (@ tptp.sup_su5525570899277871387at_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat S) (@ (@ tptp.sup_sup_set_nat S) T)) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T)) T) T)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat S) T)) S) S)))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B3) tptp.bot_bo5327735625951526323at_nat) (and (= A3 tptp.bot_bo5327735625951526323at_nat) (= B3 tptp.bot_bo5327735625951526323at_nat)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3) tptp.bot_bo8422036546324065075at_nat) (and (= A3 tptp.bot_bo8422036546324065075at_nat) (= B3 tptp.bot_bo8422036546324065075at_nat)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) tptp.bot_bo228742789529271731at_nat) (and (= A3 tptp.bot_bo228742789529271731at_nat) (= B3 tptp.bot_bo228742789529271731at_nat)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (and (= A3 tptp.bot_bo2099793752762293965at_nat) (= B3 tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A3) B3) tptp.bot_bot_set_o) (and (= A3 tptp.bot_bot_set_o) (= B3 tptp.bot_bot_set_o)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A3) B3) tptp.bot_bot_set_nat) (and (= A3 tptp.bot_bot_set_nat) (= B3 tptp.bot_bot_set_nat)))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A3) B3) tptp.bot_bot_set_int) (and (= A3 tptp.bot_bot_set_int) (= B3 tptp.bot_bot_set_int)))))
% 6.75/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.sup_sup_assn X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ (@ tptp.sup_sup_Product_unit X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) (@ (@ tptp.sup_sup_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.sup_sup_assn X) (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit X) (@ (@ tptp.inf_inf_Product_unit X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X) (@ (@ tptp.inf_in4302113700860409141at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) (@ (@ tptp.inf_in1697001100524423349at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) X) X)))
% 6.75/7.10 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int P)) (forall ((X4 tptp.product_prod_int_int)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat P)) (forall ((X4 tptp.set_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat P)) (forall ((X4 tptp.product_prod_nat_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> Bool Bool))) (= (= tptp.bot_bot_set_o (@ tptp.collect_o P)) (forall ((X4 Bool)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.nat Bool))) (= (= tptp.bot_bot_set_nat (@ tptp.collect_nat P)) (forall ((X4 tptp.nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.int Bool))) (= (= tptp.bot_bot_set_int (@ tptp.collect_int P)) (forall ((X4 tptp.int)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (= (@ tptp.collec213857154873943460nt_int P) tptp.bot_bo1796632182523588997nt_int) (forall ((X4 tptp.product_prod_int_int)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (forall ((X4 tptp.list_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (forall ((X4 Bool)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (not (@ P X4))))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_set_nat)) (= (forall ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A3))) (= A3 tptp.bot_bot_set_set_nat))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X4) A3))) (= A3 tptp.bot_bo2099793752762293965at_nat))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_o)) (= (forall ((X4 Bool)) (not (@ (@ tptp.member_o X4) A3))) (= A3 tptp.bot_bot_set_o))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_nat)) (= (forall ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A3))) (= A3 tptp.bot_bot_set_nat))))
% 6.75/7.10 (assert (forall ((A3 tptp.set_int)) (= (forall ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A3))) (= A3 tptp.bot_bot_set_int))))
% 6.75/7.10 (assert (forall ((C tptp.set_nat)) (not (@ (@ tptp.member_set_nat C) tptp.bot_bot_set_set_nat))))
% 6.75/7.10 (assert (forall ((C tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat C) tptp.bot_bo2099793752762293965at_nat))))
% 6.75/7.10 (assert (forall ((C Bool)) (not (@ (@ tptp.member_o C) tptp.bot_bot_set_o))))
% 6.75/7.10 (assert (forall ((C tptp.nat)) (not (@ (@ tptp.member_nat C) tptp.bot_bot_set_nat))))
% 6.75/7.10 (assert (forall ((C tptp.int)) (not (@ (@ tptp.member_int C) tptp.bot_bot_set_int))))
% 6.75/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat X) Y))) (= (@ (@ tptp.inf_inf_set_nat _let_1) Y) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn X) Y))) (= (@ (@ tptp.inf_inf_assn _let_1) Y) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat X) Y))) (= (@ (@ tptp.inf_inf_nat _let_1) Y) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ (@ tptp.inf_inf_Product_unit X) Y))) (= (@ (@ tptp.inf_inf_Product_unit _let_1) Y) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat X) Y))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) Y) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.inf_inf_set_nat A) B))) (= (@ (@ tptp.inf_inf_set_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ (@ tptp.inf_inf_assn A) B))) (= (@ (@ tptp.inf_inf_assn _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.inf_inf_nat A) B))) (= (@ (@ tptp.inf_inf_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ (@ tptp.inf_inf_Product_unit A) B))) (= (@ (@ tptp.inf_inf_Product_unit _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B))) (= (@ (@ tptp.inf_in2572325071724192079at_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.inf_inf_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) X) X)))
% 6.75/7.10 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.inf_inf_assn A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.inf_inf_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))) (= (@ (@ tptp.sup_su718114333110466843at_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))) (= (@ (@ tptp.sup_su3035147773818789531at_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))) (= (@ (@ tptp.sup_su5525570899277871387at_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ (@ tptp.sup_sup_set_nat A) B))) (= (@ (@ tptp.sup_sup_set_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.sup_sup_nat A) B))) (= (@ (@ tptp.sup_sup_nat _let_1) B) _let_1))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) X) X)))
% 6.75/7.10 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.sup_sup_nat X) X) X)))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) A) A)))
% 6.75/7.10 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.sup_sup_nat A) A) A)))
% 6.75/7.10 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.10 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.10 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B3)))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B3)))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (or (@ _let_1 A3) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (B3 tptp.set_o) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (B3 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc859450856879609959at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc4166570645942440679at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (=> (not (@ _let_1 B3)) (@ _let_1 A3)) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) H) (or (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H)))))
% 6.75/7.11 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.bot_bot_assn) P) tptp.bot_bot_assn)))
% 6.75/7.11 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn P) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit A))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (and (@ _let_1 B) (@ _let_1 C))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit X))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)) (and (@ _let_1 Y) (@ _let_1 Z))))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B) C)) A) (and (@ (@ tptp.ord_le3000389064537975527at_nat B) A) (@ (@ tptp.ord_le3000389064537975527at_nat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C)) A) (and (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (@ (@ tptp.ord_le8081472938463900775at_nat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C)) A) (and (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (@ (@ tptp.ord_le1268244103169919719at_nat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_set_nat B) A) (@ (@ tptp.ord_less_eq_set_nat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C)) A) (and (@ (@ tptp.ord_less_eq_set_int B) A) (@ (@ tptp.ord_less_eq_set_int C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.75/7.11 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat X) Y)) Z) (and (@ (@ tptp.ord_le3000389064537975527at_nat X) Z) (@ (@ tptp.ord_le3000389064537975527at_nat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) Z) (and (@ (@ tptp.ord_le8081472938463900775at_nat X) Z) (@ (@ tptp.ord_le8081472938463900775at_nat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) Z) (and (@ (@ tptp.ord_le1268244103169919719at_nat X) Z) (@ (@ tptp.ord_le1268244103169919719at_nat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_set_nat X) Z) (@ (@ tptp.ord_less_eq_set_nat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int X) Y)) Z) (and (@ (@ tptp.ord_less_eq_set_int X) Z) (@ (@ tptp.ord_less_eq_set_int Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_rat X) Z) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat X) Y)) Z) (and (@ (@ tptp.ord_less_eq_nat X) Z) (@ (@ tptp.ord_less_eq_nat Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int X) Y)) Z) (and (@ (@ tptp.ord_less_eq_int X) Z) (@ (@ tptp.ord_less_eq_int Y) Z)))))
% 6.75/7.11 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 6.75/7.11 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 6.75/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 6.75/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 6.75/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 6.75/7.11 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 6.75/7.11 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 6.75/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 6.75/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 6.75/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A) tptp.bot_bo5327735625951526323at_nat) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) tptp.bot_bo8422036546324065075at_nat) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) tptp.bot_bo228742789529271731at_nat) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A) tptp.bot_bo2099793752762293965at_nat) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A) tptp.bot_bot_set_o) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A) tptp.bot_bot_set_nat) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A) tptp.bot_bot_set_int) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (@ (@ tptp.sup_su718114333110466843at_nat A) B)) (and (= A tptp.bot_bo5327735625951526323at_nat) (= B tptp.bot_bo5327735625951526323at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (= tptp.bot_bo8422036546324065075at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) (and (= A tptp.bot_bo8422036546324065075at_nat) (= B tptp.bot_bo8422036546324065075at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (and (= A tptp.bot_bo228742789529271731at_nat) (= B tptp.bot_bo228742789529271731at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A) B)) (and (= A tptp.bot_bo2099793752762293965at_nat) (= B tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o A) B)) (and (= A tptp.bot_bot_set_o) (= B tptp.bot_bot_set_o)))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int A) B)) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) A) A)))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat A) B) tptp.bot_bo5327735625951526323at_nat) (and (= A tptp.bot_bo5327735625951526323at_nat) (= B tptp.bot_bo5327735625951526323at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat A) B) tptp.bot_bo8422036546324065075at_nat) (and (= A tptp.bot_bo8422036546324065075at_nat) (= B tptp.bot_bo8422036546324065075at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) tptp.bot_bo228742789529271731at_nat) (and (= A tptp.bot_bo228742789529271731at_nat) (= B tptp.bot_bo228742789529271731at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat A) B) tptp.bot_bo2099793752762293965at_nat) (and (= A tptp.bot_bo2099793752762293965at_nat) (= B tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o A) B) tptp.bot_bot_set_o) (and (= A tptp.bot_bot_set_o) (= B tptp.bot_bot_set_o)))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat A) B) tptp.bot_bot_set_nat) (and (= A tptp.bot_bot_set_nat) (= B tptp.bot_bot_set_nat)))))
% 6.75/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int A) B) tptp.bot_bot_set_int) (and (= A tptp.bot_bot_set_int) (= B tptp.bot_bot_set_int)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (= (@ (@ tptp.sup_su718114333110466843at_nat X) Y) tptp.bot_bo5327735625951526323at_nat) (and (= X tptp.bot_bo5327735625951526323at_nat) (= Y tptp.bot_bo5327735625951526323at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat X) Y) tptp.bot_bo8422036546324065075at_nat) (and (= X tptp.bot_bo8422036546324065075at_nat) (= Y tptp.bot_bo8422036546324065075at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) tptp.bot_bo228742789529271731at_nat) (and (= X tptp.bot_bo228742789529271731at_nat) (= Y tptp.bot_bo228742789529271731at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat X) Y) tptp.bot_bo2099793752762293965at_nat) (and (= X tptp.bot_bo2099793752762293965at_nat) (= Y tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.sup_sup_set_o X) Y) tptp.bot_bot_set_o) (and (= X tptp.bot_bot_set_o) (= Y tptp.bot_bot_set_o)))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.sup_sup_set_nat X) Y) tptp.bot_bot_set_nat) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.sup_sup_set_int X) Y) tptp.bot_bot_set_int) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (= tptp.bot_bo5327735625951526323at_nat (@ (@ tptp.sup_su718114333110466843at_nat X) Y)) (and (= X tptp.bot_bo5327735625951526323at_nat) (= Y tptp.bot_bo5327735625951526323at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (= tptp.bot_bo8422036546324065075at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) (and (= X tptp.bot_bo8422036546324065075at_nat) (= Y tptp.bot_bo8422036546324065075at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (= tptp.bot_bo228742789529271731at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) (and (= X tptp.bot_bo228742789529271731at_nat) (= Y tptp.bot_bo228742789529271731at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (= tptp.bot_bo2099793752762293965at_nat (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) (and (= X tptp.bot_bo2099793752762293965at_nat) (= Y tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.sup_sup_set_o X) Y)) (and (= X tptp.bot_bot_set_o) (= Y tptp.bot_bot_set_o)))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)) (and (= X tptp.bot_bot_set_nat) (= Y tptp.bot_bot_set_nat)))))
% 6.75/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.sup_sup_set_int X) Y)) (and (= X tptp.bot_bot_set_int) (= Y tptp.bot_bot_set_int)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X) tptp.bot_bo5327735625951526323at_nat) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.75/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 6.75/7.11 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) _let_1) (and (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 6.75/7.11 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))) (= (@ (@ tptp.rep_assn (@ (@ tptp.sup_sup_assn P) Q)) _let_1) (or (@ (@ tptp.rep_assn P) _let_1) (@ (@ tptp.rep_assn Q) _let_1))))))
% 6.75/7.11 (assert (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int tptp.bot_bo8147686125503663512_int_o)))
% 6.75/7.11 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat tptp.bot_bot_list_nat_o)))
% 6.75/7.11 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat tptp.bot_bot_set_nat_o)))
% 6.75/7.11 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat tptp.bot_bo482883023278783056_nat_o)))
% 6.75/7.11 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o tptp.bot_bot_o_o)))
% 6.75/7.11 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat tptp.bot_bot_nat_o)))
% 6.75/7.11 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int tptp.bot_bot_int_o)))
% 6.75/7.11 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.inf_inf_assn P) Q)) H) (and (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H)))))
% 6.75/7.11 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn tptp.bot_bot_assn) H))))
% 6.75/7.11 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (= (@ (@ tptp.times_times_assn (@ (@ tptp.sup_sup_assn A3) B3)) C3) (@ (@ tptp.sup_sup_assn (@ (@ tptp.times_times_assn A3) C3)) (@ (@ tptp.times_times_assn B3) C3)))))
% 6.75/7.11 (assert (forall ((C3 tptp.assn) (A3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn C3))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn A3) B3)) (@ (@ tptp.sup_sup_assn (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_set_nat)) (= (exists ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A3)) (not (= A3 tptp.bot_bot_set_set_nat)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (exists ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A3)) (not (= A3 tptp.bot_bo2099793752762293965at_nat)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_o)) (= (exists ((X4 Bool)) (@ (@ tptp.member_o X4) A3)) (not (= A3 tptp.bot_bot_set_o)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat)) (= (exists ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A3)) (not (= A3 tptp.bot_bot_set_nat)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_int)) (= (exists ((X4 tptp.int)) (@ (@ tptp.member_int X4) A3)) (not (= A3 tptp.bot_bot_set_int)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_set_nat)) (=> (forall ((Y3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat Y3) A3))) (= A3 tptp.bot_bot_set_set_nat))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat Y3) A3))) (= A3 tptp.bot_bo2099793752762293965at_nat))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_o)) (=> (forall ((Y3 Bool)) (not (@ (@ tptp.member_o Y3) A3))) (= A3 tptp.bot_bot_set_o))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((Y3 tptp.nat)) (not (@ (@ tptp.member_nat Y3) A3))) (= A3 tptp.bot_bot_set_nat))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_int)) (=> (forall ((Y3 tptp.int)) (not (@ (@ tptp.member_int Y3) A3))) (= A3 tptp.bot_bot_set_int))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (= A3 tptp.bot_bot_set_set_nat) (not (@ (@ tptp.member_set_nat A) A3)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (A tptp.product_prod_nat_nat)) (=> (= A3 tptp.bot_bo2099793752762293965at_nat) (not (@ (@ tptp.member8440522571783428010at_nat A) A3)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_o) (A Bool)) (=> (= A3 tptp.bot_bot_set_o) (not (@ (@ tptp.member_o A) A3)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (= A3 tptp.bot_bot_set_nat) (not (@ (@ tptp.member_nat A) A3)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_int) (A tptp.int)) (=> (= A3 tptp.bot_bot_set_int) (not (@ (@ tptp.member_int A) A3)))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.member_set_nat A) tptp.bot_bot_set_set_nat))))
% 6.75/7.11 (assert (forall ((A tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 6.75/7.11 (assert (forall ((A Bool)) (not (@ (@ tptp.member_o A) tptp.bot_bot_set_o))))
% 6.75/7.11 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.member_nat A) tptp.bot_bot_set_nat))))
% 6.75/7.11 (assert (forall ((A tptp.int)) (not (@ (@ tptp.member_int A) tptp.bot_bot_set_int))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (let ((_let_2 (@ tptp.inf_inf_Product_unit Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B))) (let ((_let_2 (@ tptp.inf_inf_set_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn B))) (let ((_let_2 (@ tptp.inf_inf_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat B))) (let ((_let_2 (@ tptp.inf_inf_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.product_unit) (A tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit B))) (let ((_let_2 (@ tptp.inf_inf_Product_unit A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.inf_inf_assn Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.inf_inf_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_Product_unit (lambda ((X4 tptp.product_unit) (Y4 tptp.product_unit)) (@ (@ tptp.inf_inf_Product_unit Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.inf_inf_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (@ (@ tptp.inf_inf_assn B5) A5))))
% 6.75/7.11 (assert (= tptp.inf_inf_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.inf_inf_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.inf_inf_Product_unit (lambda ((A5 tptp.product_unit) (B5 tptp.product_unit)) (@ (@ tptp.inf_inf_Product_unit B5) A5))))
% 6.75/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B5) A5))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (= (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit A))) (= (@ (@ tptp.inf_inf_Product_unit (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C))))))
% 6.75/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.inf_inf_assn Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.inf_inf_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_inf_Product_unit (lambda ((X4 tptp.product_unit) (Y4 tptp.product_unit)) (@ (@ tptp.inf_inf_Product_unit Y4) X4))))
% 6.75/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat Y4) X4))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (= (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ tptp.inf_inf_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ tptp.inf_inf_assn Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ tptp.inf_inf_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (let ((_let_2 (@ tptp.inf_inf_Product_unit Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat B))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat B))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat B))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat B))) (let ((_let_2 (@ tptp.sup_sup_set_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat B))) (let ((_let_2 (@ tptp.sup_sup_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.75/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_sup_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.sup_sup_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A5 tptp.set_Pr8693737435421807431at_nat) (B5 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A5 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B5) A5))))
% 6.75/7.11 (assert (= tptp.sup_sup_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.sup_sup_nat B5) A5))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B) C))))))
% 6.75/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.sup_sup_nat B) C))))))
% 6.75/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat Y4) X4))))
% 6.75/7.11 (assert (= tptp.sup_sup_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.sup_sup_nat Y4) X4))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ tptp.sup_sup_set_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ tptp.sup_sup_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (let ((_let_2 (@ _let_1 Y))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.inf_inf_set_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat B6) A6))))
% 6.75/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat B6) A6))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B3)) (@ _let_1 B3)))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B3)) (@ _let_1 B3)))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (@ _let_1 B3)))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ _let_1 B3)))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ _let_1 B3)))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B3)) (@ _let_1 A3)))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B3)) (@ _let_1 A3)))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (@ _let_1 A3)))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ _let_1 A3)))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ _let_1 A3)))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (not (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A3))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (let ((_let_2 (@ tptp.sup_sup_set_nat B3))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (let ((_let_2 (@ _let_1 B3))) (= (@ _let_1 _let_2) _let_2)))))
% 6.75/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.sup_su718114333110466843at_nat B6) A6))))
% 6.75/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.sup_su3035147773818789531at_nat B6) A6))))
% 6.75/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.sup_su5525570899277871387at_nat B6) A6))))
% 6.75/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.sup_sup_set_nat B6) A6))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) A3) A3)))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A3))) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C3))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.produc859450856879609959at_nat Bool))) (= (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X4) (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ P X4))) (and (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X4) A3) (@ P X4))) (forall ((X4 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (P (-> tptp.produc4166570645942440679at_nat Bool))) (= (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ P X4))) (and (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) A3) (@ P X4))) (forall ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ P X4))) (and (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) A3) (@ P X4))) (forall ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P (-> tptp.nat Bool))) (= (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ P X4))) (and (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (@ P X4))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (P (-> tptp.produc859450856879609959at_nat Bool))) (= (exists ((X4 tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X4) (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ P X4))) (or (exists ((X4 tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X4) A3) (@ P X4))) (exists ((X4 tptp.produc859450856879609959at_nat)) (and (@ (@ tptp.member8206827879206165904at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (P (-> tptp.produc4166570645942440679at_nat Bool))) (= (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ P X4))) (or (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) A3) (@ P X4))) (exists ((X4 tptp.produc4166570645942440679at_nat)) (and (@ (@ tptp.member6689249552917799696at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (P (-> tptp.produc3843707927480180839at_nat Bool))) (= (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ P X4))) (or (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) A3) (@ P X4))) (exists ((X4 tptp.produc3843707927480180839at_nat)) (and (@ (@ tptp.member8757157785044589968at_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P (-> tptp.nat Bool))) (= (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ P X4))) (or (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B3) (@ P X4)))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (B3 tptp.set_o) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (B3 tptp.set_int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc859450856879609959at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc4166570645942440679at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc3843707927480180839at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (B3 tptp.set_nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))))))
% 6.75/7.11 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_set_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc859450856879609959at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc4166570645942440679at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.produc3843707927480180839at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (=> (not (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.75/7.11 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.product_unit) (C tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit B) C) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 6.75/7.11 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 6.75/7.11 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 6.75/7.11 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 6.75/7.11 (assert (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit A) C) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) C))))
% 6.75/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_le3221252021190050221t_unit (lambda ((B5 tptp.product_unit) (A5 tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((B5 tptp.set_Pr1261947904930325089at_nat) (A5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (= (@ (@ tptp.inf_inf_assn A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_le3221252021190050221t_unit (lambda ((A5 tptp.product_unit) (B5 tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (= (@ (@ tptp.inf_inf_rat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ tptp.inf_inf_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (= (@ (@ tptp.inf_inf_int A5) B5) A5))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) B)))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) A)))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) A)))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (= A5 (@ (@ tptp.inf_inf_set_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (= A5 (@ (@ tptp.inf_inf_assn A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_le3221252021190050221t_unit (lambda ((A5 tptp.product_unit) (B5 tptp.product_unit)) (= A5 (@ (@ tptp.inf_inf_Product_unit A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (= A5 (@ (@ tptp.inf_inf_set_int A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (= A5 (@ (@ tptp.inf_inf_rat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (= A5 (@ (@ tptp.inf_inf_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (= A5 (@ (@ tptp.inf_inf_int A5) B5)))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_set_int Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.inf_inf_int B) C)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_Product_unit B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (= (@ (@ tptp.inf_inf_assn X) Y) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit Y) X) (= (@ (@ tptp.inf_inf_Product_unit X) Y) Y))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.inf_inf_set_int X) Y) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.inf_inf_rat X) Y) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.inf_inf_nat X) Y) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.inf_inf_int X) Y) Y))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (@ (@ tptp.inf_inf_assn X) Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit X) Y) (= (@ (@ tptp.inf_inf_Product_unit X) Y) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.inf_inf_set_int X) Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.inf_inf_rat X) Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.inf_inf_nat X) Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.inf_inf_int X) Y) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit B) A) (= (@ (@ tptp.inf_inf_Product_unit A) B) B))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ (@ tptp.inf_inf_set_int A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit A) B) (= (@ (@ tptp.inf_inf_Product_unit A) B) A))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= (@ (@ tptp.inf_inf_set_int A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (= (@ (@ tptp.inf_inf_assn X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_le3221252021190050221t_unit (lambda ((X4 tptp.product_unit) (Y4 tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.inf_inf_rat X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.inf_inf_nat X4) Y4) X4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.inf_inf_int X4) Y4) X4))))
% 6.81/7.11 (assert (forall ((F (-> 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 (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_set_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.assn tptp.assn tptp.assn)) (X tptp.assn) (Y tptp.assn)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_assn X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.product_unit tptp.product_unit tptp.product_unit)) (X tptp.product_unit) (Y tptp.product_unit)) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_Product_unit X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> 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 (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.set_int tptp.set_int tptp.set_int)) (X tptp.set_int) (Y tptp.set_int)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int) (Z2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_set_int X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.rat tptp.rat tptp.rat)) (X tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_rat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X tptp.int) (Y tptp.int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F X3) Y3)) X3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ F X3) Y3)) Y3)) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X3))) (=> (@ _let_1 Y3) (=> (@ _let_1 Z2) (@ _let_1 (@ (@ F Y3) Z2)))))) (= (@ (@ tptp.inf_inf_int X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (= A (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.ord_less_eq_assn A) B))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (= A (@ (@ tptp.inf_inf_Product_unit A) B)) (@ (@ tptp.ord_le3221252021190050221t_unit A) B))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A (@ (@ tptp.inf_inf_set_int A) B)) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (= A (@ (@ tptp.inf_inf_assn A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit A) B) (= A (@ (@ tptp.inf_inf_Product_unit A) B)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A (@ (@ tptp.inf_inf_set_int A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A (@ (@ tptp.inf_inf_rat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A (@ (@ tptp.inf_inf_nat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A (@ (@ tptp.inf_inf_int A) B)))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn B) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.product_unit) (X tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit B) X) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (X tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) X) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (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))))
% 6.81/7.11 (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))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) X) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (X tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit A) X) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (X tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) X) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (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))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (@ (@ tptp.ord_less_eq_set_nat B) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) (@ (@ tptp.inf_inf_set_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) C) (=> (@ (@ tptp.ord_less_eq_assn B) D2) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn A) B)) (@ (@ tptp.inf_inf_assn C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit) (D2 tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit A) C) (=> (@ (@ tptp.ord_le3221252021190050221t_unit B) D2) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) (@ (@ tptp.inf_inf_Product_unit C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (D2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) C) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) D2) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) (@ (@ tptp.inf_in2572325071724192079at_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C) (=> (@ (@ tptp.ord_less_eq_set_int B) D2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A) B)) (@ (@ tptp.inf_inf_set_int C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat A) B)) (@ (@ tptp.inf_inf_rat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat A) B)) (@ (@ tptp.inf_inf_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int A) B)) (@ (@ tptp.inf_inf_int C) D2))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit A) B)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (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))))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le3221252021190050221t_unit X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_Product_unit A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.81/7.11 (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))))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_int A) B)) (not (=> (@ _let_1 A) (not (@ _let_1 B))))))))
% 6.81/7.11 (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))))))))
% 6.81/7.11 (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))))))))
% 6.81/7.11 (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))))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.inf_inf_rat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.inf_inf_nat X) Y)) Y)))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.inf_inf_int X) Y)) Y)))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((A5 tptp.set_Pr8693737435421807431at_nat) (B5 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((A5 tptp.set_Pr8551490117392284871at_nat) (B5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A5 tptp.set_Pr4329608150637261639at_nat) (B5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B5) B5))))
% 6.81/7.11 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((B5 tptp.set_Pr8693737435421807431at_nat) (A5 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((B5 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B5 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (= (@ (@ tptp.sup_sup_rat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (= (@ (@ tptp.sup_sup_nat A5) B5) A5))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (= (@ (@ tptp.sup_sup_int A5) B5) A5))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat B) (@ (@ tptp.sup_su718114333110466843at_nat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat B) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B) (@ (@ tptp.sup_sup_set_nat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B) (@ (@ tptp.sup_sup_set_int A) B))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.sup_sup_rat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.sup_sup_nat A) B))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.sup_sup_int A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat A) (@ (@ tptp.sup_su718114333110466843at_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat A) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A) (@ (@ tptp.sup_sup_set_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) (@ (@ tptp.sup_sup_set_int A) B))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.sup_sup_rat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.sup_sup_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.sup_sup_int A) B))))
% 6.81/7.11 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((B5 tptp.set_Pr8693737435421807431at_nat) (A5 tptp.set_Pr8693737435421807431at_nat)) (= A5 (@ (@ tptp.sup_su718114333110466843at_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((B5 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (= A5 (@ (@ tptp.sup_su3035147773818789531at_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((B5 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (= A5 (@ (@ tptp.sup_su5525570899277871387at_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (= A5 (@ (@ tptp.sup_sup_set_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (= A5 (@ (@ tptp.sup_sup_set_int A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (= A5 (@ (@ tptp.sup_sup_rat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (= A5 (@ (@ tptp.sup_sup_nat A5) B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (= A5 (@ (@ tptp.sup_sup_int A5) B5)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) A) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C) A) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C) A) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat) (C tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (=> (@ (@ tptp.ord_less_eq_set_nat C) A) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) A) (not (@ (@ tptp.ord_le3000389064537975527at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (not (@ (@ tptp.ord_le8081472938463900775at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (not (@ (@ tptp.ord_le1268244103169919719at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_set_nat B) A) (not (@ (@ tptp.ord_less_eq_set_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (C tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_set_int B) A) (not (@ (@ tptp.ord_less_eq_set_int C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat X) Y) (= (@ (@ tptp.sup_su718114333110466843at_nat X) Y) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat X) Y) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) Y) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat X) Y) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) Y))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (@ (@ tptp.sup_sup_set_int X) Y) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.sup_sup_rat X) Y) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.sup_sup_nat X) Y) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.sup_sup_int X) Y) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y) X) (= (@ (@ tptp.sup_su718114333110466843at_nat X) Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Y) X) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) X))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.sup_sup_set_int X) Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.sup_sup_rat X) Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.sup_sup_nat X) Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.sup_sup_int X) Y) X))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A) B) (= (@ (@ tptp.sup_su718114333110466843at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A) B) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) B) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) B))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= (@ (@ tptp.sup_sup_set_int A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) A) (= (@ (@ tptp.sup_su718114333110466843at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) A))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ (@ tptp.sup_sup_set_int A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 6.81/7.11 (assert (forall ((F (-> tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat tptp.set_Pr8693737435421807431at_nat)) (X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y3) X3) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Z2) X3) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_su718114333110466843at_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat tptp.set_Pr8551490117392284871at_nat)) (X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat X3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Y3) X3) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Z2) X3) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat tptp.set_Pr4329608150637261639at_nat)) (X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y3) X3) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z2) X3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> 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) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_set_nat Z2) X3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_set_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.set_int tptp.set_int tptp.set_int)) (X tptp.set_int) (Y tptp.set_int)) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.set_int) (Y3 tptp.set_int) (Z2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y3) X3) (=> (@ (@ tptp.ord_less_eq_set_int Z2) X3) (@ (@ tptp.ord_less_eq_set_int (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_set_int X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> 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) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat) (Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y3) X3) (=> (@ (@ tptp.ord_less_eq_rat Z2) X3) (@ (@ tptp.ord_less_eq_rat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_rat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> 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) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y3) X3) (=> (@ (@ tptp.ord_less_eq_nat Z2) X3) (@ (@ tptp.ord_less_eq_nat (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_nat X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((F (-> 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) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.ord_less_eq_int Y3) (@ (@ F X3) Y3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y3) X3) (=> (@ (@ tptp.ord_less_eq_int Z2) X3) (@ (@ tptp.ord_less_eq_int (@ (@ F Y3) Z2)) X3)))) (= (@ (@ tptp.sup_sup_int X) Y) (@ (@ F X) Y)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (= A (@ (@ tptp.sup_su718114333110466843at_nat A) B)) (@ (@ tptp.ord_le3000389064537975527at_nat B) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (= A (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) (@ (@ tptp.ord_le8081472938463900775at_nat B) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (= A (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.ord_le1268244103169919719at_nat B) A))))
% 6.81/7.11 (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))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (= A (@ (@ tptp.sup_sup_set_int A) B)) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) A) (= A (@ (@ tptp.sup_su718114333110466843at_nat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) A) (= A (@ (@ tptp.sup_su3035147773818789531at_nat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) A) (= A (@ (@ tptp.sup_su5525570899277871387at_nat A) B)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A (@ (@ tptp.sup_sup_set_int A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.sup_sup_rat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.sup_sup_nat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.sup_sup_int A) B)))))
% 6.81/7.11 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (= (@ (@ tptp.sup_sup_rat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (= (@ (@ tptp.sup_sup_nat X4) Y4) Y4))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (= (@ (@ tptp.sup_sup_int X4) Y4) Y4))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Y) X) (=> (@ (@ tptp.ord_le3000389064537975527at_nat Z) X) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Y) X) (=> (@ (@ tptp.ord_le8081472938463900775at_nat Z) X) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Y) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat Z) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat) (Z tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat Y) X) (=> (@ (@ tptp.ord_less_eq_set_nat Z) X) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (=> (@ (@ tptp.ord_less_eq_set_int Z) X) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (=> (@ (@ tptp.ord_less_eq_rat Z) X) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (=> (@ (@ tptp.ord_less_eq_nat Z) X) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (=> (@ (@ tptp.ord_less_eq_int Z) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int Y) Z)) X)))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (D2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A) C) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) D2) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A) B)) (@ (@ tptp.sup_su718114333110466843at_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A) C) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) D2) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) (@ (@ tptp.sup_su3035147773818789531at_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) C) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) D2) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) (@ (@ tptp.sup_su5525570899277871387at_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat) (D2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) C) (=> (@ (@ tptp.ord_less_eq_set_nat B) D2) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A) B)) (@ (@ tptp.sup_sup_set_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (C tptp.set_int) (B tptp.set_int) (D2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) C) (=> (@ (@ tptp.ord_less_eq_set_int B) D2) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A) B)) (@ (@ tptp.sup_sup_set_int C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) C) (=> (@ (@ tptp.ord_less_eq_rat B) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat A) B)) (@ (@ tptp.sup_sup_rat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ (@ tptp.ord_less_eq_nat B) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat A) B)) (@ (@ tptp.sup_sup_nat C) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) C) (=> (@ (@ tptp.ord_less_eq_int B) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int A) B)) (@ (@ tptp.sup_sup_int C) D2))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (D2 tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C) A) (=> (@ (@ tptp.ord_le3000389064537975527at_nat D2) B) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat C) D2)) (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (D2 tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C) A) (=> (@ (@ tptp.ord_le8081472938463900775at_nat D2) B) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat C) D2)) (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (D2 tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C) A) (=> (@ (@ tptp.ord_le1268244103169919719at_nat D2) B) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat C) D2)) (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (D2 tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C) A) (=> (@ (@ tptp.ord_less_eq_set_nat D2) B) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat C) D2)) (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_int) (A tptp.set_int) (D2 tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C) A) (=> (@ (@ tptp.ord_less_eq_set_int D2) B) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int C) D2)) (@ (@ tptp.sup_sup_set_int A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (D2 tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D2) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat C) D2)) (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (D2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D2) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat C) D2)) (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.int) (A tptp.int) (D2 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D2) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int C) D2)) (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (B tptp.set_int) (A tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le3000389064537975527at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le8081472938463900775at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le1268244103169919719at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_int A) B))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y) (@ (@ tptp.sup_su718114333110466843at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y) (@ (@ tptp.sup_sup_set_int X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A) X) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B) X) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A) B)) X)))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A) X) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B) X) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) X)))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) X) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B) X) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) X)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (X tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) X) (=> (@ (@ tptp.ord_less_eq_set_int B) X) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A) B)) X)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A) B)) X) (not (=> (@ (@ tptp.ord_le3000389064537975527at_nat A) X) (not (@ (@ tptp.ord_le3000389064537975527at_nat B) X)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A) B)) X) (not (=> (@ (@ tptp.ord_le8081472938463900775at_nat A) X) (not (@ (@ tptp.ord_le8081472938463900775at_nat B) X)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A) B)) X) (not (=> (@ (@ tptp.ord_le1268244103169919719at_nat A) X) (not (@ (@ tptp.ord_le1268244103169919719at_nat B) X)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A) B)) X) (not (=> (@ (@ tptp.ord_less_eq_set_int A) X) (not (@ (@ tptp.ord_less_eq_set_int B) X)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (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)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.sup_sup_int X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y) (@ (@ tptp.sup_su718114333110466843at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y) (@ (@ tptp.sup_su3035147773818789531at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y) (@ (@ tptp.sup_su5525570899277871387at_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (X tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y) (@ (@ tptp.sup_sup_set_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y) (@ (@ tptp.sup_sup_set_int X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y) (@ (@ tptp.sup_sup_rat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y) (@ (@ tptp.sup_sup_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_int Y) (@ (@ tptp.sup_sup_int X) Y))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A3) (forall ((Y4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y4) B3) (not (= X4 Y4)))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A3) (forall ((Y4 Bool)) (=> (@ (@ tptp.member_o Y4) B3) (= X4 (not Y4)))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (forall ((Y4 tptp.nat)) (=> (@ (@ tptp.member_nat Y4) B3) (not (= X4 Y4)))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) B3) (not (= X4 Y4)))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) B3) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) B3) tptp.bot_bot_set_o)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) B3) tptp.bot_bot_set_nat)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) B3) tptp.bot_bot_set_int)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (= (@ (@ tptp.inf_inf_set_set_nat A3) B3) tptp.bot_bot_set_set_nat) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (forall ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_set_nat A3) B3) tptp.bot_bot_set_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A3) (not (@ _let_1 B3))))) (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit (@ (@ tptp.inf_inf_Product_unit Y) Z)) X) (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.sup_sup_Product_unit Y) X)) (@ (@ tptp.sup_sup_Product_unit Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z)) X) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y) X)) (@ (@ tptp.sup_su718114333110466843at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z)) X) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) X)) (@ (@ tptp.sup_su3035147773818789531at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) Z)) X) (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) X)) (@ (@ tptp.sup_sup_nat Z) X)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit X))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z)) (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.sup_sup_Product_unit Y) Z)) X) (@ (@ tptp.sup_sup_Product_unit (@ (@ tptp.inf_inf_Product_unit Y) X)) (@ (@ tptp.inf_inf_Product_unit Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) X) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat Y) X)) (@ (@ tptp.inf_in4302113700860409141at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) X)) (@ (@ tptp.inf_in1697001100524423349at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (Z tptp.nat) (X tptp.nat)) (= (@ (@ tptp.inf_inf_nat (@ (@ tptp.sup_sup_nat Y) Z)) X) (@ (@ tptp.sup_sup_nat (@ (@ tptp.inf_inf_nat Y) X)) (@ (@ tptp.inf_inf_nat Z) X)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (= (@ _let_1 (@ (@ tptp.sup_sup_Product_unit Y) Z)) (@ (@ tptp.sup_sup_Product_unit (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y3) Z2)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y3) Z2)) (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_Product_unit Y) Z)) (@ (@ tptp.sup_sup_Product_unit (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y3) Z2)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y3) Z2)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y3) Z2)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y3) Z2)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y3) Z2)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X3))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y3) Z2)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn) (Z2 tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y3) Z2)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit X))) (=> (forall ((X3 tptp.product_unit) (Y3 tptp.product_unit) (Z2 tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_Product_unit Y3) Z2)) (@ (@ tptp.sup_sup_Product_unit (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z)) (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (=> (forall ((X3 tptp.set_Pr1261947904930325089at_nat) (Y3 tptp.set_Pr1261947904930325089at_nat) (Z2 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y3) Z2)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (=> (forall ((X3 tptp.set_Pr8693737435421807431at_nat) (Y3 tptp.set_Pr8693737435421807431at_nat) (Z2 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y3) Z2)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (=> (forall ((X3 tptp.set_Pr8551490117392284871at_nat) (Y3 tptp.set_Pr8551490117392284871at_nat) (Z2 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y3) Z2)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (=> (forall ((X3 tptp.set_Pr4329608150637261639at_nat) (Y3 tptp.set_Pr4329608150637261639at_nat) (Z2 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y3) Z2)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y3) Z2)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X3))) (= (@ _let_1 (@ (@ tptp.sup_sup_nat Y3) Z2)) (@ (@ tptp.sup_sup_nat (@ _let_1 Y3)) (@ _let_1 Z2))))) (= (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z)) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) tptp.bot_bo5327735625951526323at_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) tptp.bot_bo8422036546324065075at_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) tptp.bot_bo228742789529271731at_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat A3) tptp.bot_bo2099793752762293965at_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o A3) tptp.bot_bot_set_o) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A3) tptp.bot_bot_set_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A3) tptp.bot_bot_set_int) A3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat tptp.bot_bo5327735625951526323at_nat) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat tptp.bot_bo8422036546324065075at_nat) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat tptp.bot_bo228742789529271731at_nat) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat tptp.bot_bo2099793752762293965at_nat) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o tptp.bot_bot_set_o) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat tptp.bot_bot_set_nat) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int tptp.bot_bot_set_int) B3) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3)) A3) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B3) A3)) (@ (@ tptp.sup_su6327502436637775413at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat B3) C3)) A3) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) A3)) (@ (@ tptp.sup_su718114333110466843at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat B3) C3)) A3) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B3) A3)) (@ (@ tptp.sup_su3035147773818789531at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B3) C3)) A3) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) A3)) (@ (@ tptp.sup_su5525570899277871387at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (C3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B3) C3)) A3) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B3) A3)) (@ (@ tptp.sup_sup_set_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat B3) C3)) A3) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat B3) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat B3) C3)) A3) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat B3) A3)) (@ (@ tptp.inf_in4302113700860409141at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3)) A3) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat B3) A3)) (@ (@ tptp.inf_in1697001100524423349at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3)) A3) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat B3) A3)) (@ (@ tptp.inf_in7913087082777306421at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (C3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat B3) C3)) A3) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat B3) A3)) (@ (@ tptp.inf_inf_set_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat B3) C3)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat B3) C3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B3) C3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C3)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B3) C3)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3))) (@ (@ tptp.inf_in2572325071724192079at_nat C3) A3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.sup_su6327502436637775413at_nat B3) C3))) (@ (@ tptp.sup_su6327502436637775413at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)) (@ (@ tptp.inf_in4302113700860409141at_nat B3) C3))) (@ (@ tptp.inf_in4302113700860409141at_nat C3) A3)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.sup_su718114333110466843at_nat B3) C3))) (@ (@ tptp.sup_su718114333110466843at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)) (@ (@ tptp.inf_in1697001100524423349at_nat B3) C3))) (@ (@ tptp.inf_in1697001100524423349at_nat C3) A3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3))) (@ (@ tptp.sup_su3035147773818789531at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)) (@ (@ tptp.inf_in7913087082777306421at_nat B3) C3))) (@ (@ tptp.inf_in7913087082777306421at_nat C3) A3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3))) (@ (@ tptp.sup_su5525570899277871387at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat B3) C3))) (@ (@ tptp.inf_inf_set_nat C3) A3)) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat B3) C3))) (@ (@ tptp.sup_sup_set_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (@ (@ tptp.ord_less_eq_assn (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z))) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit X))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z))) (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.sup_sup_rat X))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ (@ tptp.inf_inf_rat Y) Z))) (@ (@ tptp.inf_inf_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat X))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 (@ (@ tptp.inf_inf_nat Y) Z))) (@ (@ tptp.inf_inf_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.sup_sup_int X))) (@ (@ tptp.ord_less_eq_int (@ _let_1 (@ (@ tptp.inf_inf_int Y) Z))) (@ (@ tptp.inf_inf_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z 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) Z))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.sup_sup_set_int X))) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.inf_inf_set_int Y) Z))) (@ (@ tptp.inf_inf_set_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (@ (@ tptp.ord_le3000389064537975527at_nat (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z))) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (@ (@ tptp.ord_le8081472938463900775at_nat (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z))) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.sup_sup_Product_unit (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_Product_unit Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.inf_inf_rat X))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.sup_sup_rat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_rat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat X))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.sup_sup_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_nat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.inf_inf_int X))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.sup_sup_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_int Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z 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 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int X))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_sup_set_int Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z 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 Z))) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X))) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z))) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z))))))
% 6.81/7.11 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) tptp.bot_bot_assn) tptp.bot_bot_assn)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) tptp.bot_bot_Product_unit) tptp.bot_bot_Product_unit)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 6.81/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 6.81/7.11 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn tptp.bot_bot_assn) X) tptp.bot_bot_assn)))
% 6.81/7.11 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit tptp.bot_bot_Product_unit) X) tptp.bot_bot_Product_unit)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bot_bo2099793752762293965at_nat) X) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o tptp.bot_bot_set_o) X) tptp.bot_bot_set_o)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat tptp.bot_bot_set_nat) X) tptp.bot_bot_set_nat)))
% 6.81/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int tptp.bot_bot_set_int) X) tptp.bot_bot_set_int)))
% 6.81/7.11 (assert (= (@ (@ tptp.heap_Time_execute_a tptp.c) tptp.h2) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat tptp.r2) (@ (@ tptp.produc584006145561248582it_nat tptp.h) tptp.t)))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (exists ((As13 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As13) As23)) (= (@ (@ tptp.inf_inf_set_nat As13) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As23)))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (not (exists ((As1 tptp.set_nat) (As2 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As1) As2)) (= (@ (@ tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As2))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xb (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (= Y (not (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As12) As22)) (= (@ (@ tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As22)))))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ (@ tptp.times_assn_raw P) Q) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (and (= As (@ (@ tptp.sup_sup_set_nat As12) As22)) (= (@ (@ tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (@ P (@ _let_1 As12)) (@ Q (@ _let_1 As22))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.81/7.11 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.81/7.11 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.81/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.81/7.11 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 6.81/7.11 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.81/7.11 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.81/7.11 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.81/7.11 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A3) tptp.bot_bo2099793752762293965at_nat) (= A3 tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A3) tptp.bot_bot_set_o) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A3)))
% 6.81/7.11 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)) (and (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) C3) (and (@ (@ tptp.ord_le3000389064537975527at_nat A3) C3) (@ (@ tptp.ord_le3000389064537975527at_nat B3) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) C3) (and (@ (@ tptp.ord_le8081472938463900775at_nat A3) C3) (@ (@ tptp.ord_le8081472938463900775at_nat B3) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) C3) (and (@ (@ tptp.ord_le1268244103169919719at_nat A3) C3) (@ (@ tptp.ord_le1268244103169919719at_nat B3) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) C3) (and (@ (@ tptp.ord_less_eq_set_nat A3) C3) (@ (@ tptp.ord_less_eq_set_nat B3) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B3)) C3) (and (@ (@ tptp.ord_less_eq_set_int A3) C3) (@ (@ tptp.ord_less_eq_set_int B3) C3)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (= A5 (@ (@ tptp.inf_inf_assn A5) B5)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat) (D3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) D3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (D3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) C3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) D3) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int) (D3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C3) (=> (@ (@ tptp.ord_less_eq_set_int B3) D3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.inf_inf_set_int C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B3)) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) B3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) B3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) B3)) B3)))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= (@ (@ tptp.inf_inf_set_int A3) B3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (= (@ (@ tptp.inf_inf_set_int A3) B3) A3))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat C3))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat C3))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C3))) (=> (@ _let_1 A3) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (P (-> Bool Bool)) (Q (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.inf_inf_set_o A3) (@ tptp.collect_o P))) (@ (@ tptp.inf_inf_set_o B3) (@ tptp.collect_o Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int A3) B3) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ (@ tptp.inf_in2269163501485487111nt_int A3) (@ tptp.collec213857154873943460nt_int P))) (@ (@ tptp.inf_in2269163501485487111nt_int B3) (@ tptp.collec213857154873943460nt_int Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat) (P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B3) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ (@ tptp.inf_inf_set_list_nat A3) (@ tptp.collect_list_nat P))) (@ (@ tptp.inf_inf_set_list_nat B3) (@ tptp.collect_list_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.inf_inf_set_set_nat A3) (@ tptp.collect_set_nat P))) (@ (@ tptp.inf_inf_set_set_nat B3) (@ tptp.collect_set_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))) (@ (@ tptp.inf_inf_set_nat B3) (@ tptp.collect_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.collec3392354462482085612at_nat P))) (@ (@ tptp.inf_in2572325071724192079at_nat B3) (@ tptp.collec3392354462482085612at_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (=> (@ P X3) (@ Q X3)))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))) (@ (@ tptp.inf_inf_set_int B3) (@ tptp.collect_int Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (D3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) C3) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) D3) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.sup_su718114333110466843at_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (D3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A3) C3) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B3) D3) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.sup_su3035147773818789531at_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (D3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) C3) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) D3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.sup_su5525570899277871387at_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat) (D3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) D3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int) (D3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C3) (=> (@ (@ tptp.ord_less_eq_set_int B3) D3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.sup_sup_set_int C3) D3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) C3) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) C3) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A3) C3) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B3) C3) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) C3) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) C3) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (C3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.sup_sup_set_int A3) B3)) C3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat A3) (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat A3) (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat A3) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat A3) (@ (@ tptp.sup_sup_set_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A3) (@ (@ tptp.sup_sup_set_int A3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat B3) (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat B3) (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat B3) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.sup_sup_set_nat A3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.sup_sup_set_int A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) B3) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A3) B3) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) B3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (= (@ (@ tptp.sup_sup_set_nat A3) B3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (= (@ (@ tptp.sup_sup_set_int A3) B3) B3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B3) A3) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B3) A3) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B3) A3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ (@ tptp.sup_sup_set_nat A3) B3) A3))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= (@ (@ tptp.sup_sup_set_int A3) B3) A3))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat C3) (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (not (forall ((A7 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A7) A3) (forall ((B7 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat B7) B3) (not (= C3 (@ (@ tptp.sup_su718114333110466843at_nat A7) B7)))))))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat C3) (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (not (forall ((A7 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A7) A3) (forall ((B7 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat B7) B3) (not (= C3 (@ (@ tptp.sup_su3035147773818789531at_nat A7) B7)))))))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat C3) (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (not (forall ((A7 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A7) A3) (forall ((B7 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat B7) B3) (not (= C3 (@ (@ tptp.sup_su5525570899277871387at_nat A7) B7)))))))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C3) (@ (@ tptp.sup_sup_set_nat A3) B3)) (not (forall ((A7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) A3) (forall ((B7 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B7) B3) (not (= C3 (@ (@ tptp.sup_sup_set_nat A7) B7)))))))))))
% 6.81/7.11 (assert (forall ((C3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C3) (@ (@ tptp.sup_sup_set_int A3) B3)) (not (forall ((A7 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) A3) (forall ((B7 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B7) B3) (not (= C3 (@ (@ tptp.sup_sup_set_int A7) B7)))))))))))
% 6.81/7.11 (assert (= tptp.ord_le3000389064537975527at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat A6) B6) B6))))
% 6.81/7.11 (assert (= tptp.ord_le8081472938463900775at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A6) B6) B6))))
% 6.81/7.11 (assert (= tptp.ord_le1268244103169919719at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A6) B6) B6))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat A6) B6) B6))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int A6) B6) B6))))
% 6.81/7.11 (assert (forall ((Bs tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.relH Bs) H) H3) (=> (@ (@ tptp.ord_less_eq_set_nat As) Bs) (@ (@ (@ tptp.relH As) H) H3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C3))) (@ (@ tptp.ord_le3146513528884898305at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat A3))) (= (= (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B3) C3))) (@ (@ tptp.ord_le3000389064537975527at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat A3))) (= (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3))) (@ (@ tptp.ord_le8081472938463900775at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat A3))) (= (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3))) (@ (@ tptp.ord_le1268244103169919719at_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C3))) (@ (@ tptp.ord_less_eq_set_nat C3) A3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (= (= (@ (@ tptp.sup_sup_set_int (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_sup_set_int B3) C3))) (@ (@ tptp.ord_less_eq_set_int C3) A3)))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y4) (@ (@ tptp.ord_less_eq_set_int Y4) X4)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (@ (@ tptp.ord_less_eq_rat Y4) X4)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (@ (@ tptp.ord_less_eq_num Y4) X4)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (@ (@ tptp.ord_less_eq_nat Y4) X4)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (@ (@ tptp.ord_less_eq_int Y4) X4)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B5) A5) (@ (@ tptp.ord_less_eq_set_int A5) B5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (@ (@ tptp.ord_less_eq_rat A5) B5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (@ (@ tptp.ord_less_eq_num A5) B5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (@ (@ tptp.ord_less_eq_nat A5) B5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (@ (@ tptp.ord_less_eq_int A5) B5)))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (@ (@ tptp.ord_less_eq_set_int B5) A5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.rat) (Z3 tptp.rat)) (= Y5 Z3)) (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ tptp.ord_less_eq_rat B5) A5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ tptp.ord_less_eq_num B5) A5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3)) (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ tptp.ord_less_eq_nat B5) A5)))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)) (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ tptp.ord_less_eq_int B5) A5)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (K tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_set_nat A3) B) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.assn) (K tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_assn A3) B) (@ _let_1 (@ (@ tptp.inf_inf_assn A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_nat A3) B) (@ _let_1 (@ (@ tptp.inf_inf_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.product_unit) (K tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_inf_Product_unit A3) B) (@ _let_1 (@ (@ tptp.inf_inf_Product_unit A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A) B)))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A))) (let ((_let_2 (@ tptp.inf_inf_set_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.assn) (K tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn A))) (let ((_let_2 (@ tptp.inf_inf_assn K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_nat A))) (let ((_let_2 (@ tptp.inf_inf_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.product_unit) (K tptp.product_unit) (B tptp.product_unit) (A tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit A))) (let ((_let_2 (@ tptp.inf_inf_Product_unit K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (K tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (K tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) B) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (K tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (K tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (K tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_set_nat A3) B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ (@ tptp.sup_sup_nat A3) B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B)))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (K tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A))) (let ((_let_2 (@ tptp.sup_su718114333110466843at_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (K tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A))) (let ((_let_2 (@ tptp.sup_su3035147773818789531at_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (K tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A))) (let ((_let_2 (@ tptp.sup_su5525570899277871387at_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (K tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A))) (let ((_let_2 (@ tptp.sup_sup_set_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.sup_sup_nat A))) (let ((_let_2 (@ tptp.sup_sup_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat tptp.bot_bo2099793752762293965at_nat) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o tptp.bot_bot_set_o) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) tptp.bot_bo2099793752762293965at_nat) (= A tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) tptp.bot_bot_set_o) (= A tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat X) tptp.bot_bo5327735625951526323at_nat) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat X) tptp.bot_bo8422036546324065075at_nat) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat X) tptp.bot_bo228742789529271731at_nat) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat X) tptp.bot_bo2099793752762293965at_nat) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.sup_sup_set_o X) tptp.bot_bot_set_o) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat X) tptp.bot_bot_set_nat) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.sup_sup_set_int X) tptp.bot_bot_set_int) X)))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.inf_inf_assn X))) (= (@ _let_1 (@ (@ tptp.sup_sup_assn Y) Z)) (@ (@ tptp.sup_sup_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.inf_inf_Product_unit X))) (= (@ _let_1 (@ (@ tptp.sup_sup_Product_unit Y) Z)) (@ (@ tptp.sup_sup_Product_unit (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.inf_in4302113700860409141at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.inf_in1697001100524423349at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.inf_in7913087082777306421at_nat X))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat X))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat Y) Z)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.sup_sup_assn X))) (= (@ _let_1 (@ (@ tptp.inf_inf_assn Y) Z)) (@ (@ tptp.inf_inf_assn (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (let ((_let_1 (@ tptp.sup_sup_Product_unit X))) (= (@ _let_1 (@ (@ tptp.inf_inf_Product_unit Y) Z)) (@ (@ tptp.inf_inf_Product_unit (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.sup_su6327502436637775413at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat Y) Z)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) Z)) X) (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) X)) (@ (@ tptp.inf_inf_assn Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.sup_sup_Product_unit Y) Z)) X) (@ (@ tptp.sup_sup_Product_unit (@ (@ tptp.inf_inf_Product_unit Y) X)) (@ (@ tptp.inf_inf_Product_unit Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)) X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) X)) (@ (@ tptp.inf_in2572325071724192079at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)) X) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat Y) X)) (@ (@ tptp.inf_in4302113700860409141at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)) X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) X)) (@ (@ tptp.inf_in1697001100524423349at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)) X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) X)) (@ (@ tptp.inf_in7913087082777306421at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) Z)) X) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) X)) (@ (@ tptp.inf_inf_set_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (Z tptp.assn) (X tptp.assn)) (= (@ (@ tptp.sup_sup_assn (@ (@ tptp.inf_inf_assn Y) Z)) X) (@ (@ tptp.inf_inf_assn (@ (@ tptp.sup_sup_assn Y) X)) (@ (@ tptp.sup_sup_assn Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.product_unit) (Z tptp.product_unit) (X tptp.product_unit)) (= (@ (@ tptp.sup_sup_Product_unit (@ (@ tptp.inf_inf_Product_unit Y) Z)) X) (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.sup_sup_Product_unit Y) X)) (@ (@ tptp.sup_sup_Product_unit Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Y) Z)) X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.sup_su6327502436637775413at_nat Y) X)) (@ (@ tptp.sup_su6327502436637775413at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat) (X tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat Y) Z)) X) (@ (@ tptp.inf_in4302113700860409141at_nat (@ (@ tptp.sup_su718114333110466843at_nat Y) X)) (@ (@ tptp.sup_su718114333110466843at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat) (X tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat Y) Z)) X) (@ (@ tptp.inf_in1697001100524423349at_nat (@ (@ tptp.sup_su3035147773818789531at_nat Y) X)) (@ (@ tptp.sup_su3035147773818789531at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat) (X tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat Y) Z)) X) (@ (@ tptp.inf_in7913087082777306421at_nat (@ (@ tptp.sup_su5525570899277871387at_nat Y) X)) (@ (@ tptp.sup_su5525570899277871387at_nat Z) X)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_nat) (Z tptp.set_nat) (X tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat Y) Z)) X) (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.sup_sup_set_nat Y) X)) (@ (@ tptp.sup_sup_set_nat Z) X)))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su1419176701018045153at_nat (@ tptp.some_s579751585967276588at_nat X)) (@ tptp.some_s579751585967276588at_nat Y)) (@ tptp.some_s579751585967276588at_nat (@ (@ tptp.sup_su718114333110466843at_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su5873096292857799009at_nat (@ tptp.some_s287724117700012716at_nat X)) (@ tptp.some_s287724117700012716at_nat Y)) (@ tptp.some_s287724117700012716at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su2273273666271716065at_nat (@ tptp.some_s5890477192898017836at_nat X)) (@ tptp.some_s5890477192898017836at_nat Y)) (@ tptp.some_s5890477192898017836at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.sup_su3598758113090618626et_nat (@ tptp.some_set_nat X)) (@ tptp.some_set_nat Y)) (@ tptp.some_set_nat (@ (@ tptp.sup_sup_set_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.sup_sup_option_nat (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat (@ (@ tptp.sup_sup_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_in7812914138253463912et_nat (@ tptp.some_set_nat X)) (@ tptp.some_set_nat Y)) (@ tptp.some_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_option_assn (@ tptp.some_assn X)) (@ tptp.some_assn Y)) (@ tptp.some_assn (@ (@ tptp.inf_inf_assn X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.inf_inf_option_nat (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat (@ (@ tptp.inf_inf_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_in5800606384722953409t_unit (@ tptp.some_Product_unit X)) (@ tptp.some_Product_unit Y)) (@ tptp.some_Product_unit (@ (@ tptp.inf_inf_Product_unit X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in777885744494410645at_nat (@ tptp.some_s147305329494351046at_nat X)) (@ tptp.some_s147305329494351046at_nat Y)) (@ tptp.some_s147305329494351046at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le353528952715127954et_int (@ tptp.some_set_int X)) (@ tptp.some_set_int Y)) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_le2406147912482264968on_rat (@ tptp.some_rat X)) (@ tptp.some_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num X)) (@ tptp.some_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_le1736525451366464988on_int (@ tptp.some_int X)) (@ tptp.some_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.81/7.11 (assert (not (forall ((R2 tptp.a) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a tptp.c) tptp.h2) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) T2))))) (=> (@ (@ tptp.rep_assn (@ tptp.q R2)) (@ (@ tptp.produc7507926704131184380et_nat H5) (@ (@ (@ tptp.hoare_new_addrs tptp.h2) tptp.as1) H5))) (=> (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as1)))))) tptp.h2) H5) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit tptp.h2)) (@ tptp.lim_Product_unit H5)))))))))
% 6.81/7.11 (assert (forall ((X2 tptp.produc3260487557148687353it_nat) (Y2 tptp.produc3260487557148687353it_nat)) (= (= (@ tptp.some_P7913643980934408916it_nat X2) (@ tptp.some_P7913643980934408916it_nat Y2)) (= X2 Y2))))
% 6.81/7.11 (assert (forall ((X2 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.some_num X2) (@ tptp.some_num Y2)) (= X2 Y2))))
% 6.81/7.11 (assert (forall ((X2 tptp.produc8664842809031399944it_nat) (Y2 tptp.produc8664842809031399944it_nat)) (= (= (@ tptp.some_P1914260805536162275it_nat X2) (@ tptp.some_P1914260805536162275it_nat Y2)) (= X2 Y2))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) tptp.bot_bot_set_set_nat))))
% 6.81/7.11 (assert (= tptp.bot_bo482883023278783056_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (= tptp.bot_bot_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (= tptp.bot_bot_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (= tptp.bot_bot_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (= (@ tptp.collec213857154873943460nt_int P) tptp.bot_bo1796632182523588997nt_int) (= P tptp.bot_bo8147686125503663512_int_o))))
% 6.81/7.11 (assert (forall ((P (-> tptp.list_nat Bool))) (= (= (@ tptp.collect_list_nat P) tptp.bot_bot_set_list_nat) (= P tptp.bot_bot_list_nat_o))))
% 6.81/7.11 (assert (forall ((P (-> tptp.set_nat Bool))) (= (= (@ tptp.collect_set_nat P) tptp.bot_bot_set_set_nat) (= P tptp.bot_bot_set_nat_o))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (= (@ tptp.collec3392354462482085612at_nat P) tptp.bot_bo2099793752762293965at_nat) (= P tptp.bot_bo482883023278783056_nat_o))))
% 6.81/7.11 (assert (forall ((P (-> Bool Bool))) (= (= (@ tptp.collect_o P) tptp.bot_bot_set_o) (= P tptp.bot_bot_o_o))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool))) (= (= (@ tptp.collect_nat P) tptp.bot_bot_set_nat) (= P tptp.bot_bot_nat_o))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool))) (= (= (@ tptp.collect_int P) tptp.bot_bot_set_int) (= P tptp.bot_bot_int_o))))
% 6.81/7.11 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (A4 tptp.int) (B4 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int A4) B4))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (A2 tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (B2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A) A2) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B) B2) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A2) B2) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))))
% 6.81/7.11 (assert (forall ((A tptp.set_o) (A2 tptp.set_o) (B tptp.set_o) (B2 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A) A2) (=> (@ (@ tptp.ord_less_eq_set_o B) B2) (=> (= (@ (@ tptp.inf_inf_set_o A2) B2) tptp.bot_bot_set_o) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o))))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (A2 tptp.set_nat) (B tptp.set_nat) (B2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) A2) (=> (@ (@ tptp.ord_less_eq_set_nat B) B2) (=> (= (@ (@ tptp.inf_inf_set_nat A2) B2) tptp.bot_bot_set_nat) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (A2 tptp.set_int) (B tptp.set_int) (B2 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) A2) (=> (@ (@ tptp.ord_less_eq_set_int B) B2) (=> (= (@ (@ tptp.inf_inf_set_int A2) B2) tptp.bot_bot_set_int) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))))
% 6.81/7.11 (assert (forall ((A tptp.set_set_nat) (B tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_set_nat A) B) tptp.bot_bot_set_set_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_o) (B tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_o A) B) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_nat A) B) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A) (not (@ _let_1 B))))) (= (@ (@ tptp.inf_inf_set_int A) B) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((M tptp.set_int) (X tptp.option_set_int)) (=> (@ (@ tptp.ord_le353528952715127954et_int (@ tptp.some_set_int M)) X) (not (forall ((M2 tptp.set_int)) (=> (= X (@ tptp.some_set_int M2)) (not (@ (@ tptp.ord_less_eq_set_int M) M2))))))))
% 6.81/7.11 (assert (forall ((M tptp.rat) (X tptp.option_rat)) (=> (@ (@ tptp.ord_le2406147912482264968on_rat (@ tptp.some_rat M)) X) (not (forall ((M2 tptp.rat)) (=> (= X (@ tptp.some_rat M2)) (not (@ (@ tptp.ord_less_eq_rat M) M2))))))))
% 6.81/7.11 (assert (forall ((M tptp.num) (X tptp.option_num)) (=> (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num M)) X) (not (forall ((M2 tptp.num)) (=> (= X (@ tptp.some_num M2)) (not (@ (@ tptp.ord_less_eq_num M) M2))))))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (X tptp.option_nat)) (=> (@ (@ tptp.ord_le5914376470875661696on_nat (@ tptp.some_nat M)) X) (not (forall ((M2 tptp.nat)) (=> (= X (@ tptp.some_nat M2)) (not (@ (@ tptp.ord_less_eq_nat M) M2))))))))
% 6.81/7.11 (assert (forall ((M tptp.int) (X tptp.option_int)) (=> (@ (@ tptp.ord_le1736525451366464988on_int (@ tptp.some_int M)) X) (not (forall ((M2 tptp.int)) (=> (= X (@ tptp.some_int M2)) (not (@ (@ tptp.ord_less_eq_int M) M2))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (=> (forall ((X3 Bool)) (let ((_let_1 (@ tptp.member_o X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_o A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_nat A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A3) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_int A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= A3 B3)))))
% 6.81/7.11 (assert (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as1)))))) tptp.h2) tptp.h))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.ord_less_option_assn (@ tptp.some_assn X)) (@ tptp.some_assn Y)) (@ (@ tptp.ord_less_assn X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_option_rat (@ tptp.some_rat X)) (@ tptp.some_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_option_num (@ tptp.some_num X)) (@ tptp.some_num Y)) (@ (@ tptp.ord_less_num X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_option_nat (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_option_int (@ tptp.some_int X)) (@ tptp.some_int Y)) (@ (@ tptp.ord_less_int X) Y))))
% 6.81/7.11 (assert (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as)))))) tptp.h2) tptp.h))
% 6.81/7.11 (assert (@ (@ tptp.ord_less_eq_set_nat tptp.as2) (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as1)))))))
% 6.81/7.11 (assert (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as)))))) (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit tptp.h2)) (not (@ (@ tptp.member_nat A5) tptp.as1)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (X Bool)) (let ((_let_1 (@ tptp.member_o X))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A3)))))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (@ (@ tptp.ord_less_eq_set_int A3) B3))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= A3 B3) (@ (@ tptp.ord_less_eq_set_int B3) A3))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((T3 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (forall ((T3 Bool)) (let ((_let_1 (@ tptp.member_o T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((T3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T3 tptp.int)) (let ((_let_1 (@ tptp.member_int T3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A3) A3)))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (forall ((X3 tptp.list_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C3) (@ _let_1 C3))))))
% 6.81/7.11 (assert (= (lambda ((Y5 tptp.set_int) (Z3 tptp.set_int)) (= Y5 Z3)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su798857527126471912_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) R))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) S))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) (@ (@ tptp.sup_su6327502436637775413at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.sup_sup_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) (@ (@ tptp.sup_sup_set_o R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_set_nat) (S tptp.set_set_nat)) (= (@ (@ tptp.sup_sup_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) (@ (@ tptp.sup_sup_set_set_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.sup_sup_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) (@ (@ tptp.sup_sup_set_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su8986005896011022210_nat_o (lambda ((X4 tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X4) R))) (lambda ((X4 tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X4) S))) (lambda ((X4 tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X4) (@ (@ tptp.sup_su718114333110466843at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su6256023009775730178_nat_o (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) R))) (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) S))) (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) (@ (@ tptp.sup_su3035147773818789531at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su2080679670758317954_nat_o (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) R))) (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) S))) (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) (@ (@ tptp.sup_su5525570899277871387at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.sup_sup_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) (@ (@ tptp.sup_sup_set_nat R) S))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) A3)))
% 6.81/7.11 (assert (forall ((R tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.inf_inf_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) (@ (@ tptp.inf_inf_set_o R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_set_nat) (S tptp.set_set_nat)) (= (@ (@ tptp.inf_inf_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) (@ (@ tptp.inf_inf_set_set_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.inf_inf_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) (@ (@ tptp.inf_inf_set_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.inf_inf_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) (@ (@ tptp.inf_inf_set_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in5163264567034779214_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) R))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) S))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) (@ (@ tptp.inf_in2572325071724192079at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_sup_nat_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) R))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) S))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) (@ (@ tptp.sup_su6327502436637775413at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr3286484037609594932et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.sup_su1630790145277462993_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) (@ (@ tptp.sup_su7128418612487073120et_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8536935166611901872et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.sup_su6535292691877529429_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) (@ (@ tptp.sup_su8975264963432250076et_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S tptp.set_Pr9222295170931077689nt_int)) (= (@ (@ tptp.sup_su4182031696650224058_int_o (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) S))) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) (@ (@ tptp.sup_su3382966977382714213nt_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S tptp.set_Pr1872883991513573699nt_int)) (= (@ (@ tptp.sup_su600977994968626096_int_o (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) S))) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) (@ (@ tptp.sup_su3298353300217089135nt_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (@ (@ tptp.sup_su2191776239474528790_nat_o (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) R))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) (@ (@ tptp.sup_su3211442154794319707it_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8693737435421807431at_nat) (S tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su362511073950362882_nat_o (lambda ((X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y4)) R))) (lambda ((X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y4)) S))) (lambda ((X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y4)) (@ (@ tptp.sup_su718114333110466843at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8551490117392284871at_nat) (S tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su2200014604384089602_nat_o (lambda ((X4 tptp.multis2468970476368604999at_nat) (Y4 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat X4) Y4)) R))) (lambda ((X4 tptp.multis2468970476368604999at_nat) (Y4 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat X4) Y4)) S))) (lambda ((X4 tptp.multis2468970476368604999at_nat) (Y4 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat X4) Y4)) (@ (@ tptp.sup_su3035147773818789531at_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr4329608150637261639at_nat) (S tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su7519161239522478338_nat_o (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y4)) R))) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y4)) S))) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X4) Y4)) (@ (@ tptp.sup_su5525570899277871387at_nat R) S))))))
% 6.81/7.11 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_eq_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B6))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr3286484037609594932et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.inf_in3295504058751909687_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) (@ (@ tptp.inf_in1768905781608824518et_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8536935166611901872et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.inf_in2641120393918057659_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) (@ (@ tptp.inf_in3088352823822785602et_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S tptp.set_Pr9222295170931077689nt_int)) (= (@ (@ tptp.inf_in8045883074377559328_int_o (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) S))) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) (@ (@ tptp.inf_in2576786181675586251nt_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S tptp.set_Pr1872883991513573699nt_int)) (= (@ (@ tptp.inf_in8201999774870019094_int_o (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) S))) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) (@ (@ tptp.inf_in8806012763027673301nt_int R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (@ (@ tptp.inf_in8051596381320575356_nat_o (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) R))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) (@ (@ tptp.inf_in3493107508024165057it_nat R) S))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_inf_nat_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) R))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) S))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) (@ (@ tptp.inf_in2572325071724192079at_nat R) S))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)) (forall ((X4 tptp.product_prod_int_int)) (=> (@ P X4) (@ Q X4))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)) (forall ((X4 tptp.list_nat)) (=> (@ P X4) (@ Q X4))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)) (forall ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X4 tptp.int)) (=> (@ P X4) (@ Q X4))))))
% 6.81/7.11 (assert (= tptp.bot_bo5580076615179976505_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) tptp.bot_bo1481135142794719944et_nat))))
% 6.81/7.11 (assert (= tptp.bot_bo3790638025767943357_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) tptp.bot_bo5635537948650799172et_nat))))
% 6.81/7.11 (assert (= tptp.bot_bo8662317086119403298_int_o (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) tptp.bot_bo572930865798478029nt_int))))
% 6.81/7.11 (assert (= tptp.bot_bo1403522918969695512_int_o (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) tptp.bot_bo4508923176915781079nt_int))))
% 6.81/7.11 (assert (= tptp.bot_bo3200480807726169982_nat_o (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) tptp.bot_bo8480459777671986371it_nat))))
% 6.81/7.11 (assert (= tptp.bot_bot_nat_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) R)) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr3286484037609594932et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (= (= (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) R)) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8536935166611901872et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (= (= (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) R)) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S tptp.set_Pr9222295170931077689nt_int)) (= (= (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) R)) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S tptp.set_Pr1872883991513573699nt_int)) (= (= (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) R)) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (= (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) R)) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (= R S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le2646555220125990790_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) R))) (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) S))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr3286484037609594932et_nat) (S tptp.set_Pr3286484037609594932et_nat)) (= (@ (@ tptp.ord_le8000401564054156549_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4)) S))) (@ (@ tptp.ord_le5966269811547037844et_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr8536935166611901872et_nat) (S tptp.set_Pr8536935166611901872et_nat)) (= (@ (@ tptp.ord_le6753239538765779593_nat_o (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) R))) (lambda ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4)) S))) (@ (@ tptp.ord_le4763372923235995152et_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr9222295170931077689nt_int) (S tptp.set_Pr9222295170931077689nt_int)) (= (@ (@ tptp.ord_le5643404153117327598_int_o (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4)) S))) (@ (@ tptp.ord_le8725513860283290265nt_int R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1872883991513573699nt_int) (S tptp.set_Pr1872883991513573699nt_int)) (= (@ (@ tptp.ord_le2124322318746777828_int_o (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) R))) (lambda ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4)) S))) (@ (@ tptp.ord_le135402666524580259nt_int R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr7098220151150636591it_nat) (S tptp.set_Pr7098220151150636591it_nat)) (= (@ (@ tptp.ord_le7992815620007647562_nat_o (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) R))) (lambda ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4)) S))) (@ (@ tptp.ord_le4478181985103859343it_nat R) S))))
% 6.81/7.11 (assert (forall ((X tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X))))
% 6.81/7.11 (assert (forall ((X tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X))))
% 6.81/7.11 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.81/7.11 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.81/7.11 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z2) (@ (@ tptp.ord_less_rat Z2) Y))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (@ (@ tptp.ord_less_assn B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (= A B) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y6) X3) (@ P Y6))) (@ P X3))) (@ P A))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (not (@ (@ tptp.ord_less_assn A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) A))))
% 6.81/7.11 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.81/7.11 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.81/7.11 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.81/7.11 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P4 N) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (not (@ P4 M3)))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.rat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.rat) (B4 tptp.rat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ tptp.ord_less_num A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.num)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.nat)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_int A4) B4) (@ (@ P A4) B4))) (=> (forall ((A4 tptp.int)) (@ (@ P A4) A4)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ P B4) A4) (@ (@ P A4) B4))) (@ (@ P A) B))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_assn B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_assn B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (not (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (not (@ (@ tptp.ord_less_assn B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.assn tptp.num)) (B tptp.assn) (C tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.assn tptp.nat)) (B tptp.assn) (C tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.assn tptp.int)) (B tptp.assn) (C tptp.assn)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((X tptp.assn)) (not (@ (@ tptp.ord_less_assn X) X))))
% 6.81/7.11 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.81/7.11 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.81/7.11 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (P Bool)) (=> (@ (@ tptp.ord_less_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) X) P))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (= Y X)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (not (@ (@ tptp.ord_less_assn Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.11 (assert (forall ((S tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int S) (@ tptp.collec213857154873943460nt_int P)) (forall ((X4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int X4) S) (@ P X4))))))
% 6.81/7.11 (assert (forall ((S tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.ord_le6045566169113846134st_nat S) (@ tptp.collect_list_nat P)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) S) (@ P X4))))))
% 6.81/7.11 (assert (forall ((S tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.ord_le6893508408891458716et_nat S) (@ tptp.collect_set_nat P)) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) S) (@ P X4))))))
% 6.81/7.11 (assert (forall ((S tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.collect_nat P)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) S) (@ P X4))))))
% 6.81/7.11 (assert (forall ((S tptp.set_int) (P (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int S) (@ tptp.collect_int P)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) S) (@ P X4))))))
% 6.81/7.11 (assert (forall ((R tptp.set_Pr1261947904930325089at_nat) (S tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) R))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) S))) (@ (@ tptp.ord_le3146513528884898305at_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_o) (S tptp.set_o)) (= (@ (@ tptp.ord_less_eq_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) R))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) S))) (@ (@ tptp.ord_less_eq_set_o R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_set_nat) (S tptp.set_set_nat)) (= (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) R))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) S))) (@ (@ tptp.ord_le6893508408891458716et_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_nat) (S tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) R))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) S))) (@ (@ tptp.ord_less_eq_set_nat R) S))))
% 6.81/7.11 (assert (forall ((R tptp.set_int) (S tptp.set_int)) (= (@ (@ tptp.ord_less_eq_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) R))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) S))) (@ (@ tptp.ord_less_eq_set_int R) S))))
% 6.81/7.11 (assert (= tptp.bot_bo1796632182523588997nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) false))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_list_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) false))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_set_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) false))))
% 6.81/7.11 (assert (= tptp.bot_bo2099793752762293965at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) false))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_o (@ tptp.collect_o (lambda ((X4 Bool)) false))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) false))))
% 6.81/7.11 (assert (= tptp.bot_bot_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) false))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_in2269163501485487111nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (and (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (forall ((X Bool) (A3 tptp.set_o) (P (-> Bool Bool))) (let ((_let_1 (@ tptp.member_o X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_o A3) (@ tptp.collect_o P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.product_prod_int_int) (A3 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X))) (= (@ _let_1 (@ (@ tptp.inf_in2269163501485487111nt_int A3) (@ tptp.collec213857154873943460nt_int P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.list_nat) (A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.member_list_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_list_nat A3) (@ tptp.collect_list_nat P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.member_set_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_set_nat A3) (@ tptp.collect_set_nat P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.member_int X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.member_nat X))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (forall ((X tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.collec3392354462482085612at_nat P))) (and (@ _let_1 A3) (@ P X))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.inf_inf_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_in2269163501485487111nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.inf_in3604695632404883862_int_o (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) A6))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.inf_inf_list_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A6))) (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.inf_inf_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.inf_inf_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_inf_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.inf_inf_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.inf_in2572325071724192079at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.inf_in5163264567034779214_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) B6)))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_in2269163501485487111nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_inf_set_list_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_inf_set_set_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_inf_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_inf_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ P X4) (@ Q X4)))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.collec3392354462482085612at_nat Q)))))
% 6.81/7.11 (assert (= tptp.sup_su6327502436637775413at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_su6024340866399070445nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ tptp.collec7088162979684241874at_nat (lambda ((X4 tptp.produc859450856879609959at_nat)) (let ((_let_1 (@ tptp.member8206827879206165904at_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (let ((_let_1 (@ tptp.member6689249552917799696at_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (let ((_let_1 (@ tptp.member8757157785044589968at_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (or (@ _let_1 A6) (@ _let_1 B6))))))))
% 6.81/7.11 (assert (= tptp.sup_su6327502436637775413at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.sup_su798857527126471912_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.sup_sup_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_su6024340866399070445nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.sup_su8463660629351352368_int_o (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) A6))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_list_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.sup_sup_list_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A6))) (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.sup_sup_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.sup_sup_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_su718114333110466843at_nat (lambda ((A6 tptp.set_Pr8693737435421807431at_nat) (B6 tptp.set_Pr8693737435421807431at_nat)) (@ tptp.collec7088162979684241874at_nat (@ (@ tptp.sup_su8986005896011022210_nat_o (lambda ((X4 tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X4) A6))) (lambda ((X4 tptp.produc859450856879609959at_nat)) (@ (@ tptp.member8206827879206165904at_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_su3035147773818789531at_nat (lambda ((A6 tptp.set_Pr8551490117392284871at_nat) (B6 tptp.set_Pr8551490117392284871at_nat)) (@ tptp.collec5204685387357076818at_nat (@ (@ tptp.sup_su6256023009775730178_nat_o (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) A6))) (lambda ((X4 tptp.produc4166570645942440679at_nat)) (@ (@ tptp.member6689249552917799696at_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_su5525570899277871387at_nat (lambda ((A6 tptp.set_Pr4329608150637261639at_nat) (B6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.collec6321179662152712658at_nat (@ (@ tptp.sup_su2080679670758317954_nat_o (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) A6))) (lambda ((X4 tptp.produc3843707927480180839at_nat)) (@ (@ tptp.member8757157785044589968at_nat X4) B6)))))))
% 6.81/7.11 (assert (= tptp.sup_sup_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.sup_sup_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B6)))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su6024340866399070445nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.collect_list_nat P)) (@ tptp.collect_list_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (Q (-> tptp.produc859450856879609959at_nat Bool))) (= (@ tptp.collec7088162979684241874at_nat (lambda ((X4 tptp.produc859450856879609959at_nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.collec7088162979684241874at_nat P)) (@ tptp.collec7088162979684241874at_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.produc4166570645942440679at_nat Bool)) (Q (-> tptp.produc4166570645942440679at_nat Bool))) (= (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.collec5204685387357076818at_nat P)) (@ tptp.collec5204685387357076818at_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.collec6321179662152712658at_nat P)) (@ tptp.collec6321179662152712658at_nat Q)))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) N2) (not (@ P N3)))) (@ P N2)) (exists ((N4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat N4) N2) (@ P N4))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (or (@ (@ tptp.ord_less_assn X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (or (@ (@ tptp.ord_less_set_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_assn (@ F B)) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (F (-> tptp.assn tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_assn A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ _let_1 (@ F C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.assn)) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_assn (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.assn tptp.assn)) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.rat tptp.assn)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.num tptp.assn)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.nat tptp.assn)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (F (-> tptp.int tptp.assn)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_assn A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_assn (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_assn A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.assn tptp.rat)) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_assn B) C) (=> (forall ((X3 tptp.assn) (Y3 tptp.assn)) (=> (@ (@ tptp.ord_less_assn X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X3 tptp.rat) (Y3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X3 tptp.num) (Y3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Y3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ F Y3)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_assn Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (=> (@ (@ tptp.ord_less_assn Y) Z) (@ (@ tptp.ord_less_assn X) Z)))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (@ (@ tptp.ord_less_assn A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_assn A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_assn X) Y) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X4) Y4) (not (= X4 Y4))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (or (@ (@ tptp.ord_less_assn X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_num (lambda ((X4 tptp.num) (Y4 tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y4) (= X4 Y4)))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (@ (@ tptp.ord_less_eq_assn B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (@ (@ tptp.ord_less_eq_assn A) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B5) A5) (not (@ (@ tptp.ord_less_eq_assn A5) B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B5) A5) (not (@ (@ tptp.ord_less_eq_set_int A5) B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (not (@ (@ tptp.ord_less_eq_rat A5) B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_num (lambda ((B5 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (not (@ (@ tptp.ord_less_eq_num A5) B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (not (@ (@ tptp.ord_less_eq_nat A5) B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (not (@ (@ tptp.ord_less_eq_int A5) B5))))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (=> (@ (@ tptp.ord_less_eq_assn C) B) (@ (@ tptp.ord_less_assn C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ (@ tptp.ord_less_eq_assn B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_num (lambda ((B5 tptp.num) (A5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B5) A5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (or (@ (@ tptp.ord_less_assn B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((B5 tptp.set_int) (A5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (or (@ (@ tptp.ord_less_rat B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_num (lambda ((B5 tptp.num) (A5 tptp.num)) (or (@ (@ tptp.ord_less_num B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (or (@ (@ tptp.ord_less_nat B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((B5 tptp.int) (A5 tptp.int)) (or (@ (@ tptp.ord_less_int B5) A5) (= A5 B5)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z 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) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.81/7.11 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W) (=> (@ (@ tptp.ord_less_rat W) X) (@ (@ tptp.ord_less_eq_rat Y) W)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B5) (not (@ (@ tptp.ord_less_eq_assn B5) A5))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (@ (@ tptp.ord_less_eq_set_int B5) A5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (not (@ (@ tptp.ord_less_eq_rat B5) A5))))))
% 6.81/7.11 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (not (@ (@ tptp.ord_less_eq_num B5) A5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (not (@ (@ tptp.ord_less_eq_nat B5) A5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (not (@ (@ tptp.ord_less_eq_int B5) A5))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_assn B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_num (lambda ((A5 tptp.num) (B5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (or (@ (@ tptp.ord_less_assn A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A5 tptp.set_int) (B5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (or (@ (@ tptp.ord_less_rat A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_num (lambda ((A5 tptp.num) (B5 tptp.num)) (or (@ (@ tptp.ord_less_num A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (or (@ (@ tptp.ord_less_nat A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (or (@ (@ tptp.ord_less_int A5) B5) (= A5 B5)))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn X4) Y4) (not (@ (@ tptp.ord_less_eq_assn Y4) X4))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X4) Y4) (not (@ (@ tptp.ord_less_eq_set_int Y4) X4))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (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))))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Y) (@ (@ tptp.ord_less_eq_rat X3) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.81/7.11 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X3) (@ (@ tptp.ord_less_eq_rat Y) X3))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (= (not (@ (@ tptp.ord_less_assn X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (= (not (@ (@ tptp.ord_less_set_int X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (not (@ (@ tptp.ord_less_assn X) Y)) (= (@ (@ tptp.ord_less_eq_assn X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X) Y)) (= (@ (@ tptp.ord_less_eq_set_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (not (@ (@ tptp.ord_less_assn A) B)) (or (not (@ (@ tptp.ord_less_eq_assn A) B)) (= A B)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.81/7.11 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) X) (not (@ (@ tptp.ord_less_assn X) Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X) (not (@ (@ tptp.ord_less_set_int X) Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.81/7.11 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (= (not (= A tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.ord_le7866589430770878221at_nat tptp.bot_bo2099793752762293965at_nat) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_o)) (= (not (= A tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_set_o tptp.bot_bot_set_o) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.81/7.11 (assert (forall ((A tptp.assn)) (= (not (= A tptp.bot_bot_assn)) (@ (@ tptp.ord_less_assn tptp.bot_bot_assn) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) tptp.bot_bot_assn))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.product_unit) (C tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit B) C) (@ (@ tptp.ord_le361264281704409273t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (C tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) C) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (C tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit A) C) (@ (@ tptp.ord_le361264281704409273t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) C) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) C) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) C))))
% 6.81/7.11 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) C) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) C))))
% 6.81/7.11 (assert (= tptp.ord_less_set_nat (lambda ((A5 tptp.set_nat) (B5 tptp.set_nat)) (and (= A5 (@ (@ tptp.inf_inf_set_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_le361264281704409273t_unit (lambda ((A5 tptp.product_unit) (B5 tptp.product_unit)) (and (= A5 (@ (@ tptp.inf_inf_Product_unit A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A5 tptp.set_Pr1261947904930325089at_nat) (B5 tptp.set_Pr1261947904930325089at_nat)) (and (= A5 (@ (@ tptp.inf_in2572325071724192079at_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (and (= A5 (@ (@ tptp.inf_inf_assn A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (and (= A5 (@ (@ tptp.inf_inf_rat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (and (= A5 (@ (@ tptp.inf_inf_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (and (= A5 (@ (@ tptp.inf_inf_int A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_set_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit) (C tptp.product_unit)) (let ((_let_1 (@ tptp.ord_le361264281704409273t_unit A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_Product_unit B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat) (C tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.ord_le7866589430770878221at_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_assn B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_rat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_nat B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ (@ tptp.inf_inf_int B) C)) (not (=> (@ _let_1 B) (not (@ _let_1 C))))))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (= (@ (@ tptp.inf_inf_set_nat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit B) A) (= (@ (@ tptp.inf_inf_Product_unit A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) A) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.inf_inf_assn A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.inf_inf_rat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.inf_inf_nat A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.inf_inf_int A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (= (@ (@ tptp.inf_inf_set_nat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit A) B) (= (@ (@ tptp.inf_inf_Product_unit A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) B) (= (@ (@ tptp.inf_in2572325071724192079at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.inf_inf_assn A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.inf_inf_rat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.inf_inf_nat A) B) A))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.inf_inf_int A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (X tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.product_unit) (X tptp.product_unit) (A tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit B) X) (@ (@ tptp.ord_le361264281704409273t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (X tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (X tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) X) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (X tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((B tptp.int) (X tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (X tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) X) (@ (@ tptp.ord_less_set_nat (@ (@ tptp.inf_inf_set_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.product_unit) (X tptp.product_unit) (B tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit A) X) (@ (@ tptp.ord_le361264281704409273t_unit (@ (@ tptp.inf_inf_Product_unit A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr1261947904930325089at_nat) (X tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A) X) (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (X tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) X) (@ (@ tptp.ord_less_assn (@ (@ tptp.inf_inf_assn A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (X tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) X) (@ (@ tptp.ord_less_rat (@ (@ tptp.inf_inf_rat A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (X tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) X) (@ (@ tptp.ord_less_nat (@ (@ tptp.inf_inf_nat A) B)) X))))
% 6.81/7.11 (assert (forall ((A tptp.int) (X tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) X) (@ (@ tptp.ord_less_int (@ (@ tptp.inf_inf_int A) B)) X))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (= tptp.ord_le6428140832669894131at_nat (lambda ((B5 tptp.set_Pr8693737435421807431at_nat) (A5 tptp.set_Pr8693737435421807431at_nat)) (and (= A5 (@ (@ tptp.sup_su718114333110466843at_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_le7642048601412989811at_nat (lambda ((B5 tptp.set_Pr8551490117392284871at_nat) (A5 tptp.set_Pr8551490117392284871at_nat)) (and (= A5 (@ (@ tptp.sup_su3035147773818789531at_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_le2604355607129572851at_nat (lambda ((B5 tptp.set_Pr4329608150637261639at_nat) (A5 tptp.set_Pr4329608150637261639at_nat)) (and (= A5 (@ (@ tptp.sup_su5525570899277871387at_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_nat (lambda ((B5 tptp.set_nat) (A5 tptp.set_nat)) (and (= A5 (@ (@ tptp.sup_sup_set_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (and (= A5 (@ (@ tptp.sup_sup_assn A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (and (= A5 (@ (@ tptp.sup_sup_rat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (and (= A5 (@ (@ tptp.sup_sup_nat A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (= tptp.ord_less_int (lambda ((B5 tptp.int) (A5 tptp.int)) (and (= A5 (@ (@ tptp.sup_sup_int A5) B5)) (not (= A5 B5))))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (C tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat (@ (@ tptp.sup_su718114333110466843at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le6428140832669894131at_nat B) A) (not (@ (@ tptp.ord_le6428140832669894131at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (C tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le7642048601412989811at_nat (@ (@ tptp.sup_su3035147773818789531at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le7642048601412989811at_nat B) A) (not (@ (@ tptp.ord_le7642048601412989811at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (C tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat (@ (@ tptp.sup_su5525570899277871387at_nat B) C)) A) (not (=> (@ (@ tptp.ord_le2604355607129572851at_nat B) A) (not (@ (@ tptp.ord_le2604355607129572851at_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (C tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat (@ (@ tptp.sup_sup_set_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_set_nat B) A) (not (@ (@ tptp.ord_less_set_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (C tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ (@ tptp.sup_sup_assn B) C)) A) (not (=> (@ (@ tptp.ord_less_assn B) A) (not (@ (@ tptp.ord_less_assn C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.sup_sup_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.sup_sup_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.81/7.11 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.sup_sup_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat A) B) (= (@ (@ tptp.sup_su718114333110466843at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le7642048601412989811at_nat A) B) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat A) B) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.set_nat) (B tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A) B) (= (@ (@ tptp.sup_sup_set_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.assn) (B tptp.assn)) (=> (@ (@ tptp.ord_less_assn A) B) (= (@ (@ tptp.sup_sup_assn A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.sup_sup_rat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.sup_sup_nat A) B) B))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.sup_sup_int A) B) B))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le6428140832669894131at_nat B) A) (= (@ (@ tptp.sup_su718114333110466843at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le7642048601412989811at_nat B) A) (= (@ (@ tptp.sup_su3035147773818789531at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le2604355607129572851at_nat B) A) (= (@ (@ tptp.sup_su5525570899277871387at_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.set_nat) (A tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B) A) (= (@ (@ tptp.sup_sup_set_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.sup_sup_assn A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.sup_sup_rat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.sup_sup_nat A) B) A))))
% 6.81/7.11 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.sup_sup_int A) B) A))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (B tptp.set_nat) (A tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (B tptp.assn) (A tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (A tptp.set_Pr8693737435421807431at_nat) (B tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.ord_le6428140832669894131at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (A tptp.set_Pr8551490117392284871at_nat) (B tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.ord_le7642048601412989811at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (A tptp.set_Pr4329608150637261639at_nat) (B tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.ord_le2604355607129572851at_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (let ((_let_1 (@ tptp.ord_less_set_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_set_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.ord_less_assn X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_assn A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_rat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_nat A) B))))))
% 6.81/7.11 (assert (forall ((X tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_sup_int A) B))))))
% 6.81/7.11 (assert (= tptp.hoare_new_addrs (lambda ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat) (H7 tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.sup_sup_set_nat As5) (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) A5) (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H7)))))))))
% 6.81/7.11 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_set_int A) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_rat A) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_num A) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_nat A) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (= C D2) (@ (@ tptp.ord_less_eq_int A) D2))))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (S tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.nat tptp.nat Bool))) (let ((_let_1 (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 tptp.nat) (B4 tptp.nat)) (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat) (S tptp.set_Pr3286484037609594932et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (let ((_let_1 (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat) (S tptp.set_Pr8536935166611901872et_nat) (P (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (let ((_let_1 (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (S tptp.set_Pr9222295170931077689nt_int) (P (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (S tptp.set_Pr1872883991513573699nt_int) (P (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (let ((_let_1 (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (and (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (S tptp.set_Pr7098220151150636591it_nat) (P (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (let ((_let_1 (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A) B)) S))) (=> _let_1 (=> (=> _let_1 (@ (@ P A) B)) (exists ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (and (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) S) (@ (@ P A4) B4))))))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le3146513528884898305at_nat R3) S2))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr3286484037609594932et_nat) (S2 tptp.set_Pr3286484037609594932et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le5966269811547037844et_nat R3) S2))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr8536935166611901872et_nat) (S2 tptp.set_Pr8536935166611901872et_nat)) (=> (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le4763372923235995152et_nat R3) S2))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr9222295170931077689nt_int) (S2 tptp.set_Pr9222295170931077689nt_int)) (=> (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le8725513860283290265nt_int R3) S2))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr1872883991513573699nt_int) (S2 tptp.set_Pr1872883991513573699nt_int)) (=> (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le135402666524580259nt_int R3) S2))))
% 6.81/7.11 (assert (forall ((R3 tptp.set_Pr7098220151150636591it_nat) (S2 tptp.set_Pr7098220151150636591it_nat)) (=> (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)))) (=> (@ _let_1 R3) (@ _let_1 S2)))) (@ (@ tptp.ord_le4478181985103859343it_nat R3) S2))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (S tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) S) (not (= S tptp.bot_bot_set_set_nat)))))
% 6.81/7.11 (assert (forall ((X tptp.product_prod_nat_nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X) S) (not (= S tptp.bot_bo2099793752762293965at_nat)))))
% 6.81/7.11 (assert (forall ((X Bool) (S tptp.set_o)) (=> (@ (@ tptp.member_o X) S) (not (= S tptp.bot_bot_set_o)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.member_nat X) S) (not (= S tptp.bot_bot_set_nat)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (S tptp.set_int)) (=> (@ (@ tptp.member_int X) S) (not (= S tptp.bot_bot_set_int)))))
% 6.81/7.11 (assert (forall ((S tptp.set_set_nat)) (=> (not (= S tptp.bot_bot_set_set_nat)) (not (forall ((X3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X3) S)))))))
% 6.81/7.11 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (= S tptp.bot_bo2099793752762293965at_nat)) (not (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X3) S)))))))
% 6.81/7.11 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (not (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) S)))))))
% 6.81/7.11 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (not (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) S)))))))
% 6.81/7.11 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (not (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) S)))))))
% 6.81/7.11 (assert (forall ((S tptp.set_nat) (S3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat B3))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ (@ tptp.ord_less_eq_set_nat S) S3) (=> (= (@ _let_2 S3) (@ _let_1 S3)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 6.81/7.11 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat B3))) (let ((_let_2 (@ tptp.inf_in2572325071724192079at_nat A3))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) S3) (=> (= (@ _let_2 S3) (@ _let_1 S3)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 6.81/7.11 (assert (forall ((S tptp.set_int) (S3 tptp.set_int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int B3))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ (@ tptp.ord_less_eq_set_int S) S3) (=> (= (@ _let_2 S3) (@ _let_1 S3)) (= (@ _let_2 S) (@ _let_1 S))))))))
% 6.81/7.11 (assert (= tptp.hoare_8945653483474564448t_unit (lambda ((P4 tptp.assn) (C4 tptp.heap_T5738788834812785303t_unit) (Q3 (-> tptp.product_unit tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P4) (@ (@ tptp.produc7507926704131184380et_nat H6) As5)) (exists ((R4 tptp.product_unit) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T3 tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C4) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H7) T3))))) (@ (@ tptp.rep_assn (@ Q3 R4)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As5) H7))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H6)) (not (@ (@ tptp.member_nat A5) As5)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))
% 6.81/7.11 (assert (= tptp.hoare_hoare_triple_a (lambda ((P4 tptp.assn) (C4 tptp.heap_Time_Heap_a) (Q3 (-> tptp.a tptp.assn))) (forall ((H6 tptp.heap_e7401611519738050253t_unit) (As5 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P4) (@ (@ tptp.produc7507926704131184380et_nat H6) As5)) (exists ((R4 tptp.a) (H7 tptp.heap_e7401611519738050253t_unit)) (and (exists ((T3 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C4) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H7) T3))))) (@ (@ tptp.rep_assn (@ Q3 R4)) (@ (@ tptp.produc7507926704131184380et_nat H7) (@ (@ (@ tptp.hoare_new_addrs H6) As5) H7))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H6)) (not (@ (@ tptp.member_nat A5) As5)))))) H6) H7) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H6)) (@ tptp.lim_Product_unit H7)))))))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_T5738788834812785303t_unit) (Q (-> tptp.product_unit tptp.assn))) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (exists ((R5 tptp.product_unit) (H8 tptp.heap_e7401611519738050253t_unit) (T4 tptp.nat)) (and (= (@ (@ tptp.heap_T875086893843062177t_unit C) H4) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H8) T4)))) (@ (@ tptp.rep_assn (@ Q R5)) (@ (@ tptp.produc7507926704131184380et_nat H8) (@ (@ (@ tptp.hoare_new_addrs H4) As4) H8))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H4)) (not (@ (@ tptp.member_nat A5) As4)))))) H4) H8) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H4)) (@ tptp.lim_Product_unit H8)))))) (@ (@ (@ tptp.hoare_8945653483474564448t_unit P) C) Q))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q (-> tptp.a tptp.assn))) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (exists ((R5 tptp.a) (H8 tptp.heap_e7401611519738050253t_unit) (T4 tptp.nat)) (and (= (@ (@ tptp.heap_Time_execute_a C) H4) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R5) (@ (@ tptp.produc584006145561248582it_nat H8) T4)))) (@ (@ tptp.rep_assn (@ Q R5)) (@ (@ tptp.produc7507926704131184380et_nat H8) (@ (@ (@ tptp.hoare_new_addrs H4) As4) H8))) (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H4)) (not (@ (@ tptp.member_nat A5) As4)))))) H4) H8) (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H4)) (@ tptp.lim_Product_unit H8)))))) (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_T5738788834812785303t_unit) (Q (-> tptp.product_unit tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_8945653483474564448t_unit P) C) Q) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((R2 tptp.product_unit) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) T2))))) (=> (@ (@ tptp.rep_assn (@ Q R2)) (@ (@ tptp.produc7507926704131184380et_nat H5) (@ (@ (@ tptp.hoare_new_addrs H) As) H5))) (=> (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H)) (not (@ (@ tptp.member_nat A5) As)))))) H) H5) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H)) (@ tptp.lim_Product_unit H5))))))))))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (not (forall ((R2 tptp.a) (H5 tptp.heap_e7401611519738050253t_unit)) (=> (exists ((T2 tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H5) T2))))) (=> (@ (@ tptp.rep_assn (@ Q R2)) (@ (@ tptp.produc7507926704131184380et_nat H5) (@ (@ (@ tptp.hoare_new_addrs H) As) H5))) (=> (@ (@ (@ tptp.relH (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.ord_less_nat A5) (@ tptp.lim_Product_unit H)) (not (@ (@ tptp.member_nat A5) As)))))) H) H5) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.lim_Product_unit H)) (@ tptp.lim_Product_unit H5))))))))))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila1307241728879085301at_nat tptp.sup_su718114333110466843at_nat) tptp.bot_bo5327735625951526323at_nat) (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le6428140832669894131at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila5207306265035627125at_nat tptp.sup_su3035147773818789531at_nat) tptp.bot_bo8422036546324065075at_nat) (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le7642048601412989811at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila6534579987270727413at_nat tptp.sup_su5525570899277871387at_nat) tptp.bot_bo228742789529271731at_nat) (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le2604355607129572851at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila4918476307565957903at_nat tptp.sup_su6327502436637775413at_nat) tptp.bot_bo2099793752762293965at_nat) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le7866589430770878221at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila2554085542299052326_set_o tptp.sup_sup_set_o) tptp.bot_bot_set_o) (lambda ((X4 tptp.set_o) (Y4 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o Y4) X4))) (lambda ((X4 tptp.set_o) (Y4 tptp.set_o)) (@ (@ tptp.ord_less_set_o Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila1667268886620078168et_nat tptp.sup_sup_set_nat) tptp.bot_bot_set_nat) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y4) X4))) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila8603258263270017530r_assn tptp.sup_sup_assn) tptp.bot_bot_assn) (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y4) X4))) (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_assn Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ (@ tptp.semila6712789903965657268et_int tptp.sup_sup_set_int) tptp.bot_bot_set_int) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y4) X4))) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_set_int Y4) X4))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.81/7.11 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J2) (@ (@ tptp.ord_less_nat (@ F I3)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N) (= M3 N)))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.11 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (not (= M3 N))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X3) A3))) (@ (@ tptp.ord_le6893508408891458716et_nat A3) tptp.bot_bot_set_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X3) A3))) (@ (@ tptp.ord_le3146513528884898305at_nat A3) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (=> (forall ((X3 Bool)) (not (@ (@ tptp.member_o X3) A3))) (@ (@ tptp.ord_less_eq_set_o A3) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (not (@ (@ tptp.member_nat X3) A3))) (@ (@ tptp.ord_less_eq_set_nat A3) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (not (@ (@ tptp.member_int X3) A3))) (@ (@ tptp.ord_less_eq_set_int A3) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (not (= A3 B3)) (@ (@ tptp.ord_less_set_int A3) B3)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= A3 tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3))))
% 6.81/7.11 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (Z tptp.nat) (Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ (@ (@ tptp.semila1623282765462674594er_nat F) Z) Less_eq) Less) (= (= Z (@ (@ F A) B)) (and (= A Z) (= B Z))))))
% 6.81/7.11 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (Z tptp.nat) (Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (@ (@ (@ (@ tptp.semila1623282765462674594er_nat F) Z) Less_eq) Less) (= (= (@ (@ F A) B) Z) (and (= A Z) (= B Z))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (not (@ (@ tptp.ord_le7866589430770878221at_nat A3) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o)) (not (@ (@ tptp.ord_less_set_o A3) tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A3) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A3) tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ (@ tptp.ord_less_set_int B3) C3) (@ (@ tptp.ord_less_set_int A3) C3)))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A3))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C3) (@ _let_1 C3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int A3) B3))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int B3) A3))))))
% 6.81/7.11 (assert (= tptp.ord_less_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (and (@ (@ tptp.ord_less_eq_assn A5) B5) (not (= A5 B5))))))
% 6.81/7.11 (assert (forall ((R3 tptp.nat) (S2 tptp.nat) (R tptp.set_Pr1261947904930325089at_nat) (S4 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat R3))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((R3 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3658429121746597890et_nat) (R tptp.set_Pr3286484037609594932et_nat) (S4 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat R3))) (=> (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((R3 (-> tptp.produc3658429121746597890et_nat Bool)) (S2 tptp.produc3925858234332021118et_nat) (R tptp.set_Pr8536935166611901872et_nat) (S4 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat R3))) (=> (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((R3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (S2 tptp.product_prod_int_int) (R tptp.set_Pr9222295170931077689nt_int) (S4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int R3))) (=> (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((R3 (-> tptp.int tptp.option6357759511663192854e_term)) (S2 tptp.product_prod_int_int) (R tptp.set_Pr1872883991513573699nt_int) (S4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int R3))) (=> (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((R3 tptp.a) (S2 tptp.produc6653097349344004940it_nat) (R tptp.set_Pr7098220151150636591it_nat) (S4 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat R3))) (=> (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 S2)) R) (=> (= S4 S2) (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 S4)) R))))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.81/7.11 (assert (forall ((S2 tptp.nat) (T5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat S2) T5) (not (= S2 T5)))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N5) (@ P M4))) (@ P N5))) (@ P N2))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (not (@ P N5)) (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N5) (not (@ P M4)))))) (@ P N2))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.81/7.11 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.81/7.11 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.81/7.11 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (exists ((X3 tptp.nat)) (and (@ P X3) (forall ((Y6 tptp.nat)) (=> (@ P Y6) (@ (@ tptp.ord_less_eq_nat Y6) X3)))))))))
% 6.81/7.11 (assert (forall ((X tptp.product_prod_nat_nat) (Z4 tptp.set_Pr1261947904930325089at_nat) (X6 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat X) Z4) (=> (@ (@ tptp.ord_le3146513528884898305at_nat Z4) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X Bool) (Z4 tptp.set_o) (X6 tptp.set_o) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o X) Z4) (=> (@ (@ tptp.ord_less_eq_set_o Z4) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X tptp.product_prod_int_int) (Z4 tptp.set_Pr958786334691620121nt_int) (X6 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int X) Z4) (=> (@ (@ tptp.ord_le2843351958646193337nt_int Z4) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X tptp.list_nat) (Z4 tptp.set_list_nat) (X6 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.member_list_nat X) Z4) (=> (@ (@ tptp.ord_le6045566169113846134st_nat Z4) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X tptp.set_nat) (Z4 tptp.set_set_nat) (X6 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.member_set_nat X) Z4) (=> (@ (@ tptp.ord_le6893508408891458716et_nat Z4) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Z4 tptp.set_nat) (X6 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) Z4) (=> (@ (@ tptp.ord_less_eq_set_nat Z4) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X tptp.int) (Z4 tptp.set_int) (X6 tptp.set_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) Z4) (=> (@ (@ tptp.ord_less_eq_set_int Z4) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X6) (@ P X4))))) (@ P X)))))
% 6.81/7.11 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_o) (P (-> Bool Bool))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((X6 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X6) (@ P X4))))) X6)))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (not (@ (@ tptp.ord_less_eq_rat T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (not (@ (@ tptp.ord_less_eq_num T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (not (@ (@ tptp.ord_less_eq_nat T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (not (@ (@ tptp.ord_less_eq_int T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (@ (@ tptp.ord_less_eq_rat X7) T5))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (@ (@ tptp.ord_less_eq_num X7) T5))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (@ (@ tptp.ord_less_eq_nat X7) T5))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (@ (@ tptp.ord_less_eq_int X7) T5))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (@ (@ tptp.ord_less_eq_rat T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (@ (@ tptp.ord_less_eq_num T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (@ (@ tptp.ord_less_eq_nat T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (@ (@ tptp.ord_less_eq_int T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (not (@ (@ tptp.ord_less_eq_rat X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (not (@ (@ tptp.ord_less_eq_num X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (not (@ (@ tptp.ord_less_eq_nat X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (not (@ (@ tptp.ord_less_eq_int X7) T5)))))))
% 6.81/7.11 (assert (forall ((B2 tptp.rat) (A2 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B2) A2)) (@ (@ tptp.ord_less_rat A2) B2))))
% 6.81/7.11 (assert (forall ((B2 tptp.num) (A2 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B2) A2)) (@ (@ tptp.ord_less_num A2) B2))))
% 6.81/7.11 (assert (forall ((B2 tptp.nat) (A2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B2) A2)) (@ (@ tptp.ord_less_nat A2) B2))))
% 6.81/7.11 (assert (forall ((B2 tptp.int) (A2 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B2) A2)) (@ (@ tptp.ord_less_int A2) B2))))
% 6.81/7.11 (assert (forall ((A tptp.nat) (B tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A) C2) (@ (@ tptp.ord_less_eq_nat C2) B) (forall ((X7 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X7) (@ (@ tptp.ord_less_nat X7) C2)) (@ P X7))) (forall ((D4 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat A) X3) (@ (@ tptp.ord_less_nat X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_nat D4) C2))))))))))
% 6.81/7.11 (assert (forall ((A tptp.int) (B tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ P A) (=> (not (@ P B)) (exists ((C2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) C2) (@ (@ tptp.ord_less_eq_int C2) B) (forall ((X7 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X7) (@ (@ tptp.ord_less_int X7) C2)) (@ P X7))) (forall ((D4 tptp.int)) (=> (forall ((X3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int A) X3) (@ (@ tptp.ord_less_int X3) D4)) (@ P X3))) (@ (@ tptp.ord_less_eq_int D4) C2))))))))))
% 6.81/7.11 (assert (@ tptp.bijective_nat_nat tptp.bot_bo2099793752762293965at_nat))
% 6.81/7.11 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (= S tptp.bot_bo2099793752762293965at_nat)) (= (@ tptp.dflt_N6592383573632408824at_nat S) (@ tptp.some_s147305329494351046at_nat S)))))
% 6.81/7.11 (assert (forall ((S tptp.set_o)) (=> (not (= S tptp.bot_bot_set_o)) (= (@ tptp.dflt_None_set_o S) (@ tptp.some_set_o S)))))
% 6.81/7.11 (assert (forall ((S tptp.set_nat)) (=> (not (= S tptp.bot_bot_set_nat)) (= (@ tptp.dflt_None_set_nat S) (@ tptp.some_set_nat S)))))
% 6.81/7.11 (assert (forall ((S tptp.set_int)) (=> (not (= S tptp.bot_bot_set_int)) (= (@ tptp.dflt_None_set_int S) (@ tptp.some_set_int S)))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.times_assn_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (exists ((As13 tptp.set_nat) (As23 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As13) As23)) (= (@ (@ tptp.inf_inf_set_nat As13) As23) tptp.bot_bot_set_nat) (@ X (@ _let_1 As13)) (@ Xa (@ _let_1 As23))))))))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (C Bool)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ (@ tptp.ord_less_set_o A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_less_set_set_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A3) B3) (=> (@ _let_1 A3) (@ _let_1 B3))))))
% 6.81/7.11 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le549003669493604880_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ (@ tptp.ord_less_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_set_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_less_set_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B6))))))
% 6.81/7.11 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B6))))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (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)))))
% 6.81/7.11 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.81/7.11 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.81/7.11 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.81/7.11 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.81/7.11 (assert (forall ((A tptp.assn)) (not (@ (@ tptp.ord_less_assn A) A))))
% 6.81/7.11 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.81/7.11 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.81/7.11 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.81/7.11 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (not (@ (@ tptp.ord_less_rat X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (not (@ (@ tptp.ord_less_num X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (not (@ (@ tptp.ord_less_nat X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (not (@ (@ tptp.ord_less_int X7) T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X7) (@ (@ tptp.ord_less_rat T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X7) (@ (@ tptp.ord_less_num T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X7) (@ (@ tptp.ord_less_nat T5) X7))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X7) (@ (@ tptp.ord_less_int T5) X7))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (= (and (@ P X7) (@ Q X7)) (and (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q4 (-> tptp.rat Bool))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.rat)) (forall ((X3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q4 (-> tptp.num Bool))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.num)) (forall ((X3 tptp.num)) (=> (@ (@ tptp.ord_less_num X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q4 (-> tptp.nat Bool))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q4 (-> tptp.int Bool))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P6 X3))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ Q X3) (@ Q4 X3))))) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (= (or (@ P X7) (@ Q X7)) (or (@ P6 X7) (@ Q4 X7))))))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (not (= X7 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X7))) (=> (@ _let_1 Z2) (@ _let_1 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X7))) (=> (@ _let_1 Z2) (@ _let_1 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X7))) (=> (@ _let_1 Z2) (@ _let_1 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X7))) (=> (@ _let_1 Z2) (@ _let_1 T5)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X7) Z2) (not (@ (@ tptp.ord_less_rat T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X7 tptp.num)) (=> (@ (@ tptp.ord_less_num X7) Z2) (not (@ (@ tptp.ord_less_num T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X7) Z2) (not (@ (@ tptp.ord_less_nat T5) X7)))))))
% 6.81/7.11 (assert (forall ((T5 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (=> (@ (@ tptp.ord_less_int X7) Z2) (not (@ (@ tptp.ord_less_int T5) X7)))))))
% 6.81/7.11 (assert (= tptp.bijective_nat_nat (lambda ((R6 tptp.set_Pr1261947904930325089at_nat)) (and (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z6 tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X4))) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Y4)) R6) (@ (@ tptp.member8440522571783428010at_nat (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 tptp.nat) (Y4 tptp.nat) (Z6 tptp.nat)) (=> (and (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Z6)) R6) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (= tptp.biject2615096655818420098et_nat (lambda ((R6 tptp.set_Pr3286484037609594932et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat) (Z6 tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.produc5001842942810119800et_nat X4))) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Y4)) R6) (@ (@ tptp.member1996754912294343701et_nat (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z6 tptp.produc3658429121746597890et_nat)) (=> (and (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Z6)) R6) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (= tptp.biject1468766312547416318et_nat (lambda ((R6 tptp.set_Pr8536935166611901872et_nat)) (and (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat) (Z6 tptp.produc3925858234332021118et_nat)) (let ((_let_1 (@ tptp.produc2245416461498447860et_nat X4))) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Y4)) R6) (@ (@ tptp.member6124377750444531601et_nat (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 (-> tptp.produc3658429121746597890et_nat Bool)) (Z6 tptp.produc3925858234332021118et_nat)) (=> (and (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Z6)) R6) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (= tptp.biject383251550997737151nt_int (lambda ((R6 tptp.set_Pr9222295170931077689nt_int)) (and (forall ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int) (Z6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc5700946648718959541nt_int X4))) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Y4)) R6) (@ (@ tptp.member7618704894036264090nt_int (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Z6 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Z6)) R6) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (= tptp.biject576505603616484041nt_int (lambda ((R6 tptp.set_Pr1872883991513573699nt_int)) (and (forall ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int) (Z6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.produc4305682042979456191nt_int X4))) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Y4)) R6) (@ (@ tptp.member7034335876925520548nt_int (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 (-> tptp.int tptp.option6357759511663192854e_term)) (Z6 tptp.product_prod_int_int)) (=> (and (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Z6)) R6) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (= tptp.biject8592306251674886141it_nat (lambda ((R6 tptp.set_Pr7098220151150636591it_nat)) (and (forall ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat) (Z6 tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.produc9178034014595674355it_nat X4))) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Y4)) R6) (@ (@ tptp.member4554412811331277712it_nat (@ _let_1 Z6)) R6)) (= Y4 Z6)))) (forall ((X4 tptp.a) (Y4 tptp.a) (Z6 tptp.produc6653097349344004940it_nat)) (=> (and (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Z6)) R6) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat Y4) Z6)) R6)) (= X4 Y4)))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (= Y (exists ((As12 tptp.set_nat) (As22 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As12) As22)) (= (@ (@ tptp.inf_inf_set_nat As12) As22) tptp.bot_bot_set_nat) (@ X (@ _let_1 As12)) (@ Xa (@ _let_1 As22)))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.times_assn_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.times_assn_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (exists ((As1 tptp.set_nat) (As2 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H4))) (and (= As4 (@ (@ tptp.sup_sup_set_nat As1) As2)) (= (@ (@ tptp.inf_inf_set_nat As1) As2) tptp.bot_bot_set_nat) (@ X (@ _let_1 As1)) (@ Xa (@ _let_1 As2)))))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.the_de3668382347305825784at_nat tptp.bot_bo2099793752762293965at_nat) (@ tptp.dflt_N6592383573632408824at_nat X)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.the_default_set_o tptp.bot_bot_set_o) (@ tptp.dflt_None_set_o X)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.the_default_set_nat tptp.bot_bot_set_nat) (@ tptp.dflt_None_set_nat X)) X)))
% 6.81/7.11 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.the_default_set_int tptp.bot_bot_set_int) (@ tptp.dflt_None_set_int X)) X)))
% 6.81/7.11 (assert (forall ((R1 (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)) (R22 (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_le3355651325779393058_nat_o R1) R22) (@ (@ tptp.ord_le729326519192465773_nat_o (@ tptp.accp_P5801069581201407417et_nat R22)) (@ tptp.accp_P5801069581201407417et_nat R1)))))
% 6.81/7.11 (assert (forall ((R1 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (R22 (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2556027599737686990_num_o R1) R22) (@ (@ tptp.ord_le2239182809043710856_num_o (@ tptp.accp_P3113834385874906142um_num R22)) (@ tptp.accp_P3113834385874906142um_num R1)))))
% 6.81/7.11 (assert (forall ((R1 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (R22 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le5604493270027003598_nat_o R1) R22) (@ (@ tptp.ord_le704812498762024988_nat_o (@ tptp.accp_P4275260045618599050at_nat R22)) (@ tptp.accp_P4275260045618599050at_nat R1)))))
% 6.81/7.11 (assert (forall ((R1 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (R22 (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le1598226405681992910_int_o R1) R22) (@ (@ tptp.ord_le8369615600986905444_int_o (@ tptp.accp_P1096762738010456898nt_int R22)) (@ tptp.accp_P1096762738010456898nt_int R1)))))
% 6.81/7.11 (assert (forall ((R1 (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)) (R22 (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool))) (=> (@ (@ tptp.ord_le7226304311989208114_nat_o R1) R22) (@ (@ tptp.ord_le1658592502415435381_nat_o (@ tptp.accp_P1862375125659990705et_nat R22)) (@ tptp.accp_P1862375125659990705et_nat R1)))))
% 6.81/7.11 (assert (forall ((D3 (-> tptp.produc3658429121746597890et_nat Bool)) (R (-> tptp.produc3658429121746597890et_nat tptp.produc3658429121746597890et_nat Bool)) (X tptp.produc3658429121746597890et_nat) (P (-> tptp.produc3658429121746597890et_nat Bool))) (=> (@ (@ tptp.ord_le729326519192465773_nat_o D3) (@ tptp.accp_P5801069581201407417et_nat R)) (=> (forall ((X3 tptp.produc3658429121746597890et_nat) (Z2 tptp.produc3658429121746597890et_nat)) (=> (@ D3 X3) (=> (@ (@ R Z2) X3) (@ D3 Z2)))) (=> (@ D3 X) (=> (forall ((X3 tptp.produc3658429121746597890et_nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.produc3658429121746597890et_nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.81/7.11 (assert (forall ((D3 (-> tptp.product_prod_num_num Bool)) (R (-> tptp.product_prod_num_num tptp.product_prod_num_num Bool)) (X tptp.product_prod_num_num) (P (-> tptp.product_prod_num_num Bool))) (=> (@ (@ tptp.ord_le2239182809043710856_num_o D3) (@ tptp.accp_P3113834385874906142um_num R)) (=> (forall ((X3 tptp.product_prod_num_num) (Z2 tptp.product_prod_num_num)) (=> (@ D3 X3) (=> (@ (@ R Z2) X3) (@ D3 Z2)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_num_num)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.81/7.11 (assert (forall ((D3 (-> tptp.product_prod_nat_nat Bool)) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le704812498762024988_nat_o D3) (@ tptp.accp_P4275260045618599050at_nat R)) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (=> (@ D3 X3) (=> (@ (@ R Z2) X3) (@ D3 Z2)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_nat_nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.81/7.11 (assert (forall ((D3 (-> tptp.product_prod_int_int Bool)) (R (-> tptp.product_prod_int_int tptp.product_prod_int_int Bool)) (X tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le8369615600986905444_int_o D3) (@ tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X3 tptp.product_prod_int_int) (Z2 tptp.product_prod_int_int)) (=> (@ D3 X3) (=> (@ (@ R Z2) X3) (@ D3 Z2)))) (=> (@ D3 X) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.product_prod_int_int)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.81/7.11 (assert (forall ((D3 (-> tptp.produc2732055786443039994et_nat Bool)) (R (-> tptp.produc2732055786443039994et_nat tptp.produc2732055786443039994et_nat Bool)) (X tptp.produc2732055786443039994et_nat) (P (-> tptp.produc2732055786443039994et_nat Bool))) (=> (@ (@ tptp.ord_le1658592502415435381_nat_o D3) (@ tptp.accp_P1862375125659990705et_nat R)) (=> (forall ((X3 tptp.produc2732055786443039994et_nat) (Z2 tptp.produc2732055786443039994et_nat)) (=> (@ D3 X3) (=> (@ (@ R Z2) X3) (@ D3 Z2)))) (=> (@ D3 X) (=> (forall ((X3 tptp.produc2732055786443039994et_nat)) (=> (@ D3 X3) (=> (forall ((Z5 tptp.produc2732055786443039994et_nat)) (=> (@ (@ R Z5) X3) (@ P Z5))) (@ P X3)))) (@ P X)))))))
% 6.81/7.11 (assert (@ (@ (@ tptp.orderi2172309028950807442at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le7866589430770878221at_nat Y4) X4))) tptp.bot_bo2099793752762293965at_nat))
% 6.81/7.11 (assert (@ (@ (@ tptp.ordering_top_set_o (lambda ((X4 tptp.set_o) (Y4 tptp.set_o)) (@ (@ tptp.ord_less_eq_set_o Y4) X4))) (lambda ((X4 tptp.set_o) (Y4 tptp.set_o)) (@ (@ tptp.ord_less_set_o Y4) X4))) tptp.bot_bot_set_o))
% 6.81/7.11 (assert (@ (@ (@ tptp.ordering_top_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y4) X4))) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat Y4) X4))) tptp.bot_bot_set_nat))
% 6.81/7.11 (assert (@ (@ (@ tptp.ordering_top_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y4) X4))) (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_assn Y4) X4))) tptp.bot_bot_assn))
% 6.81/7.11 (assert (@ (@ (@ tptp.ordering_top_set_int (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y4) X4))) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_set_int Y4) X4))) tptp.bot_bot_set_int))
% 6.81/7.11 (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.bot_bot_nat))
% 6.81/7.11 (assert (forall ((B Bool) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B)) (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat)) B)))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (exists ((H5 tptp.heap_e7401611519738050253t_unit) (R2 tptp.a) (T2 tptp.nat)) (and (@ (@ (@ (@ (@ tptp.heap_Time_effect_a C) H) H5) R2) T2) (@ (@ tptp.rep_assn (@ Q R2)) (@ (@ tptp.produc7507926704131184380et_nat H5) (@ (@ (@ tptp.hoare_new_addrs H) As) H5)))))))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5672175589177086241at_nat tptp.sup_su718114333110466843at_nat) (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le3000389064537975527at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr8693737435421807431at_nat) (Y4 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_le6428140832669894131at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5174734335190411425at_nat tptp.sup_su3035147773818789531at_nat) (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le8081472938463900775at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr8551490117392284871at_nat) (Y4 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_le7642048601412989811at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6976360593897529633at_nat tptp.sup_su5525570899277871387at_nat) (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le1268244103169919719at_nat Y4) X4))) (lambda ((X4 tptp.set_Pr4329608150637261639at_nat) (Y4 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_le2604355607129572851at_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic3109210760196336428et_nat tptp.sup_sup_set_nat) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat Y4) X4))) (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5623431474481994958t_assn tptp.sup_sup_assn) (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_eq_assn Y4) X4))) (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.ord_less_assn Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic8154731777541915528et_int tptp.sup_sup_set_int) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int Y4) X4))) (lambda ((X4 tptp.set_int) (Y4 tptp.set_int)) (@ (@ tptp.ord_less_set_int Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5374021519246970238et_rat tptp.sup_sup_rat) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat Y4) X4))) (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (@ (@ tptp.ord_less_rat Y4) X4))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6009151579333465974et_nat tptp.sup_sup_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))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6006661108824415698et_int tptp.sup_sup_int) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_eq_int Y4) X4))) (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ (@ tptp.ord_less_int Y4) X4))))
% 6.81/7.11 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (=> (@ tptp.in_range _let_1) (=> (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (= (@ (@ tptp.inf_inf_set_nat As) As6) tptp.bot_bot_set_nat) (=> (@ (@ (@ tptp.relH As) H) H5) (=> (@ tptp.in_range (@ _let_1 As)) (=> (@ (@ tptp.rep_assn Q) (@ _let_1 As6)) (@ (@ tptp.rep_assn R) (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As6))))))))) (@ (@ tptp.rep_assn (@ (@ tptp.wand_assn Q) R)) _let_1))))))
% 6.81/7.11 (assert (forall ((P Bool) (Q Bool)) (= (= (@ tptp.pure_assn P) (@ tptp.pure_assn Q)) (= P Q))))
% 6.81/7.11 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.times_times_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 6.81/7.11 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.sup_sup_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (or A B)))))
% 6.81/7.11 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.bot_bot_assn) (not P))))
% 6.81/7.11 (assert (= (@ tptp.pure_assn false) tptp.bot_bot_assn))
% 6.81/7.11 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.inf_inf_assn (@ tptp.pure_assn A)) (@ tptp.pure_assn B)) (@ tptp.pure_assn (and A B)))))
% 6.81/7.11 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (B Bool) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B))) H) (and (@ (@ tptp.rep_assn P) H) B))))
% 6.81/7.11 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat) (As3 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (= (@ tptp.in_range (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As3))) (and (@ tptp.in_range (@ _let_1 As)) (@ tptp.in_range (@ _let_1 As3)))))))
% 6.81/7.11 (assert (forall ((Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (Top tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.ordering_top_nat Less_eq) Less) Top) (=> (@ (@ Less_eq Top) A) (= A Top)))))
% 6.81/7.11 (assert (forall ((Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (Top tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.ordering_top_nat Less_eq) Less) Top) (= (not (= A Top)) (@ (@ Less A) Top)))))
% 6.81/7.11 (assert (forall ((Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (Top tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.ordering_top_nat Less_eq) Less) Top) (= (@ (@ Less_eq Top) A) (= A Top)))))
% 6.81/7.11 (assert (forall ((Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (Top tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.ordering_top_nat Less_eq) Less) Top) (not (@ (@ Less Top) A)))))
% 6.81/7.11 (assert (forall ((Less_eq (-> tptp.nat tptp.nat Bool)) (Less (-> tptp.nat tptp.nat Bool)) (Top tptp.nat) (A tptp.nat)) (=> (@ (@ (@ tptp.ordering_top_nat Less_eq) Less) Top) (@ (@ Less_eq A) Top))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) (@ tptp.in_range H))))
% 6.81/7.11 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H) H3) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H3) As)))))
% 6.81/7.11 (assert (forall ((As tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit) (H3 tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ (@ tptp.relH As) H) H3) (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As)))))
% 6.81/7.11 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ (@ tptp.relH As) H) H))))
% 6.81/7.11 (assert (forall ((As tptp.set_nat) (As3 tptp.set_nat) (H tptp.heap_e7401611519738050253t_unit)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H))) (=> (@ (@ tptp.ord_less_eq_set_nat As) As3) (=> (@ tptp.in_range (@ _let_1 As3)) (@ tptp.in_range (@ _let_1 As)))))))
% 6.81/7.11 (assert (forall ((C tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (R3 tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit C) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R3) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (@ (@ (@ (@ (@ tptp.heap_T6553295506729943825t_unit C) H) H3) R3) N2))))
% 6.81/7.11 (assert (forall ((C tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (R3 tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat)) (=> (= (@ (@ tptp.heap_Time_execute_a C) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R3) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (@ (@ (@ (@ (@ tptp.heap_Time_effect_a C) H) H3) R3) N2))))
% 6.81/7.11 (assert (= tptp.heap_T6553295506729943825t_unit (lambda ((C4 tptp.heap_T5738788834812785303t_unit) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R4 tptp.product_unit) (N tptp.nat)) (= (@ (@ tptp.heap_T875086893843062177t_unit C4) H6) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))
% 6.81/7.11 (assert (= tptp.heap_Time_effect_a (lambda ((C4 tptp.heap_Time_Heap_a) (H6 tptp.heap_e7401611519738050253t_unit) (H7 tptp.heap_e7401611519738050253t_unit) (R4 tptp.a) (N tptp.nat)) (= (@ (@ tptp.heap_Time_execute_a C4) H6) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R4) (@ (@ tptp.produc584006145561248582it_nat H7) N)))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As4) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H4))))))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (not (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) As4) (@ (@ tptp.ord_less_nat X7) (@ tptp.lim_Product_unit H4)))))))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (= Y (not (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) As4) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H4))))))))))))
% 6.81/7.11 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ tptp.in_range (@ (@ tptp.produc7507926704131184380et_nat H) As)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) As) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H)))))))
% 6.81/7.11 (assert (forall ((F tptp.heap_Time_Heap_a) (G tptp.heap_Time_Heap_a)) (=> (forall ((H4 tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_a F) H4) (@ (@ tptp.heap_Time_execute_a G) H4))) (= F G))))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic3109210760196336428et_nat tptp.inf_inf_set_nat) tptp.ord_less_eq_set_nat) tptp.ord_less_set_nat))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5111740090977526247t_unit tptp.inf_inf_Product_unit) tptp.ord_le3221252021190050221t_unit) tptp.ord_le361264281704409273t_unit))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6529551498584149819at_nat tptp.inf_in2572325071724192079at_nat) tptp.ord_le3146513528884898305at_nat) tptp.ord_le7866589430770878221at_nat))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5623431474481994958t_assn tptp.inf_inf_assn) tptp.ord_less_eq_assn) tptp.ord_less_assn))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic8154731777541915528et_int tptp.inf_inf_set_int) tptp.ord_less_eq_set_int) tptp.ord_less_set_int))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic5374021519246970238et_rat tptp.inf_inf_rat) tptp.ord_less_eq_rat) tptp.ord_less_rat))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6009151579333465974et_nat tptp.inf_inf_nat) tptp.ord_less_eq_nat) tptp.ord_less_nat))
% 6.81/7.11 (assert (@ (@ (@ tptp.lattic6006661108824415698et_int tptp.inf_inf_int) tptp.ord_less_eq_int) tptp.ord_less_int))
% 6.81/7.11 (assert (forall ((Uu tptp.produc3260487557148687353it_nat) (X tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.the_de542837501814275618it_nat Uu) (@ tptp.some_P7913643980934408916it_nat X)) X)))
% 6.81/7.11 (assert (forall ((Uu tptp.num) (X tptp.num)) (= (@ (@ tptp.the_default_num Uu) (@ tptp.some_num X)) X)))
% 6.81/7.11 (assert (forall ((Uu tptp.produc8664842809031399944it_nat) (X tptp.produc8664842809031399944it_nat)) (= (@ (@ tptp.the_de2487931475039285041it_nat Uu) (@ tptp.some_P1914260805536162275it_nat X)) X)))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H5) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As6))))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (not (and (@ tptp.in_range _let_1) (forall ((H8 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H8))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H8) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As7)))))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (= Y (not (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As8) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H7) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As8))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As8))))))))))))))))
% 6.81/7.11 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Q (-> tptp.produc3658429121746597890et_nat Bool)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H) As))) (= (@ (@ (@ tptp.wand_raw P) Q) _let_1) (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As) As8) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As) H) H7) (@ tptp.in_range (@ _let_1 As)) (@ P (@ _let_1 As8))) (@ Q (@ _let_1 (@ (@ tptp.sup_sup_set_nat As) As8)))))))))))
% 6.81/7.11 (assert (forall ((X tptp.nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ tptp.measure_nat F)) (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ (@ tptp.wand_raw X) Xa) Xb)) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (and (@ tptp.in_range _let_1) (forall ((H5 tptp.heap_e7401611519738050253t_unit) (As6 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H5))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As6) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H5) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As6))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As6))))))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.wand_raw X) Xa) Xb) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1))) (not (and (@ tptp.in_range _let_1) (forall ((H8 tptp.heap_e7401611519738050253t_unit) (As7 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H8))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As7) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H8) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As7))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As7)))))))))))))))))
% 6.81/7.11 (assert (forall ((X (-> tptp.produc3658429121746597890et_nat Bool)) (Xa (-> tptp.produc3658429121746597890et_nat Bool)) (Xb tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ (@ tptp.wand_raw X) Xa) Xb) Y) (=> (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) Xb))) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xb _let_1) (=> (= Y (and (@ tptp.in_range _let_1) (forall ((H7 tptp.heap_e7401611519738050253t_unit) (As8 tptp.set_nat)) (let ((_let_1 (@ tptp.produc7507926704131184380et_nat H7))) (=> (and (= (@ (@ tptp.inf_inf_set_nat As4) As8) tptp.bot_bot_set_nat) (@ (@ (@ tptp.relH As4) H4) H7) (@ tptp.in_range (@ _let_1 As4)) (@ X (@ _let_1 As8))) (@ Xa (@ _let_1 (@ (@ tptp.sup_sup_set_nat As4) As8)))))))) (not (@ (@ tptp.accp_P1862375125659990705et_nat tptp.wand_raw_rel) (@ (@ tptp.produc2245416461498447860et_nat X) (@ (@ tptp.produc5001842942810119800et_nat Xa) _let_1)))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.in_range X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) As4) (@ (@ tptp.ord_less_nat X3) (@ tptp.lim_Product_unit H4)))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.in_range X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1) (not (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) As4) (@ (@ tptp.ord_less_nat X7) (@ tptp.lim_Product_unit H4))))))))))))))
% 6.81/7.11 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.in_range X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (= Y (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) As4) (@ (@ tptp.ord_less_nat X4) (@ tptp.lim_Product_unit H4))))) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.in_range_rel) _let_1)))))))))))
% 6.81/7.11 (assert (= tptp.wand_assn (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.wand_raw (@ tptp.rep_assn P4)) (@ tptp.rep_assn Q3))))))
% 6.81/7.11 (assert (= tptp.sup_su1419176701018045153at_nat (lambda ((X4 tptp.option2158460348403737357at_nat) (Y4 tptp.option2158460348403737357at_nat)) (@ (@ (@ tptp.case_o7467001542679133189at_nat Y4) (lambda ((X8 tptp.set_Pr8693737435421807431at_nat)) (@ (@ (@ tptp.case_o7467001542679133189at_nat X4) (lambda ((Z6 tptp.set_Pr8693737435421807431at_nat)) (@ tptp.some_s579751585967276588at_nat (@ (@ tptp.sup_su718114333110466843at_nat X8) Z6)))) Y4))) X4))))
% 6.81/7.11 (assert (= tptp.sup_su5873096292857799009at_nat (lambda ((X4 tptp.option2498585697089621389at_nat) (Y4 tptp.option2498585697089621389at_nat)) (@ (@ (@ tptp.case_o8757249484648823045at_nat Y4) (lambda ((X8 tptp.set_Pr8551490117392284871at_nat)) (@ (@ (@ tptp.case_o8757249484648823045at_nat X4) (lambda ((Z6 tptp.set_Pr8551490117392284871at_nat)) (@ tptp.some_s287724117700012716at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X8) Z6)))) Y4))) X4))))
% 6.81/7.11 (assert (= tptp.sup_su2273273666271716065at_nat (lambda ((X4 tptp.option1583680563626158861at_nat) (Y4 tptp.option1583680563626158861at_nat)) (@ (@ (@ tptp.case_o9080059180780454917at_nat Y4) (lambda ((X8 tptp.set_Pr4329608150637261639at_nat)) (@ (@ (@ tptp.case_o9080059180780454917at_nat X4) (lambda ((Z6 tptp.set_Pr4329608150637261639at_nat)) (@ tptp.some_s5890477192898017836at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X8) Z6)))) Y4))) X4))))
% 6.81/7.11 (assert (= tptp.sup_su3598758113090618626et_nat (lambda ((X4 tptp.option_set_nat) (Y4 tptp.option_set_nat)) (@ (@ (@ tptp.case_o4054078431260844265et_nat Y4) (lambda ((X8 tptp.set_nat)) (@ (@ (@ tptp.case_o4054078431260844265et_nat X4) (lambda ((Z6 tptp.set_nat)) (@ tptp.some_set_nat (@ (@ tptp.sup_sup_set_nat X8) Z6)))) Y4))) X4))))
% 6.81/7.11 (assert (= tptp.sup_sup_option_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat Y4) (lambda ((X8 tptp.nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat X4) (lambda ((Z6 tptp.nat)) (@ tptp.some_nat (@ (@ tptp.sup_sup_nat X8) Z6)))) Y4))) X4))))
% 6.81/7.11 (assert (= tptp.dflt_N6592383573632408824at_nat (lambda ((S5 tptp.set_Pr1261947904930325089at_nat)) (@ (@ (@ tptp.if_opt7704869406773131885at_nat (= S5 tptp.bot_bo2099793752762293965at_nat)) tptp.none_s625347054029921090at_nat) (@ tptp.some_s147305329494351046at_nat S5)))))
% 6.81/7.11 (assert (= tptp.dflt_None_set_o (lambda ((S5 tptp.set_o)) (@ (@ (@ tptp.if_option_set_o (= S5 tptp.bot_bot_set_o)) tptp.none_set_o) (@ tptp.some_set_o S5)))))
% 6.81/7.11 (assert (= tptp.dflt_None_set_nat (lambda ((S5 tptp.set_nat)) (@ (@ (@ tptp.if_option_set_nat (= S5 tptp.bot_bot_set_nat)) tptp.none_set_nat) (@ tptp.some_set_nat S5)))))
% 6.81/7.11 (assert (= tptp.dflt_None_set_int (lambda ((S5 tptp.set_int)) (@ (@ (@ tptp.if_option_set_int (= S5 tptp.bot_bot_set_int)) tptp.none_set_int) (@ tptp.some_set_int S5)))))
% 6.81/7.11 (assert (= tptp.times_times_assn (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (@ (@ tptp.times_assn_raw (@ tptp.rep_assn P4)) (@ tptp.rep_assn Q3))))))
% 6.81/7.11 (assert (= tptp.is_emp1662574758705540307at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (= A6 tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.11 (assert (= tptp.is_empty_o (lambda ((A6 tptp.set_o)) (= A6 tptp.bot_bot_set_o))))
% 6.81/7.11 (assert (= tptp.is_empty_nat (lambda ((A6 tptp.set_nat)) (= A6 tptp.bot_bot_set_nat))))
% 6.81/7.11 (assert (= tptp.is_empty_int (lambda ((A6 tptp.set_int)) (= A6 tptp.bot_bot_set_int))))
% 6.81/7.11 (assert (forall ((P tptp.assn) (C tptp.heap_Time_Heap_a) (Q (-> tptp.a tptp.assn)) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (=> (@ (@ (@ tptp.hoare_hoare_triple_a P) C) Q) (=> (@ (@ tptp.rep_assn P) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (@ (@ tptp.heap_Time_success_a C) H)))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (let ((_let_1 (@ tptp.ord_le3146513528884898305at_nat B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) A3) (@ P X4))))) (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (P (-> Bool Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_o B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr958786334691620121nt_int) (A3 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le2843351958646193337nt_int B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) A3) (@ P X4))))) (forall ((X4 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.ord_le6045566169113846134st_nat B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A3) (@ P X4))))) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A3) (@ P X4))))) (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_int B3))) (=> (@ _let_1 A3) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) B3) (@ P X4))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (Q (-> tptp.product_prod_nat_nat Bool)) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) B3) (@ Q X4))))) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (Q (-> Bool Bool)) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_eq_set_o B3) A3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_less_eq_set_o (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) B3) (@ Q X4))))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_Pr958786334691620121nt_int) (A3 tptp.set_Pr958786334691620121nt_int) (Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.product_prod_int_int Bool))) (=> (@ (@ tptp.ord_le2843351958646193337nt_int B3) A3) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (@ (@ tptp.member5262025264175285858nt_int X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) B3) (@ Q X4))))) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat) (Q (-> tptp.list_nat Bool)) (P (-> tptp.list_nat Bool))) (=> (@ (@ tptp.ord_le6045566169113846134st_nat B3) A3) (=> (forall ((X3 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) B3) (@ Q X4))))) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat) (Q (-> tptp.set_nat Bool)) (P (-> tptp.set_nat Bool))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B3) A3) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) B3) (@ Q X4))))) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (Q (-> tptp.nat Bool)) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) B3) (@ Q X4))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (Q (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) B3) (=> (@ Q X3) (@ P X3)))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) B3) (@ Q X4))))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4)))))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (let ((_let_1 (@ tptp.ord_le2843351958646193337nt_int A3))) (= (@ _let_1 (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ P X4) (@ Q X4))))) (and (@ _let_1 (@ tptp.collec213857154873943460nt_int P)) (@ _let_1 (@ tptp.collec213857154873943460nt_int Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (let ((_let_1 (@ tptp.ord_le6045566169113846134st_nat A3))) (= (@ _let_1 (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P X4) (@ Q X4))))) (and (@ _let_1 (@ tptp.collect_list_nat P)) (@ _let_1 (@ tptp.collect_list_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.ord_le6893508408891458716et_nat A3))) (= (@ _let_1 (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P X4) (@ Q X4))))) (and (@ _let_1 (@ tptp.collect_set_nat P)) (@ _let_1 (@ tptp.collect_set_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A3))) (= (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P X4) (@ Q X4))))) (and (@ _let_1 (@ tptp.collect_nat P)) (@ _let_1 (@ tptp.collect_nat Q)))))))
% 6.81/7.11 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (let ((_let_1 (@ tptp.ord_less_eq_set_int A3))) (= (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P X4) (@ Q X4))))) (and (@ _let_1 (@ tptp.collect_int P)) (@ _let_1 (@ tptp.collect_int Q)))))))
% 6.81/7.11 (assert (forall ((X tptp.option3562590408128118217it_nat)) (= (not (= X tptp.none_P2651198173097904984it_nat)) (exists ((Y4 tptp.produc3260487557148687353it_nat)) (= X (@ tptp.some_P7913643980934408916it_nat Y4))))))
% 6.81/7.11 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y4 tptp.num)) (= X (@ tptp.some_num Y4))))))
% 6.81/7.11 (assert (forall ((X tptp.option8956607266484857688it_nat)) (= (not (= X tptp.none_P9117596204409417319it_nat)) (exists ((Y4 tptp.produc8664842809031399944it_nat)) (= X (@ tptp.some_P1914260805536162275it_nat Y4))))))
% 6.81/7.11 (assert (forall ((X tptp.option3562590408128118217it_nat)) (= (forall ((Y4 tptp.produc3260487557148687353it_nat)) (not (= X (@ tptp.some_P7913643980934408916it_nat Y4)))) (= X tptp.none_P2651198173097904984it_nat))))
% 6.81/7.11 (assert (forall ((X tptp.option_num)) (= (forall ((Y4 tptp.num)) (not (= X (@ tptp.some_num Y4)))) (= X tptp.none_num))))
% 6.81/7.11 (assert (forall ((X tptp.option8956607266484857688it_nat)) (= (forall ((Y4 tptp.produc8664842809031399944it_nat)) (not (= X (@ tptp.some_P1914260805536162275it_nat Y4)))) (= X tptp.none_P9117596204409417319it_nat))))
% 6.81/7.11 (assert (forall ((X tptp.assn)) (= (@ tptp.abs_assn (@ tptp.rep_assn X)) X)))
% 6.81/7.11 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 6.81/7.11 (assert (forall ((X tptp.option_num)) (not (@ (@ tptp.ord_less_option_num X) tptp.none_num))))
% 6.81/7.11 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_le6622620407824499402on_num (@ tptp.some_num X)) tptp.none_num))))
% 6.81/7.11 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 6.81/7.11 (assert (= (@ tptp.dflt_N6592383573632408824at_nat tptp.bot_bo2099793752762293965at_nat) tptp.none_s625347054029921090at_nat))
% 6.81/7.11 (assert (= (@ tptp.dflt_None_set_o tptp.bot_bot_set_o) tptp.none_set_o))
% 6.81/7.11 (assert (= (@ tptp.dflt_None_set_nat tptp.bot_bot_set_nat) tptp.none_set_nat))
% 6.81/7.11 (assert (= (@ tptp.dflt_None_set_int tptp.bot_bot_set_int) tptp.none_set_int))
% 6.81/7.11 (assert (forall ((F1 tptp.int) (F22 (-> tptp.num tptp.int))) (= (@ (@ (@ tptp.case_option_int_num F1) F22) tptp.none_num) F1)))
% 6.81/7.11 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num))) (= (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F22) tptp.none_num) F1)))
% 6.81/7.11 (assert (forall ((F1 tptp.num) (F22 (-> tptp.num tptp.num))) (= (@ (@ (@ tptp.case_option_num_num F1) F22) tptp.none_num) F1)))
% 6.81/7.11 (assert (= tptp.bot_bot_option_num tptp.none_num))
% 6.81/7.11 (assert (forall ((H (-> tptp.int tptp.int)) (F1 tptp.int) (F22 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F22) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.int tptp.option_num)) (F1 tptp.int) (F22 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F22) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.int tptp.num)) (F1 tptp.int) (F22 (-> tptp.num tptp.int)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_int_num F1) F22) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.option_num tptp.int)) (F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F22) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F22) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.option_num tptp.num)) (F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F22) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.num tptp.int)) (F1 tptp.num) (F22 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F22) Option)) (@ (@ (@ tptp.case_option_int_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.num tptp.option_num)) (F1 tptp.num) (F22 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F22) Option)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((H (-> tptp.num tptp.num)) (F1 tptp.num) (F22 (-> tptp.num tptp.num)) (Option tptp.option_num)) (= (@ H (@ (@ (@ tptp.case_option_num_num F1) F22) Option)) (@ (@ (@ tptp.case_option_num_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) Option))))
% 6.81/7.11 (assert (forall ((X2 tptp.produc3260487557148687353it_nat)) (not (= tptp.none_P2651198173097904984it_nat (@ tptp.some_P7913643980934408916it_nat X2)))))
% 6.81/7.11 (assert (forall ((X2 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X2)))))
% 6.81/7.11 (assert (forall ((X2 tptp.produc8664842809031399944it_nat)) (not (= tptp.none_P9117596204409417319it_nat (@ tptp.some_P1914260805536162275it_nat X2)))))
% 6.81/7.11 (assert (forall ((Option tptp.option3562590408128118217it_nat) (X2 tptp.produc3260487557148687353it_nat)) (=> (= Option (@ tptp.some_P7913643980934408916it_nat X2)) (not (= Option tptp.none_P2651198173097904984it_nat)))))
% 6.81/7.11 (assert (forall ((Option tptp.option_num) (X2 tptp.num)) (=> (= Option (@ tptp.some_num X2)) (not (= Option tptp.none_num)))))
% 6.81/7.11 (assert (forall ((Option tptp.option8956607266484857688it_nat) (X2 tptp.produc8664842809031399944it_nat)) (=> (= Option (@ tptp.some_P1914260805536162275it_nat X2)) (not (= Option tptp.none_P9117596204409417319it_nat)))))
% 6.81/7.11 (assert (forall ((Y tptp.option3562590408128118217it_nat)) (=> (not (= Y tptp.none_P2651198173097904984it_nat)) (not (forall ((X22 tptp.produc3260487557148687353it_nat)) (not (= Y (@ tptp.some_P7913643980934408916it_nat X22))))))))
% 6.81/7.12 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X22 tptp.num)) (not (= Y (@ tptp.some_num X22))))))))
% 6.81/7.12 (assert (forall ((Y tptp.option8956607266484857688it_nat)) (=> (not (= Y tptp.none_P9117596204409417319it_nat)) (not (forall ((X22 tptp.produc8664842809031399944it_nat)) (not (= Y (@ tptp.some_P1914260805536162275it_nat X22))))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option3562590408128118217it_nat Bool))) (exists ((X5 tptp.option3562590408128118217it_nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.option3562590408128118217it_nat Bool))) (or (@ P4 tptp.none_P2651198173097904984it_nat) (exists ((X4 tptp.produc3260487557148687353it_nat)) (@ P4 (@ tptp.some_P7913643980934408916it_nat X4)))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option_num Bool))) (exists ((X5 tptp.option_num)) (@ P5 X5))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option8956607266484857688it_nat Bool))) (exists ((X5 tptp.option8956607266484857688it_nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.option8956607266484857688it_nat Bool))) (or (@ P4 tptp.none_P9117596204409417319it_nat) (exists ((X4 tptp.produc8664842809031399944it_nat)) (@ P4 (@ tptp.some_P1914260805536162275it_nat X4)))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option3562590408128118217it_nat Bool))) (forall ((X5 tptp.option3562590408128118217it_nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.option3562590408128118217it_nat Bool))) (and (@ P4 tptp.none_P2651198173097904984it_nat) (forall ((X4 tptp.produc3260487557148687353it_nat)) (@ P4 (@ tptp.some_P7913643980934408916it_nat X4)))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option_num Bool))) (forall ((X5 tptp.option_num)) (@ P5 X5))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X4 tptp.num)) (@ P4 (@ tptp.some_num X4)))))))
% 6.81/7.12 (assert (= (lambda ((P5 (-> tptp.option8956607266484857688it_nat Bool))) (forall ((X5 tptp.option8956607266484857688it_nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.option8956607266484857688it_nat Bool))) (and (@ P4 tptp.none_P9117596204409417319it_nat) (forall ((X4 tptp.produc8664842809031399944it_nat)) (@ P4 (@ tptp.some_P1914260805536162275it_nat X4)))))))
% 6.81/7.12 (assert (forall ((X tptp.option3562590408128118217it_nat) (P (-> tptp.option3562590408128118217it_nat tptp.option3562590408128118217it_nat Bool)) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (@ tptp.some_P7913643980934408916it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option3562590408128118217it_nat) (P (-> tptp.option3562590408128118217it_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.num)) (=> (= X (@ tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (@ tptp.some_num B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option3562590408128118217it_nat) (P (-> tptp.option3562590408128118217it_nat tptp.option8956607266484857688it_nat Bool)) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P2651198173097904984it_nat) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.produc3260487557148687353it_nat) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_P7913643980934408916it_nat A4)) (=> (= Y (@ tptp.some_P1914260805536162275it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option3562590408128118217it_nat Bool)) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_P7913643980934408916it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.num)) (=> (= X (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_num B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option8956607266484857688it_nat Bool)) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.num) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_num A4)) (=> (= Y (@ tptp.some_P1914260805536162275it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option8956607266484857688it_nat) (P (-> tptp.option8956607266484857688it_nat tptp.option3562590408128118217it_nat Bool)) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_P2651198173097904984it_nat) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (@ tptp.some_P7913643980934408916it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option8956607266484857688it_nat) (P (-> tptp.option8956607266484857688it_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.num)) (=> (= X (@ tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (@ tptp.some_num B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option8956607266484857688it_nat) (P (-> tptp.option8956607266484857688it_nat tptp.option8956607266484857688it_nat Bool)) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P9117596204409417319it_nat) _let_1) (=> (=> (= Y tptp.none_P9117596204409417319it_nat) _let_1) (=> (forall ((A4 tptp.produc8664842809031399944it_nat) (B4 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_P1914260805536162275it_nat A4)) (=> (= Y (@ tptp.some_P1914260805536162275it_nat B4)) (@ (@ P X) Y)))) _let_1))))))
% 6.81/7.12 (assert (forall ((X tptp.option_num)) (@ (@ tptp.ord_le6622620407824499402on_num tptp.none_num) X)))
% 6.81/7.12 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_le6622620407824499402on_num X) tptp.none_num) (= X tptp.none_num))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (= (@ P H4) (@ (@ tptp.rep_assn Pr) H4))) (= (@ tptp.abs_assn P) Pr))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc3658429121746597890et_nat Bool)) (Pr tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (= (@ P H4) (@ (@ tptp.rep_assn Pr) H4))) (= Pr (@ tptp.abs_assn P)))))
% 6.81/7.12 (assert (forall ((F1 tptp.int) (F22 (-> tptp.num tptp.int)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_option_int_num F1) F22) (@ tptp.some_num X2)) (@ F22 X2))))
% 6.81/7.12 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_o6005452278849405969um_num F1) F22) (@ tptp.some_num X2)) (@ F22 X2))))
% 6.81/7.12 (assert (forall ((F1 tptp.num) (F22 (-> tptp.num tptp.num)) (X2 tptp.num)) (= (@ (@ (@ tptp.case_option_num_num F1) F22) (@ tptp.some_num X2)) (@ F22 X2))))
% 6.81/7.12 (assert (forall ((X tptp.num)) (= (@ (@ tptp.the_default_num X) tptp.none_num) X)))
% 6.81/7.12 (assert (= tptp.inf_in7812914138253463912et_nat (lambda ((X4 tptp.option_set_nat) (Y4 tptp.option_set_nat)) (@ (@ (@ tptp.case_o4054078431260844265et_nat tptp.none_set_nat) (lambda ((Z6 tptp.set_nat)) (@ (@ (@ tptp.case_o4054078431260844265et_nat tptp.none_set_nat) (lambda ((Aa tptp.set_nat)) (@ tptp.some_set_nat (@ (@ tptp.inf_inf_set_nat Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.inf_inf_option_assn (lambda ((X4 tptp.option_assn) (Y4 tptp.option_assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Z6 tptp.assn)) (@ (@ (@ tptp.case_o4484465799723439917n_assn tptp.none_assn) (lambda ((Aa tptp.assn)) (@ tptp.some_assn (@ (@ tptp.inf_inf_assn Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.inf_inf_option_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Z6 tptp.nat)) (@ (@ (@ tptp.case_o7429725398727453821at_nat tptp.none_nat) (lambda ((Aa tptp.nat)) (@ tptp.some_nat (@ (@ tptp.inf_inf_nat Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.inf_in5800606384722953409t_unit (lambda ((X4 tptp.option_Product_unit) (Y4 tptp.option_Product_unit)) (@ (@ (@ tptp.case_o2985186191577459077t_unit tptp.none_Product_unit) (lambda ((Z6 tptp.product_unit)) (@ (@ (@ tptp.case_o2985186191577459077t_unit tptp.none_Product_unit) (lambda ((Aa tptp.product_unit)) (@ tptp.some_Product_unit (@ (@ tptp.inf_inf_Product_unit Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.inf_in777885744494410645at_nat (lambda ((X4 tptp.option8963830502488799655at_nat) (Y4 tptp.option8963830502488799655at_nat)) (@ (@ (@ tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat) (lambda ((Z6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ (@ tptp.case_o311359030874850053at_nat tptp.none_s625347054029921090at_nat) (lambda ((Aa tptp.set_Pr1261947904930325089at_nat)) (@ tptp.some_s147305329494351046at_nat (@ (@ tptp.inf_in2572325071724192079at_nat Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.bot_bot_assn (@ tptp.abs_assn (lambda ((Uu2 tptp.produc3658429121746597890et_nat)) false))))
% 6.81/7.12 (assert (forall ((X tptp.option_num)) (=> (@ (@ tptp.ord_less_option_num tptp.none_num) X) (exists ((Z2 tptp.num)) (= X (@ tptp.some_num Z2))))))
% 6.81/7.12 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_option_num tptp.none_num) (@ tptp.some_num X))))
% 6.81/7.12 (assert (= tptp.sup_sup_assn (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (or (@ (@ tptp.rep_assn P4) H6) (@ (@ tptp.rep_assn Q3) H6)))))))
% 6.81/7.12 (assert (= tptp.inf_inf_assn (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ (@ tptp.rep_assn P4) H6) (@ (@ tptp.rep_assn Q3) H6)))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.heap_T584514906347983379t_unit F) H) (not (forall ((R2 tptp.product_unit) (H5 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R2) H5)))))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ (@ tptp.heap_Time_success_a F) H) (not (forall ((R2 tptp.a) (H5 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R2) H5)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.rel_of_nat_nat (lambda ((X4 tptp.nat)) tptp.none_nat)) P) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.12 (assert (= (@ tptp.set_to_map_nat_nat tptp.bot_bo2099793752762293965at_nat) (lambda ((X4 tptp.nat)) tptp.none_nat)))
% 6.81/7.12 (assert (= (@ tptp.map_to_set_nat_nat (lambda ((X4 tptp.nat)) tptp.none_nat)) tptp.bot_bo2099793752762293965at_nat))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.num Bool)) (X tptp.option_num) (R (-> tptp.int Bool)) (F tptp.int) (G (-> tptp.num tptp.int))) (=> (@ (@ (@ tptp.case_option_o_num P) Q) X) (=> (=> P (@ R F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q Q5) (@ R (@ G Q5)))) (@ R (@ (@ (@ tptp.case_option_int_num F) G) X)))))))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.num Bool)) (X tptp.option_num) (R (-> tptp.option_num Bool)) (F tptp.option_num) (G (-> tptp.num tptp.option_num))) (=> (@ (@ (@ tptp.case_option_o_num P) Q) X) (=> (=> P (@ R F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q Q5) (@ R (@ G Q5)))) (@ R (@ (@ (@ tptp.case_o6005452278849405969um_num F) G) X)))))))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.num Bool)) (X tptp.option_num) (R (-> tptp.num Bool)) (F tptp.num) (G (-> tptp.num tptp.num))) (=> (@ (@ (@ tptp.case_option_o_num P) Q) X) (=> (=> P (@ R F)) (=> (forall ((Q5 tptp.num)) (=> (@ Q Q5) (@ R (@ G Q5)))) (@ R (@ (@ (@ tptp.case_option_num_num F) G) X)))))))
% 6.81/7.12 (assert (= tptp.pure_assn (lambda ((B5 Bool)) (@ tptp.abs_assn (@ tptp.pure_a825153325127701367it_nat B5)))))
% 6.81/7.12 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (= (lambda ((X4 tptp.nat)) tptp.none_nat) (@ tptp.set_to_map_nat_nat S)) (= S tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.12 (assert (forall ((V tptp.option5190343406534369742et_nat)) (= (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3658429121746597890et_nat)) (not (= V (@ tptp.some_P750831030444334937et_nat (@ (@ tptp.produc5001842942810119800et_nat X4) Y4))))) (= V tptp.none_P4972525538344268765et_nat))))
% 6.81/7.12 (assert (forall ((V tptp.option2860828798490689354et_nat)) (= (forall ((X4 (-> tptp.produc3658429121746597890et_nat Bool)) (Y4 tptp.produc3925858234332021118et_nat)) (not (= V (@ tptp.some_P1630309045189364437et_nat (@ (@ tptp.produc2245416461498447860et_nat X4) Y4))))) (= V tptp.none_P199884684680593241et_nat))))
% 6.81/7.12 (assert (forall ((V tptp.option7541221861074943443nt_int)) (= (forall ((X4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (not (= V (@ tptp.some_P2355398578364412894nt_int (@ (@ tptp.produc5700946648718959541nt_int X4) Y4))))) (= V tptp.none_P1286213070022356066nt_int))))
% 6.81/7.12 (assert (forall ((V tptp.option4256020574406277085nt_int)) (= (forall ((X4 (-> tptp.int tptp.option6357759511663192854e_term)) (Y4 tptp.product_prod_int_int)) (not (= V (@ tptp.some_P7455497367792166888nt_int (@ (@ tptp.produc4305682042979456191nt_int X4) Y4))))) (= V tptp.none_P3773570700014501484nt_int))))
% 6.81/7.12 (assert (forall ((V tptp.option3562590408128118217it_nat)) (= (forall ((X4 tptp.a) (Y4 tptp.produc6653097349344004940it_nat)) (not (= V (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X4) Y4))))) (= V tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (forall ((V tptp.option8956607266484857688it_nat)) (= (forall ((X4 tptp.product_unit) (Y4 tptp.produc6653097349344004940it_nat)) (not (= V (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X4) Y4))))) (= V tptp.none_P9117596204409417319it_nat))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (G (-> tptp.a tptp.heap_Time_Heap_a))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_a_a F) G)) H) tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (forall ((Option tptp.option_num)) (= (not (= Option tptp.none_num)) (@ (@ (@ tptp.case_option_o_num false) (lambda ((Uu2 tptp.num)) true)) Option))))
% 6.81/7.12 (assert (forall ((Option tptp.option_num)) (= (= Option tptp.none_num) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Uu2 tptp.num)) false)) Option))))
% 6.81/7.12 (assert (= tptp.heap_Time_success_a (lambda ((F3 tptp.heap_Time_Heap_a) (H6 tptp.heap_e7401611519738050253t_unit)) (not (= (@ (@ tptp.heap_Time_execute_a F3) H6) tptp.none_P2651198173097904984it_nat)))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (= (@ (@ tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat)) (@ (@ tptp.heap_Time_success_a F) H))))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.option3562590408128118217it_nat)) (=> (@ (@ (@ tptp.case_o3267218206291580230it_nat P) Q) X) (=> (=> (= X tptp.none_P2651198173097904984it_nat) (not P)) (not (forall ((Y3 tptp.produc3260487557148687353it_nat)) (=> (= X (@ tptp.some_P7913643980934408916it_nat Y3)) (not (@ Q Y3)))))))))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.num Bool)) (X tptp.option_num)) (=> (@ (@ (@ tptp.case_option_o_num P) Q) X) (=> (=> (= X tptp.none_num) (not P)) (not (forall ((Y3 tptp.num)) (=> (= X (@ tptp.some_num Y3)) (not (@ Q Y3)))))))))
% 6.81/7.12 (assert (forall ((P Bool) (Q (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.option8956607266484857688it_nat)) (=> (@ (@ (@ tptp.case_o2686588417244861013it_nat P) Q) X) (=> (=> (= X tptp.none_P9117596204409417319it_nat) (not P)) (not (forall ((Y3 tptp.produc8664842809031399944it_nat)) (=> (= X (@ tptp.some_P1914260805536162275it_nat Y3)) (not (@ Q Y3)))))))))
% 6.81/7.12 (assert (forall ((M (-> tptp.nat tptp.option_nat))) (= (= (@ tptp.map_to_set_nat_nat M) tptp.bot_bo2099793752762293965at_nat) (= M (lambda ((X4 tptp.nat)) tptp.none_nat)))))
% 6.81/7.12 (assert (forall ((M (-> tptp.nat tptp.option_nat))) (= (= tptp.bot_bo2099793752762293965at_nat (@ tptp.map_to_set_nat_nat M)) (= M (lambda ((X4 tptp.nat)) tptp.none_nat)))))
% 6.81/7.12 (assert (= tptp.ord_le353528952715127954et_int (lambda ((X4 tptp.option_set_int) (Y4 tptp.option_set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int true) (lambda ((Z6 tptp.set_int)) (@ (@ (@ tptp.case_o223999843215110191et_int false) (@ tptp.ord_less_eq_set_int Z6)) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.ord_le2406147912482264968on_rat (lambda ((X4 tptp.option_rat) (Y4 tptp.option_rat)) (@ (@ (@ tptp.case_option_o_rat true) (lambda ((Z6 tptp.rat)) (@ (@ (@ tptp.case_option_o_rat false) (@ tptp.ord_less_eq_rat Z6)) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.ord_le6622620407824499402on_num (lambda ((X4 tptp.option_num) (Y4 tptp.option_num)) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Z6 tptp.num)) (@ (@ (@ tptp.case_option_o_num false) (@ tptp.ord_less_eq_num Z6)) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.ord_le5914376470875661696on_nat (lambda ((X4 tptp.option_nat) (Y4 tptp.option_nat)) (@ (@ (@ tptp.case_option_o_nat true) (lambda ((Z6 tptp.nat)) (@ (@ (@ tptp.case_option_o_nat false) (@ tptp.ord_less_eq_nat Z6)) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.ord_le1736525451366464988on_int (lambda ((X4 tptp.option_int) (Y4 tptp.option_int)) (@ (@ (@ tptp.case_option_o_int true) (lambda ((Z6 tptp.int)) (@ (@ (@ tptp.case_option_o_int false) (@ tptp.ord_less_eq_int Z6)) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.ord_less_option_assn (lambda ((X4 tptp.option_assn) (__flatten_var_0 tptp.option_assn)) (@ (@ (@ tptp.case_option_o_assn false) (lambda ((Y4 tptp.assn)) (@ (@ (@ tptp.case_option_o_assn true) (lambda ((Z6 tptp.assn)) (@ (@ tptp.ord_less_assn Z6) Y4))) X4))) __flatten_var_0))))
% 6.81/7.12 (assert (= tptp.ord_less_option_rat (lambda ((X4 tptp.option_rat) (__flatten_var_0 tptp.option_rat)) (@ (@ (@ tptp.case_option_o_rat false) (lambda ((Y4 tptp.rat)) (@ (@ (@ tptp.case_option_o_rat true) (lambda ((Z6 tptp.rat)) (@ (@ tptp.ord_less_rat Z6) Y4))) X4))) __flatten_var_0))))
% 6.81/7.12 (assert (= tptp.ord_less_option_num (lambda ((X4 tptp.option_num) (__flatten_var_0 tptp.option_num)) (@ (@ (@ tptp.case_option_o_num false) (lambda ((Y4 tptp.num)) (@ (@ (@ tptp.case_option_o_num true) (lambda ((Z6 tptp.num)) (@ (@ tptp.ord_less_num Z6) Y4))) X4))) __flatten_var_0))))
% 6.81/7.12 (assert (= tptp.ord_less_option_nat (lambda ((X4 tptp.option_nat) (__flatten_var_0 tptp.option_nat)) (@ (@ (@ tptp.case_option_o_nat false) (lambda ((Y4 tptp.nat)) (@ (@ (@ tptp.case_option_o_nat true) (lambda ((Z6 tptp.nat)) (@ (@ tptp.ord_less_nat Z6) Y4))) X4))) __flatten_var_0))))
% 6.81/7.12 (assert (= tptp.ord_less_option_int (lambda ((X4 tptp.option_int) (__flatten_var_0 tptp.option_int)) (@ (@ (@ tptp.case_option_o_int false) (lambda ((Y4 tptp.int)) (@ (@ (@ tptp.case_option_o_int true) (lambda ((Z6 tptp.int)) (@ (@ tptp.ord_less_int Z6) Y4))) X4))) __flatten_var_0))))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.product_unit) (H5 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X3) H5))))) (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) tptp.none_P9117596204409417319it_nat))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit)) (=> (forall ((X3 tptp.a) (H5 tptp.produc6653097349344004940it_nat)) (not (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X3) H5))))) (= (@ (@ tptp.heap_Time_execute_a F) H) tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (forall ((X tptp.produc4453839368661128058it_nat)) (=> (forall ((N5 tptp.nat) (R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc4111269673004989362it_nat N5) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H4) N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (@ (@ tptp.produc4111269673004989362it_nat N5) tptp.none_P2651198173097904984it_nat))))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3911288613690379145it_nat)) (=> (forall ((N5 tptp.nat) (R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (not (= X (@ (@ tptp.produc638857205735767105it_nat N5) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat R2) (@ (@ tptp.produc584006145561248582it_nat H4) N4))))))) (not (forall ((N5 tptp.nat)) (not (= X (@ (@ tptp.produc638857205735767105it_nat N5) tptp.none_P9117596204409417319it_nat))))))))
% 6.81/7.12 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.set_to_map_nat_nat S) (lambda ((X4 tptp.nat)) tptp.none_nat)) (= S tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (and (= As4 tptp.bot_bot_set_nat) X)))))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (not (and (= As4 tptp.bot_bot_set_nat) X))))))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= Xa (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (= Y (not (and (= As4 tptp.bot_bot_set_nat) X)))))))))
% 6.81/7.12 (assert (forall ((B Bool) (H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ (@ tptp.pure_a825153325127701367it_nat B) (@ (@ tptp.produc7507926704131184380et_nat H) As)) (and (= As tptp.bot_bot_set_nat) B))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) Y) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xa _let_1) (=> (= Y (and (= As4 tptp.bot_bot_set_nat) X)) (not (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1))))))))))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.pure_a825153325127701367it_nat X) Xa) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (not (and (= As4 tptp.bot_bot_set_nat) X)))))))))))
% 6.81/7.12 (assert (forall ((X Bool) (Xa tptp.produc3658429121746597890et_nat)) (=> (not (@ (@ tptp.pure_a825153325127701367it_nat X) Xa)) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) Xa)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= Xa _let_1) (=> (@ (@ tptp.accp_P8458817951426537472et_nat tptp.pure_a6022498039421069578it_nat) (@ (@ tptp.produc3762353314782720579et_nat X) _let_1)) (and (= As4 tptp.bot_bot_set_nat) X))))))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.product_unit tptp.heap_Time_Heap_a))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_T757603679106148408unit_a F) G)) H) (@ (@ tptp.heap_T7616092557645711335rame_a N2) (@ (@ tptp.heap_Time_execute_a (@ G X)) H3))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.a tptp.heap_Time_Heap_a))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_a_a F) G)) H) (@ (@ tptp.heap_T7616092557645711335rame_a N2) (@ (@ tptp.heap_Time_execute_a (@ G X)) H3))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.product_unit tptp.heap_T5738788834812785303t_unit)) (Y tptp.product_unit) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat Y))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit (@ G X)) H3) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T2633723481742716231t_unit F) G)) H) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit) (H tptp.heap_e7401611519738050253t_unit) (X tptp.product_unit) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.product_unit tptp.heap_Time_Heap_a)) (Y tptp.a) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat Y))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit F) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_a (@ G X)) H3) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_T757603679106148408unit_a F) G)) H) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.a tptp.heap_T5738788834812785303t_unit)) (Y tptp.product_unit) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat Y))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (=> (= (@ (@ tptp.heap_T875086893843062177t_unit (@ G X)) H3) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T8685611227969916822t_unit F) G)) H) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a) (H tptp.heap_e7401611519738050253t_unit) (X tptp.a) (H3 tptp.heap_e7401611519738050253t_unit) (N2 tptp.nat) (G (-> tptp.a tptp.heap_Time_Heap_a)) (Y tptp.a) (H9 tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H9))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat Y))) (=> (= (@ (@ tptp.heap_Time_execute_a F) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H3) N2)))) (=> (= (@ (@ tptp.heap_Time_execute_a (@ G X)) H3) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N6)))) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_a_a F) G)) H) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))))
% 6.81/7.12 (assert (= tptp.set_to_map_nat_nat (lambda ((S5 tptp.set_Pr1261947904930325089at_nat) (K3 tptp.nat)) (@ tptp.eps_Opt_nat (lambda ((V2 tptp.nat)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat K3) V2)) S5))))))
% 6.81/7.12 (assert (= tptp.set_to6040779677306527128et_nat (lambda ((S5 tptp.set_Pr3286484037609594932et_nat) (K3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.eps_Op2013419657081471078et_nat (lambda ((V2 tptp.produc3658429121746597890et_nat)) (@ (@ tptp.member1996754912294343701et_nat (@ (@ tptp.produc5001842942810119800et_nat K3) V2)) S5))))))
% 6.81/7.12 (assert (= tptp.set_to2047380710992656148et_nat (lambda ((S5 tptp.set_Pr8536935166611901872et_nat) (K3 (-> tptp.produc3658429121746597890et_nat Bool))) (@ tptp.eps_Op6423059015816587746et_nat (lambda ((V2 tptp.produc3925858234332021118et_nat)) (@ (@ tptp.member6124377750444531601et_nat (@ (@ tptp.produc2245416461498447860et_nat K3) V2)) S5))))))
% 6.81/7.12 (assert (= tptp.set_to6585427216324510421nt_int (lambda ((S5 tptp.set_Pr9222295170931077689nt_int) (K3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term))) (@ tptp.eps_Op2446201859369042517nt_int (lambda ((V2 tptp.product_prod_int_int)) (@ (@ tptp.member7618704894036264090nt_int (@ (@ tptp.produc5700946648718959541nt_int K3) V2)) S5))))))
% 6.81/7.12 (assert (= tptp.set_to1653371902132773855nt_int (lambda ((S5 tptp.set_Pr1872883991513573699nt_int) (K3 (-> tptp.int tptp.option6357759511663192854e_term))) (@ tptp.eps_Op2446201859369042517nt_int (lambda ((V2 tptp.product_prod_int_int)) (@ (@ tptp.member7034335876925520548nt_int (@ (@ tptp.produc4305682042979456191nt_int K3) V2)) S5))))))
% 6.81/7.12 (assert (= tptp.set_to2008915276733485075it_nat (lambda ((S5 tptp.set_Pr7098220151150636591it_nat) (K3 tptp.a)) (@ tptp.eps_Op8301357815426737072it_nat (lambda ((V2 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat K3) V2)) S5))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (=> (@ P H) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T8440541562793052209t_unit P) F)) H) (@ tptp.some_P1914260805536162275it_nat (@ F H))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (=> (@ P H) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_guard_a P) F)) H) (@ tptp.some_P7913643980934408916it_nat (@ F H))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (=> (@ (@ tptp.ord_less_eq_nat (@ F X)) (@ F Y)) (=> (@ _let_1 R) (@ _let_1 (@ (@ tptp.mlex_prod_nat F) R)))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ F (@ (@ tptp.produc5001842942810119800et_nat A) B)) (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A) B))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ F (@ (@ tptp.produc2245416461498447860et_nat A) B)) (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A) B))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2285326912895808259nt_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ F (@ (@ tptp.produc5700946648718959541nt_int A) B)) (@ (@ (@ tptp.produc730925184835016917_int_o F) A) B))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc7773217078559923341nt_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ F (@ (@ tptp.produc4305682042979456191nt_int A) B)) (@ (@ (@ tptp.produc9098658269643458507_int_o F) A) B))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat Bool)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (@ F (@ (@ tptp.produc9178034014595674355it_nat A) B)) (@ (@ (@ tptp.produc3709033845735585303_nat_o F) A) B))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.produc3260487557148687353it_nat)) (= (@ tptp.eps_Op1741419982095519837it_nat (@ (lambda ((Y5 tptp.produc3260487557148687353it_nat) (Z3 tptp.produc3260487557148687353it_nat)) (= Y5 Z3)) X)) (@ tptp.some_P7913643980934408916it_nat X))))
% 6.81/7.12 (assert (forall ((X tptp.num)) (= (@ tptp.eps_Opt_num (@ (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3)) X)) (@ tptp.some_num X))))
% 6.81/7.12 (assert (forall ((X tptp.produc8664842809031399944it_nat)) (= (@ tptp.eps_Op3393321821070424684it_nat (@ (lambda ((Y5 tptp.produc8664842809031399944it_nat) (Z3 tptp.produc8664842809031399944it_nat)) (= Y5 Z3)) X)) (@ tptp.some_P1914260805536162275it_nat X))))
% 6.81/7.12 (assert (forall ((X tptp.produc3260487557148687353it_nat)) (= (@ tptp.eps_Op1741419982095519837it_nat (lambda ((Y4 tptp.produc3260487557148687353it_nat)) (= Y4 X))) (@ tptp.some_P7913643980934408916it_nat X))))
% 6.81/7.12 (assert (forall ((X tptp.num)) (= (@ tptp.eps_Opt_num (lambda ((Y4 tptp.num)) (= Y4 X))) (@ tptp.some_num X))))
% 6.81/7.12 (assert (forall ((X tptp.produc8664842809031399944it_nat)) (= (@ tptp.eps_Op3393321821070424684it_nat (lambda ((Y4 tptp.produc8664842809031399944it_nat)) (= Y4 X))) (@ tptp.some_P1914260805536162275it_nat X))))
% 6.81/7.12 (assert (= (@ tptp.eps_Opt_num (lambda ((Uu2 tptp.num)) false)) tptp.none_num))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N5 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N5))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M3) K3))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A) B) (@ F (@ (@ tptp.produc5001842942810119800et_nat A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A) B) (@ F (@ (@ tptp.produc2245416461498447860et_nat A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2285326912895808259nt_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc730925184835016917_int_o F) A) B) (@ F (@ (@ tptp.produc5700946648718959541nt_int A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc7773217078559923341nt_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc9098658269643458507_int_o F) A) B) (@ F (@ (@ tptp.produc4305682042979456191nt_int A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat Bool)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ (@ tptp.produc3709033845735585303_nat_o F) A) B) (@ F (@ (@ tptp.produc9178034014595674355it_nat A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3925858234332021118et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ (@ tptp.produc6216949301066131538_nat_o F) A) B) (@ F (@ (@ tptp.produc5001842942810119800et_nat A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2732055786443039994et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ (@ tptp.produc5101573711933517782_nat_o F) A) B) (@ F (@ (@ tptp.produc2245416461498447860et_nat A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc2285326912895808259nt_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc730925184835016917_int_o F) A) B) (@ F (@ (@ tptp.produc5700946648718959541nt_int A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc7773217078559923341nt_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.produc9098658269643458507_int_o F) A) B) (@ F (@ (@ tptp.produc4305682042979456191nt_int A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat Bool)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ (@ tptp.produc3709033845735585303_nat_o F) A) B) (@ F (@ (@ tptp.produc9178034014595674355it_nat A) B)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (R3 tptp.a) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R3))) (= (@ (@ tptp.heap_T7616092557645711335rame_a N2) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N6)))) (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (R3 tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit) (N6 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R3))) (= (@ (@ tptp.heap_T3616969660504097270t_unit N2) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N6)))) (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat N2) N6)))))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Xa tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (=> (= (@ (@ tptp.heap_T7616092557645711335rame_a X) Xa) Y) (=> (forall ((R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H4))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R2))) (=> (= Xa (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N4)))) (not (= Y (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4)))))))))) (not (=> (= Xa tptp.none_P2651198173097904984it_nat) (not (= Y tptp.none_P2651198173097904984it_nat))))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Xa tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (=> (= (@ (@ tptp.heap_T3616969660504097270t_unit X) Xa) Y) (=> (forall ((R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H4))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R2))) (=> (= Xa (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N4)))) (not (= Y (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4)))))))))) (not (=> (= Xa tptp.none_P9117596204409417319it_nat) (not (= Y tptp.none_P9117596204409417319it_nat))))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M5 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M5) N5) (@ (@ tptp.ord_less_nat (@ F M5)) (@ F N5)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (forall ((X9 tptp.produc3260487557148687353it_nat)) (=> (@ P X) (=> (@ P X9) (= X9 X)))) (= (= (@ tptp.eps_Op1741419982095519837it_nat P) (@ tptp.some_P7913643980934408916it_nat X)) (@ P X)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (forall ((X9 tptp.num)) (=> (@ P X) (=> (@ P X9) (= X9 X)))) (= (= (@ tptp.eps_Opt_num P) (@ tptp.some_num X)) (@ P X)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.produc8664842809031399944it_nat)) (=> (forall ((X9 tptp.produc8664842809031399944it_nat)) (=> (@ P X) (=> (@ P X9) (= X9 X)))) (= (= (@ tptp.eps_Op3393321821070424684it_nat P) (@ tptp.some_P1914260805536162275it_nat X)) (@ P X)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc3260487557148687353it_nat Bool)) (X tptp.produc3260487557148687353it_nat)) (=> (= (@ tptp.eps_Op1741419982095519837it_nat P) (@ tptp.some_P7913643980934408916it_nat X)) (@ P X))))
% 6.81/7.12 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (= (@ tptp.eps_Opt_num P) (@ tptp.some_num X)) (@ P X))))
% 6.81/7.12 (assert (forall ((P (-> tptp.produc8664842809031399944it_nat Bool)) (X tptp.produc8664842809031399944it_nat)) (=> (= (@ tptp.eps_Op3393321821070424684it_nat P) (@ tptp.some_P1914260805536162275it_nat X)) (@ P X))))
% 6.81/7.12 (assert (forall ((P (-> tptp.heap_e7401611519738050253t_unit Bool)) (H tptp.heap_e7401611519738050253t_unit) (F (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (=> (not (@ P H)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_guard_a P) F)) H) tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (X tptp.nat) (Y tptp.nat) (R tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_nat (@ F X)) (@ F Y)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.mlex_prod_nat F) R)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (F (-> tptp.nat tptp.nat)) (R tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X) Y)))) (let ((_let_2 (@ F Y))) (let ((_let_3 (@ F X))) (= (@ _let_1 (@ (@ tptp.mlex_prod_nat F) R)) (or (@ (@ tptp.ord_less_nat _let_3) _let_2) (and (= _let_3 _let_2) (@ _let_1 R)))))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Xa tptp.option3562590408128118217it_nat) (Y tptp.option3562590408128118217it_nat)) (let ((_let_1 (@ tptp.produc4111269673004989362it_nat X))) (let ((_let_2 (@ tptp.accp_P6263092265436569219it_nat tptp.heap_T8132184524487034138_rel_a))) (=> (= (@ (@ tptp.heap_T7616092557645711335rame_a X) Xa) Y) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((R2 tptp.a) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H4))) (let ((_let_2 (@ tptp.produc9178034014595674355it_nat R2))) (let ((_let_3 (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 N4))))) (=> (= Xa _let_3) (=> (= Y (@ tptp.some_P7913643980934408916it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4))))) (not (@ (@ tptp.accp_P6263092265436569219it_nat tptp.heap_T8132184524487034138_rel_a) (@ (@ tptp.produc4111269673004989362it_nat X) _let_3))))))))) (not (=> (= Xa tptp.none_P2651198173097904984it_nat) (=> (= Y tptp.none_P2651198173097904984it_nat) (not (@ _let_2 (@ _let_1 tptp.none_P2651198173097904984it_nat)))))))))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Xa tptp.option8956607266484857688it_nat) (Y tptp.option8956607266484857688it_nat)) (let ((_let_1 (@ tptp.produc638857205735767105it_nat X))) (let ((_let_2 (@ tptp.accp_P414730952086964626it_nat tptp.heap_T996182799752388649t_unit))) (=> (= (@ (@ tptp.heap_T3616969660504097270t_unit X) Xa) Y) (=> (@ _let_2 (@ _let_1 Xa)) (=> (forall ((R2 tptp.product_unit) (H4 tptp.heap_e7401611519738050253t_unit) (N4 tptp.nat)) (let ((_let_1 (@ tptp.produc584006145561248582it_nat H4))) (let ((_let_2 (@ tptp.produc7133225469290080770it_nat R2))) (let ((_let_3 (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 N4))))) (=> (= Xa _let_3) (=> (= Y (@ tptp.some_P1914260805536162275it_nat (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat X) N4))))) (not (@ (@ tptp.accp_P414730952086964626it_nat tptp.heap_T996182799752388649t_unit) (@ (@ tptp.produc638857205735767105it_nat X) _let_3))))))))) (not (=> (= Xa tptp.none_P9117596204409417319it_nat) (=> (= Y tptp.none_P9117596204409417319it_nat) (not (@ _let_2 (@ _let_1 tptp.none_P9117596204409417319it_nat)))))))))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_rat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_nat (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D2)) (@ (@ tptp.plus_plus_int (@ _let_2 D2)) (@ _let_1 C)))))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L))))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (A3 tptp.nat) (B tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) A3) (=> (@ (@ tptp.ord_less_nat B) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N7)) B)) (@ (@ tptp.times_times_nat A3) N7))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (N7 tptp.nat) (B2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) A2) (=> (@ (@ tptp.ord_less_nat B) N7) (=> (@ (@ tptp.ord_less_nat B2) N7) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N7)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (= A A2) (=> (@ (@ tptp.ord_less_nat B) B2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N7)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) A2) (=> (@ (@ tptp.ord_less_eq_nat B) B2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) N7)) B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A2) N7)) B2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (= tptp.times_3573771949741848930nteger (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger B5) A5))))
% 6.81/7.12 (assert (= tptp.times_times_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (@ (@ tptp.times_times_assn B5) A5))))
% 6.81/7.12 (assert (= tptp.times_times_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.times_times_rat B5) A5))))
% 6.81/7.12 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.times_times_nat B5) A5))))
% 6.81/7.12 (assert (= tptp.times_times_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.times_times_int B5) A5))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger B))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((B tptp.assn) (A tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.times_times_assn B))) (let ((_let_2 (@ tptp.times_times_assn A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (exists ((C4 tptp.nat)) (= B5 (@ (@ tptp.plus_plus_nat A5) C4))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D2))))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.81/7.12 (assert (forall ((W2 tptp.code_integer) (Y tptp.code_integer) (X tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger X))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger W2))) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 Z)) (@ _let_1 Y))) (or (= W2 X) (= Y Z)))))))
% 6.81/7.12 (assert (forall ((W2 tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W2))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W2 X) (= Y Z)))))))
% 6.81/7.12 (assert (forall ((W2 tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W2))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W2 X) (= Y Z)))))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W2))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W2 X) (= Y Z)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) E)) C))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.81/7.12 (assert (forall ((S2 tptp.list_char)) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_raise_a S2)) (lambda ((Uu2 tptp.heap_e7401611519738050253t_unit)) tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (= tptp.heap_Time_guard_a (lambda ((P4 (-> tptp.heap_e7401611519738050253t_unit Bool)) (F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc3260487557148687353it_nat))) (@ tptp.heap_Time_Heap_a2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.if_opt6883606601682554499it_nat (@ P4 H6)) (@ tptp.some_P7913643980934408916it_nat (@ F3 H6))) tptp.none_P2651198173097904984it_nat))))))
% 6.81/7.12 (assert (= tptp.heap_T8440541562793052209t_unit (lambda ((P4 (-> tptp.heap_e7401611519738050253t_unit Bool)) (F3 (-> tptp.heap_e7401611519738050253t_unit tptp.produc8664842809031399944it_nat))) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.if_opt1729522071442692626it_nat (@ P4 H6)) (@ tptp.some_P1914260805536162275it_nat (@ F3 H6))) tptp.none_P9117596204409417319it_nat))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (not (@ P X)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_assert_a P) X)) H) tptp.none_P2651198173097904984it_nat))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ (@ tptp.times_times_assn Q) (@ tptp.pure_assn B))) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H6) B)) (@ _let_1 Q))))))
% 6.81/7.12 (assert (forall ((F tptp.heap_Time_Heap_a)) (= (@ tptp.heap_Time_Heap_a2 (@ tptp.heap_Time_execute_a F)) F)))
% 6.81/7.12 (assert (forall ((F tptp.heap_T5738788834812785303t_unit)) (= (@ tptp.heap_T6183433275982383450t_unit (@ tptp.heap_T875086893843062177t_unit F)) F)))
% 6.81/7.12 (assert (forall ((P tptp.assn) (B Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ tptp.pure_assn B))) Q) (=> B (@ (@ tptp.entails P) Q)))))
% 6.81/7.12 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.entails P) tptp.bot_bot_assn) (forall ((H6 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H6))))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (let ((_let_1 (@ tptp.entails P))) (=> (@ _let_1 Q) (=> (@ (@ tptp.entails Q) R) (@ _let_1 R))))))
% 6.81/7.12 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) P)))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) B3) (=> (@ (@ tptp.entails B3) A3) (= A3 B3)))))
% 6.81/7.12 (assert (= tptp.heap_T2927564422264180874t_unit (lambda ((S6 tptp.list_char)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((Uu2 tptp.heap_e7401611519738050253t_unit)) tptp.none_P9117596204409417319it_nat)))))
% 6.81/7.12 (assert (= tptp.entails (lambda ((P4 tptp.assn) (Q3 tptp.assn)) (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P4) H6) (@ (@ tptp.rep_assn Q3) H6))))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn)) (=> (forall ((H4 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H4) (@ (@ tptp.rep_assn Q) H4))) (@ (@ tptp.entails P) Q))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.entails P) Q) (=> (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn Q) H)))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat) (Q tptp.assn)) (=> (@ (@ tptp.rep_assn P) H) (=> (@ (@ tptp.entails P) Q) (@ (@ tptp.rep_assn Q) H)))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (P6 tptp.assn) (Q tptp.assn) (Q4 tptp.assn)) (=> (@ (@ tptp.entails P) P6) (=> (@ (@ tptp.entails Q) Q4) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) Q)) (@ (@ tptp.times_times_assn P6) Q4))))))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) C3) (=> (@ (@ tptp.entails B3) C3) (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn A3) B3)) C3)))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails P) R))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.sup_sup_assn P) Q)) R) (@ (@ tptp.entails Q) R))))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 C3) (@ _let_1 (@ (@ tptp.sup_sup_assn B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (B3 tptp.assn)) (@ (@ tptp.entails A3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 6.81/7.12 (assert (forall ((B3 tptp.assn) (A3 tptp.assn)) (@ (@ tptp.entails B3) (@ (@ tptp.sup_sup_assn A3) B3))))
% 6.81/7.12 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.option3562590408128118217it_nat))) (= (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_Heap_a2 F)) F)))
% 6.81/7.12 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.option8956607266484857688it_nat))) (= (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T6183433275982383450t_unit F)) F)))
% 6.81/7.12 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails tptp.bot_bot_assn) P)))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (B3 tptp.assn) (C3 tptp.assn)) (let ((_let_1 (@ tptp.entails A3))) (=> (@ _let_1 B3) (=> (@ _let_1 C3) (@ _let_1 (@ (@ tptp.inf_inf_assn B3) C3)))))))
% 6.81/7.12 (assert (forall ((A3 tptp.assn) (C3 tptp.assn) (B3 tptp.assn)) (=> (@ (@ tptp.entails A3) C3) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A3) B3)) C3))))
% 6.81/7.12 (assert (forall ((B3 tptp.assn) (C3 tptp.assn) (A3 tptp.assn)) (=> (@ (@ tptp.entails B3) C3) (@ (@ tptp.entails (@ (@ tptp.inf_inf_assn A3) B3)) C3))))
% 6.81/7.12 (assert (forall ((Q tptp.assn) (P tptp.assn) (R tptp.assn)) (=> (@ (@ tptp.entails (@ (@ tptp.times_times_assn Q) P)) R) (@ (@ tptp.entails P) (@ (@ tptp.wand_assn Q) R)))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (Q tptp.assn)) (@ (@ tptp.entails (@ (@ tptp.times_times_assn P) (@ (@ tptp.wand_assn P) Q))) Q)))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.product_unit Bool)) (X tptp.product_unit) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ P X) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ (@ tptp.heap_T4208721593536448476t_unit P) X)) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat X) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.a Bool)) (X tptp.a) (H tptp.heap_e7401611519738050253t_unit)) (=> (@ P X) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_assert_a P) X)) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat X) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (= (@ tptp.heap_T4436805183663264329t_unit tptp.bot_bo8105976889876132193t_unit) (@ tptp.heap_T6183433275982383450t_unit (lambda ((X4 tptp.heap_e7401611519738050253t_unit)) tptp.none_P9117596204409417319it_nat))))
% 6.81/7.12 (assert (forall ((P tptp.assn) (B Bool)) (let ((_let_1 (@ tptp.entails P))) (= (@ _let_1 (@ tptp.pure_assn B)) (and (forall ((H6 tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H6) B)) (@ _let_1 tptp.one_one_assn))))))
% 6.81/7.12 (assert (forall ((X (-> tptp.int tptp.option6357759511663192854e_term)) (Xa tptp.product_prod_int_int) (Y tptp.produc6576344331059438605e_term)) (=> (= (@ (@ tptp.pairse3534876335208825186e_term X) Xa) Y) (=> (@ (@ tptp.accp_P8928870874622223812nt_int tptp.pairse6848479906795794847e_term) (@ (@ tptp.produc4305682042979456191nt_int X) Xa)) (not (forall ((A4 tptp.int) (B4 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int A4) B4))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.produc5950683997804057413e_term (@ X A4)) (@ X B4))) (not (@ (@ tptp.accp_P8928870874622223812nt_int tptp.pairse6848479906795794847e_term) (@ (@ tptp.produc4305682042979456191nt_int X) _let_1))))))))))))
% 6.81/7.12 (assert (forall ((H tptp.heap_e7401611519738050253t_unit) (As tptp.set_nat)) (= (@ tptp.one_assn_raw (@ (@ tptp.produc7507926704131184380et_nat H) As)) (= As tptp.bot_bot_set_nat))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (= Y (not (= As4 tptp.bot_bot_set_nat)))))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (not (= As4 tptp.bot_bot_set_nat))))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (=> (= X (@ (@ tptp.produc7507926704131184380et_nat H4) As4)) (= As4 tptp.bot_bot_set_nat)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.81/7.12 (assert (= tptp.combin5819755802923621690it_nat (lambda ((F3 (-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)) (X4 tptp.option3562590408128118217it_nat) (Y4 tptp.option3562590408128118217it_nat)) (@ (@ (@ tptp.case_o6061097939050036047it_nat Y4) (lambda ((Z6 tptp.produc3260487557148687353it_nat)) (@ (@ (@ tptp.case_o6061097939050036047it_nat (@ tptp.some_P7913643980934408916it_nat Z6)) (lambda ((Aa tptp.produc3260487557148687353it_nat)) (@ tptp.some_P7913643980934408916it_nat (@ (@ F3 Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.combin4318129983670048329it_nat (lambda ((F3 (-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)) (X4 tptp.option8956607266484857688it_nat) (Y4 tptp.option8956607266484857688it_nat)) (@ (@ (@ tptp.case_o2963978774867076333it_nat Y4) (lambda ((Z6 tptp.produc8664842809031399944it_nat)) (@ (@ (@ tptp.case_o2963978774867076333it_nat (@ tptp.some_P1914260805536162275it_nat Z6)) (lambda ((Aa tptp.produc8664842809031399944it_nat)) (@ tptp.some_P1914260805536162275it_nat (@ (@ F3 Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (= tptp.combine_options_num (lambda ((F3 (-> tptp.num tptp.num tptp.num)) (X4 tptp.option_num) (Y4 tptp.option_num)) (@ (@ (@ tptp.case_o6005452278849405969um_num Y4) (lambda ((Z6 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num Z6)) (lambda ((Aa tptp.num)) (@ tptp.some_num (@ (@ F3 Z6) Aa)))) Y4))) X4))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= A B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 6.81/7.12 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat tptp.produc3260487557148687353it_nat)) (A tptp.produc3260487557148687353it_nat) (B tptp.produc3260487557148687353it_nat)) (= (@ (@ (@ tptp.combin5819755802923621690it_nat F) (@ tptp.some_P7913643980934408916it_nat A)) (@ tptp.some_P7913643980934408916it_nat B)) (@ tptp.some_P7913643980934408916it_nat (@ (@ F A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.combine_options_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat tptp.produc8664842809031399944it_nat)) (A tptp.produc8664842809031399944it_nat) (B tptp.produc8664842809031399944it_nat)) (= (@ (@ (@ tptp.combin4318129983670048329it_nat F) (@ tptp.some_P1914260805536162275it_nat A)) (@ tptp.some_P1914260805536162275it_nat B)) (@ tptp.some_P1914260805536162275it_nat (@ (@ F A) B)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (X tptp.option_num)) (= (@ (@ (@ tptp.combine_options_num F) X) tptp.none_num) X)))
% 6.81/7.12 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (Y tptp.option_num)) (= (@ (@ (@ tptp.combine_options_num F) tptp.none_num) Y) Y)))
% 6.81/7.12 (assert (= (@ tptp.pure_assn true) tptp.one_one_assn))
% 6.81/7.12 (assert (forall ((P Bool)) (= (= (@ tptp.pure_assn P) tptp.one_one_assn) P)))
% 6.81/7.12 (assert (not (= tptp.bot_bot_assn tptp.one_one_assn)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (@ _let_1 A)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) A)) (@ _let_1 A)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger C) B)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger C) A) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (= C (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (= B tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) C) (or (= C tptp.zero_z3403309356797280102nteger) (= A tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((B Bool) (Q tptp.assn)) (= (@ (@ tptp.entails (@ tptp.pure_assn B)) Q) (=> B (@ (@ tptp.entails tptp.one_one_assn) Q)))))
% 6.81/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.81/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.81/7.12 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.81/7.12 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.81/7.12 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) X) (not (= X tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (= tptp.one_one_assn (@ tptp.abs_assn tptp.one_assn_raw)))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.one_one_Code_integer) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) A)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.81/7.12 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) tptp.one_one_Code_integer) A)))
% 6.81/7.12 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.times_times_assn A) tptp.one_one_assn) A)))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.81/7.12 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger)) (and (not (= A tptp.zero_z3403309356797280102nteger)) (not (= B tptp.zero_z3403309356797280102nteger))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger) (or (= A tptp.zero_z3403309356797280102nteger) (= B tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (not (= (@ (@ tptp.times_3573771949741848930nteger A) B) tptp.zero_z3403309356797280102nteger))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (= A B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (not (@ P N5)) (exists ((M4 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N5) (not (@ P M4))))))) (@ P N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((P tptp.assn)) (= (@ (@ tptp.times_times_assn tptp.one_one_assn) P) P)))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.one_one_Code_integer))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger C) B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.one_one_Code_integer))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) C) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V 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 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A)))))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.81/7.12 (assert (= (lambda ((X4 tptp.code_integer)) X4) (@ tptp.times_3573771949741848930nteger tptp.one_one_Code_integer)))
% 6.81/7.12 (assert (= (lambda ((X4 tptp.assn)) X4) (@ tptp.times_times_assn tptp.one_one_assn)))
% 6.81/7.12 (assert (= (lambda ((X4 tptp.rat)) X4) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.81/7.12 (assert (= (lambda ((X4 tptp.nat)) X4) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.81/7.12 (assert (= (lambda ((X4 tptp.int)) X4) (@ tptp.times_times_int tptp.one_one_int)))
% 6.81/7.12 (assert (= (lambda ((H6 tptp.code_integer)) tptp.zero_z3403309356797280102nteger) (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (= (lambda ((H6 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.81/7.12 (assert (= (lambda ((H6 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.81/7.12 (assert (= (lambda ((H6 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (Y tptp.code_integer) (U tptp.code_integer) (V 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 V) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger U) V) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger U) X)) (@ (@ tptp.times_3573771949741848930nteger V) Y))) A)))))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer))))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.81/7.12 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.81/7.12 (assert (forall ((M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger M) N2)))))))
% 6.81/7.12 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M) N2)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.81/7.12 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) tptp.zero_z3403309356797280102nteger) (= (= (@ (@ tptp.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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.plus_p5714425477246183910nteger X) Y) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger A) C)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.81/7.12 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) tptp.zero_z3403309356797280102nteger) (or (@ (@ tptp.ord_le6747313008572928689nteger X) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger Y) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (and (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.zero_z3403309356797280102nteger) (or (and (@ _let_1 A) (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger)) (and (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ _let_1 B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.times_3573771949741848930nteger A) B))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((R3 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger R3))) (=> (not (= R3 tptp.zero_z3403309356797280102nteger)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ _let_1 C)) (@ (@ tptp.plus_p5714425477246183910nteger B) (@ _let_1 D2)))))))))
% 6.81/7.12 (assert (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R3))) (=> (not (= R3 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D2)))))))))
% 6.81/7.12 (assert (forall ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R3))) (=> (not (= R3 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D2)))))))))
% 6.81/7.12 (assert (forall ((R3 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R3))) (=> (not (= R3 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D2))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D2)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.81/7.12 (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))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) C) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) D2) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D2) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D2) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D2) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) C) (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.one_one_assn) (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z2) (=> (@ (@ tptp.ord_less_rat Z2) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z2) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger Z))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.81/7.12 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.81/7.12 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le3102999989581377725nteger X) Y)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.81/7.12 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.81/7.12 (assert (forall ((X7 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X7))))
% 6.81/7.12 (assert (forall ((X7 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X7) X_1))))
% 6.81/7.12 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Z) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger X) Z)) (@ (@ tptp.times_3573771949741848930nteger Y) Z)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.81/7.12 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((Q6 tptp.code_integer) (R3 tptp.code_integer)) (= (@ tptp.unique5706413561485394159nteger (@ (@ tptp.produc1086072967326762835nteger Q6) R3)) (= R3 tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((Q6 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q6) R3)) (= R3 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((Q6 tptp.int) (R3 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q6) R3)) (= R3 tptp.zero_zero_int))))
% 6.81/7.12 (assert (= tptp.heap_Time_tap_a (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.a))) (@ tptp.heap_Time_Heap_a2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat (@ F3 H6)) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat))))))))
% 6.81/7.12 (assert (= tptp.heap_T560649228465745139t_unit (lambda ((F3 (-> tptp.heap_e7401611519738050253t_unit tptp.product_unit))) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat (@ F3 H6)) (@ (@ tptp.produc584006145561248582it_nat H6) tptp.one_one_nat))))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.product_unit)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_T875086893843062177t_unit (@ tptp.heap_T560649228465745139t_unit F)) H) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat (@ F H)) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.heap_e7401611519738050253t_unit tptp.a)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_a (@ tptp.heap_Time_tap_a F)) H) (@ tptp.some_P7913643980934408916it_nat (@ (@ tptp.produc9178034014595674355it_nat (@ F H)) (@ (@ tptp.produc584006145561248582it_nat H) tptp.one_one_nat))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (not (@ tptp.one_assn_raw X)) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (= As4 tptp.bot_bot_set_nat))))))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat)) (=> (@ tptp.one_assn_raw X) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1) (not (= As4 tptp.bot_bot_set_nat)))))))))))
% 6.81/7.12 (assert (forall ((X tptp.produc3658429121746597890et_nat) (Y Bool)) (=> (= (@ tptp.one_assn_raw X) Y) (=> (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) X) (not (forall ((H4 tptp.heap_e7401611519738050253t_unit) (As4 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.produc7507926704131184380et_nat H4) As4))) (=> (= X _let_1) (=> (= Y (= As4 tptp.bot_bot_set_nat)) (not (@ (@ tptp.accp_P5801069581201407417et_nat tptp.one_assn_raw_rel) _let_1)))))))))))
% 6.81/7.12 (assert (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M6 tptp.nat)) (=> (@ P X) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.ord_less_eq_nat X3) M6))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X7 tptp.nat)) (=> (@ P X7) (@ (@ tptp.ord_less_eq_nat X7) M5)))))))))))
% 6.81/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.81/7.12 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (M tptp.nat) (N2 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 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.81/7.12 (assert (= tptp.set_fo2584398358068434914at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat B5) A5)) Acc) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat F3) (@ (@ tptp.plus_plus_nat A5) tptp.one_one_nat)) B5) (@ (@ F3 A5) Acc))))))
% 6.81/7.12 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X Xa) Xc))))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) B)) A) B))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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_le6747313008572928689nteger (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) N2) tptp.zero_z3403309356797280102nteger) (and (= A tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (M tptp.nat) (N2 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 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger X) N2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger Y))) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ _let_2 _let_1)))))))
% 6.81/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn X) N2))) (let ((_let_2 (@ tptp.times_times_assn Y))) (=> (= (@ (@ tptp.times_times_assn X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_assn _let_1) Y) (@ _let_2 _let_1)))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N2))) (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)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N2))) (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)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N2))) (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (B tptp.assn) (N2 tptp.nat)) (= (@ (@ tptp.power_power_assn (@ (@ tptp.times_times_assn A) B)) N2) (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn A) N2)) (@ (@ tptp.power_power_assn B) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) A) (@ (@ tptp.times_3573771949741848930nteger A) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_assn A) N2))) (= (@ (@ tptp.times_times_assn _let_1) A) (@ (@ tptp.times_times_assn A) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W2)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W2 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) W2)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_3573771949741848930nteger X) Y) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)) tptp.one_one_Code_integer))))
% 6.81/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_assn X) Y) tptp.one_one_assn) (= (@ (@ tptp.times_times_assn (@ (@ tptp.power_power_assn X) N2)) (@ (@ tptp.power_power_assn Y) N2)) tptp.one_one_assn))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W2) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W2) Y)))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_assn (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 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) N2)) tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (X tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W2) (=> (@ (@ tptp.ord_less_eq_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2))))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (W2 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W2) (=> (@ (@ tptp.ord_less_rat W2) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W2)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 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) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger A) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N7)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_8256067586552552935nteger tptp.zero_z3403309356797280102nteger) N2) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 6.81/7.12 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat X) (@ (@ tptp.produc487386426758144856at_nat Xa) (@ (@ tptp.product_Pair_nat_nat Xb) Xc)))))) (let ((_let_2 (@ tptp.set_fo2584398358068434914at_nat X))) (let ((_let_3 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_2 Xa) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y Xc)) (=> (not _let_3) (= Y (@ (@ (@ _let_2 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X Xa) Xc))))) (not _let_1))))))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat) (Acc2 tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat F))) (let ((_let_2 (@ (@ (@ _let_1 A) B) Acc2))) (let ((_let_3 (@ (@ tptp.ord_less_nat B) A))) (=> (@ (@ tptp.accp_P6019419558468335806at_nat tptp.set_fo3699595496184130361el_nat) (@ (@ tptp.produc3209952032786966637at_nat F) (@ (@ tptp.produc487386426758144856at_nat A) (@ (@ tptp.product_Pair_nat_nat B) Acc2)))) (and (=> _let_3 (= _let_2 Acc2)) (=> (not _let_3) (= _let_2 (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) B) (@ (@ F A) Acc2)))))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (=> (@ (@ 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))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.12 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ 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 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ 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 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (N7 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N7) (=> (@ (@ 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 N7)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_8256067586552552935nteger A) N2) (@ (@ tptp.power_8256067586552552935nteger B) N2)) (= A B))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (= A B))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A) N2) (@ (@ tptp.power_8256067586552552935nteger B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C) B))) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C))) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C) B)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C)) A)) B) (@ (@ tptp.plus_p4538020629002901425atural C) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide5121882707175180666atural A) B))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural A) B)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))))
% 6.81/7.12 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (let ((_let_2 (@ (@ tptp.divide5121882707175180666atural (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z2226904508553997617atural))) (and (=> _let_3 (= _let_2 tptp.zero_z2226904508553997617atural)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide5121882707175180666atural A) B)))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))))
% 6.81/7.12 (assert (forall ((Q6 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q6)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q6))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))))
% 6.81/7.12 (assert (forall ((Q6 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q6) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q6)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q6)) N2)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I4)) J3)) (@ P I4))))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))))
% 6.81/7.12 (assert (forall ((A3 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A3) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N2))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N2)) (or (@ _let_1 X) (= N2 tptp.zero_zero_nat))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger X)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_nat_nat (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.nO_MATCH_int_nat (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger (@ (@ tptp.divide6298287555418463151nteger X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MAT7795273704451493282er_rat (@ (@ tptp.divide6298287555418463151nteger X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.nO_MATCH_nat_nat (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.nO_MATCH_int_nat (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger (@ (@ tptp.divide6298287555418463151nteger X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MAT7795273704451493282er_rat (@ (@ tptp.divide6298287555418463151nteger X) Y)) A) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q7 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q7)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q7))) (@ P Q7))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (= tptp.power_8256067586552552935nteger (lambda ((P7 tptp.code_integer) (M3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger P7) (@ (@ tptp.power_8256067586552552935nteger P7) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (= tptp.power_power_assn (lambda ((P7 tptp.assn) (M3 tptp.nat)) (@ (@ (@ tptp.if_assn (= M3 tptp.zero_zero_nat)) tptp.one_one_assn) (@ (@ tptp.times_times_assn P7) (@ (@ tptp.power_power_assn P7) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (= tptp.power_power_rat (lambda ((P7 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P7) (@ (@ tptp.power_power_rat P7) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (= tptp.power_power_nat (lambda ((P7 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P7) (@ (@ tptp.power_power_nat P7) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (= tptp.power_power_int (lambda ((P7 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P7) (@ (@ tptp.power_power_int P7) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (let ((_let_2 (@ (@ tptp.divide5121882707175180666atural (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.81/7.12 (assert (forall ((W2 tptp.num) (B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.81/7.12 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.81/7.12 (assert (forall ((X2 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X2) (@ tptp.suc Y2)) (= X2 Y2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) (@ tptp.semiri4939895301339042750nteger N2)) (= M N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.12 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W2)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W2))) Z))))
% 6.81/7.12 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2))) Z))))
% 6.81/7.12 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2))) Z))))
% 6.81/7.12 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2))) Z))))
% 6.81/7.12 (assert (forall ((V tptp.num) (W2 tptp.num) (Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural V)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural W2)) Z)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ (@ tptp.times_times_num V) W2))) Z))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural M)) (@ tptp.numera5444537566228673987atural N2)) (@ tptp.numera5444537566228673987atural (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.num) (N2 tptp.num) (B tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (M tptp.num) (N2 tptp.num) (B tptp.assn)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.ord_le6747313008572928689nteger B) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural V)))) (= (@ _let_1 (@ (@ tptp.plus_p4538020629002901425atural B) C)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (V tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural V))) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural A) B)) _let_1) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural B) _let_1))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger V))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger B) _let_1))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural B) A)) B) tptp.zero_z2226904508553997617atural)))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) B) tptp.zero_z2226904508553997617atural)))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))))
% 6.81/7.12 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.81/7.12 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.81/7.12 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.81/7.12 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural C) B))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural B) C))) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.81/7.12 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural C) B)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.81/7.12 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) C)) A)) B) (@ (@ tptp.modulo8411746178871703098atural A) B))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))))
% 6.81/7.12 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.81/7.12 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.81/7.12 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.81/7.12 (assert (= (@ tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc M)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.semiri4939895301339042750nteger M)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (B tptp.nat) (W2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W2)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (W2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.semiri4939895301339042750nteger B)) W2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W2)) X))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.semiri3763490453095760265atural X)) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural I2)) N2)) (@ tptp.semiri3763490453095760265atural X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.semiri3763490453095760265atural X)) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural I2)) N2)) (@ tptp.semiri3763490453095760265atural X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger I2)) N2)) (@ tptp.semiri4939895301339042750nteger X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.81/7.12 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P3 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) P3) (=> (@ (@ tptp.ord_less_nat M) P3) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N5) P3) (=> (@ P N5) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N5)) P3))))) (@ P M)))))))
% 6.81/7.12 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N)) N)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (I2 tptp.nat)) (=> (@ P K) (=> (forall ((N5 tptp.nat)) (=> (@ P (@ tptp.suc N5)) (@ P N5))) (@ P (@ (@ tptp.minus_minus_nat K) I2))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (= (@ tptp.suc N2) M) (= N2 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri4939895301339042750nteger (@ tptp.suc N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C)) (@ (@ tptp.modulo8411746178871703098atural B) C))) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (A2 tptp.nat) (B tptp.nat) (B2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A2) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B2) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A2) B2)) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (A2 tptp.int) (B tptp.int) (B2 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A2) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B2) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A2) B2)) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A2 tptp.code_integer) (B tptp.code_integer) (B2 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A2) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B2) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A2) B2)) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (A2 tptp.code_natural) (B tptp.code_natural) (B2 tptp.code_natural)) (=> (= (@ (@ tptp.modulo8411746178871703098atural A) C) (@ (@ tptp.modulo8411746178871703098atural A2) C)) (=> (= (@ (@ tptp.modulo8411746178871703098atural B) C) (@ (@ tptp.modulo8411746178871703098atural B2) C)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A2) B2)) C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) B)) C))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural C))) (= (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural A) B)) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) C)) B)) C) (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C))) C) (@ (@ tptp.modulo8411746178871703098atural (@ _let_1 B)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D2) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D2) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D2)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (D2 tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D2) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D2) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D2)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D2)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D2)))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) C)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.81/7.12 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.code_integer Bool)) (D3 tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D3))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D3))))) (forall ((X7 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K4) D3)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X7 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K4) D3)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X7 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K4) D3)))) (= (and (@ P X7) (@ Q X7)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.code_integer Bool)) (D3 tptp.code_integer) (Q (-> tptp.code_integer Bool))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ P X3) (@ P (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D3))))) (=> (forall ((X3 tptp.code_integer) (K2 tptp.code_integer)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_8373710615458151222nteger X3) (@ (@ tptp.times_3573771949741848930nteger K2) D3))))) (forall ((X7 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K4) D3)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.rat Bool)) (D3 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_rat X3) (@ (@ tptp.times_times_rat K2) D3))))) (forall ((X7 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K4) D3)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (D3 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ Q X3) (@ Q (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (forall ((X7 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K4) D3)))) (= (or (@ P X7) (@ Q X7)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.81/7.12 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N5 tptp.nat)) (=> (@ P (@ tptp.suc N5)) (@ P N5))) (@ P tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (@ (@ P X3) tptp.zero_zero_nat)) (=> (forall ((Y3 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (@ (@ P X3) Y3) (@ (@ P (@ tptp.suc X3)) (@ tptp.suc Y3)))) (@ (@ P M) N2))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (@ P (@ tptp.suc N5)))) (@ P N2)))))
% 6.81/7.12 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.81/7.12 (assert (forall ((Nat tptp.nat) (X2 tptp.nat)) (=> (= Nat (@ tptp.suc X2)) (not (= Nat tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.81/7.12 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((X2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N2)) (@ P I4))) (or (@ P N2) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N2) (@ P I4)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N2)) (@ P I4))) (and (@ P N2) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ P I4)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M7 tptp.nat)) (and (= M (@ tptp.suc M7)) (@ (@ tptp.ord_less_nat N2) M7))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (@ (@ P I3) (@ tptp.suc I3))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I3))) (=> (@ (@ tptp.ord_less_nat I3) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I3 tptp.nat)) (=> (= J (@ tptp.suc I3)) (@ P I3))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) J) (=> (@ P (@ tptp.suc I3)) (@ P I3)))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N2) L)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.81/7.12 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M8) (exists ((M5 tptp.nat)) (= M8 (@ tptp.suc M5))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M4)) N5) (@ P M4))) (@ P N5))) (@ P N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N5) (=> (@ P N5) (@ P (@ tptp.suc N5))))) (@ P N2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (forall ((X3 tptp.nat)) (@ (@ R X3) X3)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((N5 tptp.nat)) (@ (@ R N5) (@ tptp.suc N5))) (@ (@ R M) N2)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.81/7.12 (assert (forall ((A3 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A3 (@ _let_1 A)) (= (@ tptp.suc A3) (@ _let_1 (@ tptp.suc A)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger (@ (@ tptp.divide6298287555418463151nteger X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.nO_MAT7795273704451493282er_rat (@ (@ tptp.divide6298287555418463151nteger X) Y)) C) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.nO_MAT8427913294028938742er_int (@ (@ tptp.divide6298287555418463151nteger X) Y)) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.nO_MAT243659986023775650nteger (@ (@ tptp.divide_divide_rat X) Y)) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8694959213317031834nteger (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_nat_rat (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (Y tptp.nat) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_nat_int (@ (@ tptp.divide_divide_nat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT9066612773553876470nteger (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MATCH_int_rat (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MATCH_int_int (@ (@ tptp.divide_divide_int X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger (@ (@ tptp.divide6298287555418463151nteger X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (=> (@ (@ tptp.nO_MAT7795273704451493282er_rat (@ (@ tptp.divide6298287555418463151nteger X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.nO_MAT8427913294028938742er_int (@ (@ tptp.divide6298287555418463151nteger X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.nO_MAT243659986023775650nteger (@ (@ tptp.divide_divide_rat X) Y)) A) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C)) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 B)) (@ _let_1 C)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural M))) (let ((_let_2 (@ tptp.modulo8411746178871703098atural A))) (let ((_let_3 (@ tptp.semiri3763490453095760265atural N2))) (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)))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (=> (@ (@ tptp.ord_less_eq_nat K) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat K) (@ tptp.suc tptp.zero_zero_nat))) M)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.81/7.12 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) M) (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.81/7.12 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N)) N))))))
% 6.81/7.12 (assert (= tptp.ord_less_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri4939895301339042750nteger N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D)))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D)))))))))
% 6.81/7.12 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B5)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A5) B5)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A5) B5)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.81/7.12 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((A5 tptp.code_integer) (B5 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A5) B5)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (= tptp.ord_less_rat (lambda ((A5 tptp.rat) (B5 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A5) B5)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (= tptp.ord_less_int (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A5) B5)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N2) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri4939895301339042750nteger I2)) (@ tptp.semiri4939895301339042750nteger J)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o X) Y) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X) Y))))
% 6.81/7.12 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.minus_minus_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) Y))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (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))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (let ((_let_2 (@ tptp.semiri3763490453095760265atural M))) (let ((_let_3 (@ tptp.divide5121882707175180666atural A))) (= (@ _let_3 (@ (@ tptp.times_2397367101498566445atural _let_2) _let_1)) (@ (@ tptp.divide5121882707175180666atural (@ _let_3 _let_2)) _let_1)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C) D2))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D2))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (= C (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) (@ (@ tptp.times_3573771949741848930nteger Y) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) (@ (@ tptp.minus_8373710615458151222nteger X) Y)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le1926595141338095240atural tptp.zero_z2226904508553997617atural) (@ tptp.numera5444537566228673987atural N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) (@ tptp.numera5444537566228673987atural N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural N2)) tptp.zero_z2226904508553997617atural))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le1926595141338095240atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 6.81/7.12 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.assn)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N2) N6) (@ (@ tptp.ord_less_assn (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N2) N6) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N2) N6) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N2) N6) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_nat N2) N6) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.assn)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_assn (@ F N5)) (@ F (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_assn (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N5)) (@ F (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_rat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N5)) (@ F (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N5)) (@ F (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N5)) (@ F (@ tptp.suc N5)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F (@ tptp.suc N5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N6))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N5))) (@ F N5))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_set_int (@ F N6)) (@ F N2))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N5))) (@ F N5))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_rat (@ F N6)) (@ F N2))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N5))) (@ F N5))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_num (@ F N6)) (@ F N2))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N5))) (@ F N5))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_nat (@ F N6)) (@ F N2))))))
% 6.81/7.12 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N6 tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N5))) (@ F N5))) (=> (@ (@ tptp.ord_less_eq_nat N2) N6) (@ (@ tptp.ord_less_eq_int (@ F N6)) (@ F N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_assn (@ _let_1 N2)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_assn A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_assn A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N2)) (@ P I4))) (or (@ P tptp.zero_zero_nat) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_nat I4) N2) (@ P (@ tptp.suc I4))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M3 tptp.nat)) (= N2 (@ tptp.suc M3))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.suc N2)) (@ P I4))) (and (@ P tptp.zero_zero_nat) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ P (@ tptp.suc I4))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N2)))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (forall ((Nn tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Nn) N5) (@ P Nn))) (@ P (@ tptp.suc N5)))) (@ P N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P N5) (@ P (@ tptp.suc N5)))))) (@ P J))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N5) (=> (@ (@ tptp.ord_less_nat N5) J) (=> (@ P (@ tptp.suc N5)) (@ P N5))))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (and (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat B) (@ tptp.suc A))) (= B A))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (= (and (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat B) _let_1)) (= B _let_1)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q5 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q5)))))))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.81/7.12 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K3)))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.81/7.12 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.81/7.12 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))))
% 6.81/7.12 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 6.81/7.12 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.81/7.12 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.81/7.12 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.81/7.12 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural A) B))) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) B)) (@ (@ tptp.modulo8411746178871703098atural A) B))) C) (@ (@ tptp.plus_p4538020629002901425atural A) C))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (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)))
% 6.81/7.12 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.81/7.12 (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)))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C))) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 (@ (@ tptp.modulo8411746178871703098atural B) C))) C))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le3102999989581377725nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (E tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger A) E)) C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) E)) D2)) (@ (@ tptp.ord_le6747313008572928689nteger C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D2)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D2)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D2)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_8256067586552552935nteger A) _let_2) (@ (@ tptp.power_8256067586552552935nteger B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) (@ (@ tptp.power_8256067586552552935nteger B) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.81/7.12 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (Q6 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q6) (@ (@ tptp.modulo_modulo_nat N2) Q6)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S7 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q6) S7))))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (Q6 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q6) (@ (@ tptp.modulo_modulo_nat N2) Q6)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S7 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q6) S7))))))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q5 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q5))))))))
% 6.81/7.12 (assert (forall ((A3 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A3) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A3) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A3) N2)) (@ (@ tptp.divide_divide_nat B3) N2))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N2)))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D5 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D5)) (@ P D5)))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D5 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D5)) (not (@ P D5)))))))))
% 6.81/7.12 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ P tptp.one_one_nat) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ P N5) (@ P (@ tptp.suc N5))))) (@ P N2))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.81/7.12 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W2 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W2) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W2) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I4 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I4)) J3)) (@ P J3))))))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.81/7.12 (assert (forall ((W2 tptp.num) (B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 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 N2))) A)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N2))) A)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) A)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) A)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 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 N2))) tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N2))) tptp.one_one_rat)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) tptp.one_one_int)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((A tptp.code_natural) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural A))) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.81/7.12 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.81/7.12 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.81/7.12 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N))))))
% 6.81/7.12 (assert (forall ((N2 tptp.nat) (Q6 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q6)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q6))) (= (@ (@ tptp.divide_divide_nat M) N2) Q6))))))
% 6.81/7.12 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((U tptp.rat) (V tptp.rat) (R3 tptp.rat) (S2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (=> (@ (@ tptp.ord_less_eq_rat R3) S2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R3) (@ (@ tptp.minus_minus_rat V) U))) S2))) V))))))
% 6.81/7.12 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W2))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.81/7.12 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N5 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N5)))) E)))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N5)) X))))))
% 6.81/7.12 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I4 tptp.rat)) (@ (@ tptp.plus_plus_rat I4) tptp.one_one_rat))) N) tptp.zero_zero_rat))))
% 6.81/7.12 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I4 tptp.int)) (@ (@ tptp.plus_plus_int I4) tptp.one_one_int))) N) tptp.zero_zero_int))))
% 6.81/7.12 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) N) tptp.zero_zero_nat))))
% 6.81/7.12 (assert (= tptp.semiri4939895301339042750nteger (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri4055485073559036834nteger (lambda ((I4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger I4) tptp.one_one_Code_integer))) N) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.12 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (=> (@ (@ P N5) (@ (@ tptp.modulo_modulo_nat M5) N5)) (@ (@ P M5) N5)))) (@ (@ P M) N2)))))
% 6.81/7.12 (assert (forall ((X (-> tptp.produc3260487557148687353it_nat tptp.nat)) (X2 tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.size_o1731029420616209814it_nat X) (@ tptp.some_P7913643980934408916it_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((X (-> tptp.produc8664842809031399944it_nat tptp.nat)) (X2 tptp.produc8664842809031399944it_nat)) (= (@ (@ tptp.size_o29782932136985253it_nat X) (@ tptp.some_P1914260805536162275it_nat X2)) (@ (@ tptp.plus_plus_nat (@ X X2)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.81/7.12 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N tptp.nat)) (@ (@ (@ tptp.if_rat (= N tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((O tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.81/7.12 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.81/7.12 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= N 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 N) tptp.one_one_nat)) tptp.one_one_Code_integer)))))
% 6.81/7.12 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.81/7.12 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) A3) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A3) A3) tptp.bot_bot_set_o)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) A3) tptp.bot_bot_set_int)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) A3) tptp.bot_bot_set_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat tptp.bot_bo2099793752762293965at_nat) A3) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o tptp.bot_bot_set_o) A3) tptp.bot_bot_set_o)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A3) tptp.bot_bot_set_int)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A3) tptp.bot_bot_set_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) tptp.bot_bo2099793752762293965at_nat) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.minus_minus_set_o A3) tptp.bot_bot_set_o) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A3) tptp.bot_bot_set_int) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) tptp.bot_bot_set_nat) A3)))
% 6.81/7.12 (assert (forall ((B3 tptp.set_Pr8693737435421807431at_nat) (A3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat B3) A3)) A3) (@ (@ tptp.sup_su718114333110466843at_nat B3) A3))))
% 6.81/7.12 (assert (forall ((B3 tptp.set_Pr8551490117392284871at_nat) (A3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat B3) A3)) A3) (@ (@ tptp.sup_su3035147773818789531at_nat B3) A3))))
% 6.81/7.12 (assert (forall ((B3 tptp.set_Pr4329608150637261639at_nat) (A3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat B3) A3)) A3) (@ (@ tptp.sup_su5525570899277871387at_nat B3) A3))))
% 6.81/7.12 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat B3) A3)) A3) (@ (@ tptp.sup_sup_set_nat B3) A3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.sup_su718114333110466843at_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_8321449233255521966at_nat B3) A3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.sup_su3035147773818789531at_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_5060654252129873198at_nat B3) A3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.sup_su5525570899277871387at_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_3314409938677909166at_nat B3) A3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.sup_sup_set_nat A3))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A3) B3) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A3) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ (@ tptp.minus_1356011639430497352at_nat B3) A3)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) (@ (@ tptp.minus_minus_set_o B3) A3)) tptp.bot_bot_set_o)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ (@ tptp.minus_minus_set_int B3) A3)) tptp.bot_bot_set_int)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ (@ tptp.minus_minus_set_nat B3) A3)) tptp.bot_bot_set_nat)))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A3) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N2))))))
% 6.81/7.12 (assert (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A3) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A3) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A3) N2)) (@ (@ tptp.divide_divide_int B3) N2))))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) K)) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ (@ P I4) J3)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))))
% 6.81/7.12 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I2) K) I2) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.81/7.12 (assert (forall ((D2 tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X3) (= (@ P X3) (@ P6 X3))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.81/7.12 (assert (forall ((D2 tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P1 X3) (@ P1 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (=> (exists ((Z5 tptp.int)) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_int X3) Z5) (= (@ P X3) (@ P1 X3))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.81/7.12 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P N2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P J3))))))))
% 6.81/7.12 (assert (forall ((B2 tptp.int) (Q8 tptp.int) (R7 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) Q8)) R7)) (=> (@ (@ tptp.ord_less_int R7) B2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (@ _let_1 Q8)))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (Q6 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q8 tptp.int) (R7 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) Q8)) R7))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R3) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R7) 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 Q6) Q8)))))))))))
% 6.81/7.12 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D2)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X7 tptp.int)) (=> (@ P X7) (@ P (@ (@ tptp.plus_plus_int X7) (@ (@ tptp.times_times_int K) D2))))))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (Q6 tptp.int) (R3 tptp.int) (B2 tptp.int) (Q8 tptp.int) (R7 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B2) Q8)) R7))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) 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) R7) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B2) (=> (@ (@ tptp.ord_less_eq_int B2) B) (@ (@ tptp.ord_less_eq_int Q8) Q6))))))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (Q8 tptp.int) (R7 tptp.int) (Q6 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q8)) R7)) (@ (@ tptp.plus_plus_int (@ _let_1 Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R7) (=> (@ (@ tptp.ord_less_int R7) B) (=> (@ (@ tptp.ord_less_int R3) B) (@ (@ tptp.ord_less_eq_int Q8) Q6))))))))
% 6.81/7.12 (assert (forall ((B tptp.int) (Q8 tptp.int) (R7 tptp.int) (Q6 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 Q8)) R7)) (@ (@ tptp.plus_plus_int (@ _let_2 Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ _let_1 R3) (=> (@ _let_1 R7) (@ (@ tptp.ord_less_eq_int Q6) Q8)))))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (X10 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X10))) (=> (= X X10) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X) P) (=> _let_2 P6))))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (X10 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X10))) (=> (= X X10) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X) P) (and _let_2 P6))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I4 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I4)) J3))) (@ P I4))))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.divide_divide_int A) B) Q6))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q6)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.divide_divide_int A) B) Q6))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.81/7.12 (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)))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((K tptp.int) (I2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I2) K)) (@ (@ tptp.ord_less_eq_int K) I2))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I2) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I2) (@ (@ tptp.ord_less_int I2) K)) (and (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I2))))))
% 6.81/7.12 (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))))))))
% 6.81/7.12 (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))))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.81/7.12 (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)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (D3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat D3) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat C3) D3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (C3 tptp.set_int) (D3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) C3) (=> (@ (@ tptp.ord_less_eq_set_int D3) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B3)) (@ (@ tptp.minus_minus_set_int C3) D3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C3) A3)) A3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C3) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C3) A3)) A3)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) C3) (@ (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C3)) (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) C3) (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C3)) (@ (@ tptp.inf_inf_set_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((C3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat C3))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat C3))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ _let_1 B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ _let_1 B3)) (@ (@ tptp.inf_inf_set_nat A3) B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) C3)))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (C3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat (@ (@ tptp.inf_inf_set_nat A3) C3)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C3)) (@ _let_1 B3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat A3))) (= (@ (@ tptp.minus_1356011639430497352at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.minus_8321449233255521966at_nat A3))) (= (@ (@ tptp.minus_8321449233255521966at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A3))) (= (@ (@ tptp.minus_5060654252129873198at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A3))) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.minus_8321449233255521966at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) C3) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) C3)) (@ (@ tptp.minus_8321449233255521966at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.minus_5060654252129873198at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) C3) (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat A3) C3)) (@ (@ tptp.minus_5060654252129873198at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.minus_3314409938677909166at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) C3) (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) C3)) (@ (@ tptp.minus_3314409938677909166at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) C3) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A3) C3)) (@ (@ tptp.minus_minus_set_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A3) B3) (exists ((B4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B4) (@ (@ tptp.minus_1356011639430497352at_nat B3) A3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (=> (@ (@ tptp.ord_less_set_o A3) B3) (exists ((B4 Bool)) (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A3) B3) (exists ((B4 tptp.set_nat)) (@ (@ tptp.member_set_nat B4) (@ (@ tptp.minus_2163939370556025621et_nat B3) A3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A3) B3) (exists ((B4 tptp.int)) (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B3) A3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A3) B3) (exists ((B4 tptp.nat)) (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B3) A3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (= (@ (@ tptp.minus_minus_set_o A3) B3) tptp.bot_bot_set_o))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (= (@ (@ tptp.minus_minus_set_nat A3) B3) tptp.bot_bot_set_nat))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (= (@ (@ tptp.minus_minus_set_int A3) B3) tptp.bot_bot_set_int))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (not (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3)) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (not (= (@ (@ tptp.minus_minus_set_o A3) B3) A3)) (not (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (not (= (@ (@ tptp.minus_minus_set_int A3) B3) A3)) (not (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (not (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3)) (not (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.minus_minus_set_o A3) B3) A3) (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A3) B3) A3) (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3) (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.minus_minus_set_o A3) B3)) tptp.bot_bot_set_o)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.minus_minus_set_int A3) B3)) tptp.bot_bot_set_int)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat A3) B3)) tptp.bot_bot_set_nat)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) B3) A3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ (@ tptp.minus_minus_set_o A3) B3) A3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ (@ tptp.minus_minus_set_int A3) B3) A3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ (@ tptp.minus_minus_set_nat A3) B3) A3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (=> (@ (@ tptp.ord_le3000389064537975527at_nat A3) B3) (= (@ (@ tptp.sup_su718114333110466843at_nat A3) (@ (@ tptp.minus_8321449233255521966at_nat B3) A3)) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (=> (@ (@ tptp.ord_le8081472938463900775at_nat A3) B3) (= (@ (@ tptp.sup_su3035147773818789531at_nat A3) (@ (@ tptp.minus_5060654252129873198at_nat B3) A3)) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (=> (@ (@ tptp.ord_le1268244103169919719at_nat A3) B3) (= (@ (@ tptp.sup_su5525570899277871387at_nat A3) (@ (@ tptp.minus_3314409938677909166at_nat B3) A3)) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (= (@ (@ tptp.sup_sup_set_nat A3) (@ (@ tptp.minus_minus_set_nat B3) A3)) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (= (@ (@ tptp.sup_sup_set_int A3) (@ (@ tptp.minus_minus_set_int B3) A3)) B3))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B3)) C3) (@ (@ tptp.ord_le3000389064537975527at_nat A3) (@ (@ tptp.sup_su718114333110466843at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.minus_5060654252129873198at_nat A3) B3)) C3) (@ (@ tptp.ord_le8081472938463900775at_nat A3) (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B3)) C3) (@ (@ tptp.ord_le1268244103169919719at_nat A3) (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) C3) (@ (@ tptp.ord_less_eq_set_nat A3) (@ (@ tptp.sup_sup_set_nat B3) C3)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (C3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A3) B3)) C3) (@ (@ tptp.ord_less_eq_set_int A3) (@ (@ tptp.sup_sup_set_int B3) C3)))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s8582702949713902594nteger X) N2))))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X) N2))))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X) N2))))))
% 6.81/7.12 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X) N2))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B3)) (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.minus_5060654252129873198at_nat A3) B3)) (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B3)) (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.sup_su6327502436637775413at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)) (@ (@ tptp.minus_8321449233255521966at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.sup_su3035147773818789531at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)) (@ (@ tptp.minus_5060654252129873198at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.sup_su5525570899277871387at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)) (@ (@ tptp.minus_3314409938677909166at_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.minus_minus_set_nat A3) B3)) A3)))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat B3) C3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.minus_8321449233255521966at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat B3) C3)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat B3) C3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat B3) C3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_nat B3) C3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.minus_1356011639430497352at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat B3) C3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (C3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.minus_8321449233255521966at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat B3) C3)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (C3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.minus_5060654252129873198at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat B3) C3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (C3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.minus_3314409938677909166at_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat B3) C3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (C3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A3))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat B3) C3)) (@ (@ tptp.inf_inf_set_nat (@ _let_1 B3)) (@ _let_1 C3))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_rat)))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.81/7.12 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.comm_s8582702949713902594nteger X) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.rat) (N2 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) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X) N2)))))
% 6.81/7.12 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X) N2)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le7866589430770878221at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) A3) (not (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (@ (@ tptp.ord_less_set_o (@ (@ tptp.minus_minus_set_o A3) B3)) A3) (not (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A3) B3)) A3) (not (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int)))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) A3) (not (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat)))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) (@ _let_1 N2))))))
% 6.81/7.12 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))))
% 6.81/7.12 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger N2)))))))
% 6.81/7.12 (assert (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) M))))))
% 6.81/7.12 (assert (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 6.81/7.12 (assert (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 6.81/7.12 (assert (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 N2)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger N2))) M))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.comm_s8582702949713902594nteger Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger Z) (@ tptp.semiri4939895301339042750nteger M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.81/7.12 (assert (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N5)))))
% 6.81/7.12 (assert (forall ((X tptp.rat)) (exists ((N5 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N5)))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W2) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W2) Z))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W2) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 6.81/7.12 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N5 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (= K (@ tptp.semiri1314217659103216013at_int N5)))))))
% 6.81/7.12 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N5 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.81/7.12 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N5 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N5))))))))
% 6.81/7.12 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N5 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N5))))))
% 6.81/7.12 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.12 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B3) _let_1))))
% 6.81/7.12 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (and (@ _let_1 A3) (not (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B3)) (and (@ _let_1 A3) (not (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B3)) (and (@ _let_1 A3) (not (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (and (@ _let_1 A3) (not (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (and (@ _let_1 A3) (not (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)))))))
% 6.81/7.12 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A3) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)))))))
% 6.81/7.12 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ (@ tptp.minus_2270307095948843157_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6))) (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (@ (@ tptp.minus_minus_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6))) (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.minus_711738161318947805_int_o (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) A6))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ (@ tptp.minus_1139252259498527702_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A6))) (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6))) (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6))) (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) B6)))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6))) (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) B6)))))))
% 6.81/7.12 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (not (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B3)) (not (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B3)) (not (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (not (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (not (@ _let_1 B3))))))
% 6.81/7.12 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ _let_1 A3)))))
% 6.81/7.12 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B3)) (@ _let_1 A3)))))
% 6.81/7.12 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B3)) (@ _let_1 A3)))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (@ _let_1 A3)))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ _let_1 A3)))))
% 6.81/7.12 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (not (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C Bool) (A3 tptp.set_o) (B3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_o A3) B3)) (not (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A3) B3)) (not (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.int) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (not (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 6.81/7.12 (assert (forall ((C tptp.nat) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (not (=> (@ _let_1 A3) (@ _let_1 B3)))))))
% 6.81/7.12 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_o (lambda ((A6 tptp.set_o) (B6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (let ((_let_1 (@ tptp.member_o X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_7954133019191499631st_nat (lambda ((A6 tptp.set_list_nat) (B6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ tptp.member_list_nat X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int K) I2) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_int I2) K) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I2 tptp.int)) (=> (@ P K) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((K tptp.int) (I2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int K) I2) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I3) (=> (@ P I3) (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W2 Z))))))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (K tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int I2) K) (=> (@ P (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.ord_less_int I3) K) (=> (@ P I3) (@ P (@ (@ tptp.minus_minus_int I3) tptp.one_one_int))))) (@ P I2))))))
% 6.81/7.12 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.81/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.81/7.12 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.81/7.12 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.81/7.12 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W2) Z))))
% 6.81/7.12 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W2) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W2) tptp.one_one_int)) Z))))
% 6.81/7.12 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.81/7.12 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.81/7.12 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.81/7.12 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z6 tptp.int)) (exists ((N tptp.nat)) (= Z6 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K))))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int) (Q6 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q6) R3)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q6)) 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) (= Q6 tptp.zero_zero_int)))))))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K)))))
% 6.81/7.13 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K)))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K)))))
% 6.81/7.13 (assert (forall ((X tptp.assn)) (= (@ tptp.uminus_uminus_assn (@ tptp.uminus_uminus_assn X)) X)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit)) (= (@ tptp.uminus2952777764628376836t_unit (@ tptp.uminus2952777764628376836t_unit X)) X)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ tptp.uminus_uminus_assn X) (@ tptp.uminus_uminus_assn Y)) (= X Y))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ tptp.uminus2952777764628376836t_unit X) (@ tptp.uminus2952777764628376836t_unit Y)) (= X Y))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B3)) (@ tptp.uminus1532241313380277803et_int A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A3)) (@ tptp.uminus1532241313380277803et_int B3)) (@ (@ tptp.ord_less_eq_set_int B3) A3))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)) (@ (@ tptp.ord_less_eq_assn Y) X))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ tptp.uminus2952777764628376836t_unit Y)) (@ (@ tptp.ord_le3221252021190050221t_unit Y) X))))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.ord_less_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)) (@ (@ tptp.ord_less_assn Y) X))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ tptp.uminus2952777764628376836t_unit Y)) (@ (@ tptp.ord_le361264281704409273t_unit Y) X))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) A3) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o A3)) A3) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) A3) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int A3)) A3) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.uminus6524753893492686040at_nat A3)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o A3) (@ tptp.uminus_uminus_set_o A3)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) tptp.bot_bot_set_int)))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)) (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)) (@ (@ tptp.minus_minus_set_nat A3) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)) (@ (@ tptp.inf_inf_set_nat A3) B3))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.minus_8321449233255521966at_nat A3) B3)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.minus_5060654252129873198at_nat A3) B3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.minus_3314409938677909166at_nat A3) B3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) B3))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.81/7.13 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.uminus_uminus_assn P)) H) (and (@ tptp.in_range H) (not (@ (@ tptp.rep_assn P) H))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.81/7.13 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.81/7.13 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat X)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ tptp.uminus_uminus_set_o X)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat X)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ tptp.uminus1532241313380277803et_int X)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn X)) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.uminus2952777764628376836t_unit X)) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) X) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) X) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) X) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) X) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) X) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) X) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat Y) (@ tptp.uminus6524753893492686040at_nat X))) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ (@ tptp.inf_inf_set_o Y) (@ tptp.uminus_uminus_set_o X))) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat Y) (@ tptp.uminus5710092332889474511et_nat X))) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int Y) (@ tptp.uminus1532241313380277803et_int X))) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn Y) (@ tptp.uminus_uminus_assn X))) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ (@ tptp.inf_inf_Product_unit Y) (@ tptp.uminus2952777764628376836t_unit X))) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) Y)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o X) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) Y)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat X) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) Y)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int X) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) Y)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn X) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) Y)) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit X) (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) Y)) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) (@ (@ tptp.inf_inf_set_o X) Y)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ (@ tptp.inf_inf_set_nat X) Y)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.inf_inf_set_int X) Y)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) (@ (@ tptp.inf_inf_assn X) Y)) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ (@ tptp.inf_inf_Product_unit X) Y)) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat X) Y)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.sup_su718114333110466843at_nat X) Y)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ tptp.uminus4384627049435823934at_nat X)) (@ tptp.uminus4384627049435823934at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.sup_su3035147773818789531at_nat X) Y)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ tptp.uminus2330091110623919550at_nat X)) (@ tptp.uminus2330091110623919550at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.sup_su5525570899277871387at_nat X) Y)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ tptp.uminus935396558254630718at_nat X)) (@ tptp.uminus935396558254630718at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat X) Y)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ tptp.uminus_uminus_assn (@ (@ tptp.sup_sup_assn X) Y)) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ tptp.uminus2952777764628376836t_unit (@ (@ tptp.sup_sup_Product_unit X) Y)) (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat X)) (@ tptp.uminus6524753893492686040at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.inf_in4302113700860409141at_nat X) Y)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat X)) (@ tptp.uminus4384627049435823934at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.inf_in1697001100524423349at_nat X) Y)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat X)) (@ tptp.uminus2330091110623919550at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat X)) (@ tptp.uminus935396558254630718at_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat X) Y)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat X)) (@ tptp.uminus5710092332889474511et_nat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ tptp.uminus_uminus_assn (@ (@ tptp.inf_inf_assn X) Y)) (@ (@ tptp.sup_sup_assn (@ tptp.uminus_uminus_assn X)) (@ tptp.uminus_uminus_assn Y)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (@ tptp.uminus2952777764628376836t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) (@ (@ tptp.sup_sup_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W2))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W2))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W2)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W2)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((V tptp.num) (W2 tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W2)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W2)))) Y))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2)) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))))
% 6.81/7.13 (assert (forall ((X tptp.product_prod_int_int)) (not (forall ((D tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D) I3)))))))
% 6.81/7.13 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (D tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int D) I3))))))))
% 6.81/7.13 (assert (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D tptp.int) (I3 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F2) (@ (@ tptp.product_Pair_int_int D) I3))))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int) (Q8 tptp.int) (R7 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q8) R7)) (= R3 R7))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int) (Q8 tptp.int) (R7 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q6) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q8) R7)) (= Q6 Q8))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.81/7.13 (assert (= tptp.abs_abs_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I4) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I4)) I4))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn (@ tptp.uminus_uminus_assn Y)) X) (@ (@ tptp.ord_less_eq_assn (@ tptp.uminus_uminus_assn X)) Y))))
% 6.81/7.13 (assert (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.uminus2952777764628376836t_unit Y)) X) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.uminus2952777764628376836t_unit X)) Y))))
% 6.81/7.13 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X)) Y))))
% 6.81/7.13 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn Y) (@ tptp.uminus_uminus_assn X)) (@ (@ tptp.ord_less_eq_assn X) (@ tptp.uminus_uminus_assn Y)))))
% 6.81/7.13 (assert (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit Y) (@ tptp.uminus2952777764628376836t_unit X)) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 6.81/7.13 (assert (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X)) (@ (@ tptp.ord_less_eq_set_int X) (@ tptp.uminus1532241313380277803et_int Y)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (=> (@ (@ tptp.ord_less_eq_assn X) Y) (@ (@ tptp.ord_less_eq_assn (@ tptp.uminus_uminus_assn Y)) (@ tptp.uminus_uminus_assn X)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (=> (@ (@ tptp.ord_le3221252021190050221t_unit X) Y) (@ (@ tptp.ord_le3221252021190050221t_unit (@ tptp.uminus2952777764628376836t_unit Y)) (@ tptp.uminus2952777764628376836t_unit X)))))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X)))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.81/7.13 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_assn Y) (@ tptp.uminus_uminus_assn X)) (@ (@ tptp.ord_less_assn X) (@ tptp.uminus_uminus_assn Y)))))
% 6.81/7.13 (assert (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit Y) (@ tptp.uminus2952777764628376836t_unit X)) (@ (@ tptp.ord_le361264281704409273t_unit X) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 6.81/7.13 (assert (forall ((Y tptp.assn) (X tptp.assn)) (=> (@ (@ tptp.ord_less_assn (@ tptp.uminus_uminus_assn Y)) X) (@ (@ tptp.ord_less_assn (@ tptp.uminus_uminus_assn X)) Y))))
% 6.81/7.13 (assert (forall ((Y tptp.product_unit) (X tptp.product_unit)) (=> (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.uminus2952777764628376836t_unit Y)) X) (@ (@ tptp.ord_le361264281704409273t_unit (@ tptp.uminus2952777764628376836t_unit X)) Y))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (= tptp.minus_minus_assn (lambda ((A5 tptp.assn) (B5 tptp.assn)) (@ (@ tptp.inf_inf_assn A5) (@ tptp.uminus_uminus_assn B5)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su6024340866399070445nt_int (@ tptp.uminus6221592323253981072nt_int (@ tptp.collec213857154873943460nt_int P))) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_list_nat (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P))) (@ tptp.collect_list_nat Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_set_nat (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P))) (@ tptp.collect_set_nat Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P))) (@ tptp.collect_int Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.produc859450856879609959at_nat Bool)) (Q (-> tptp.produc859450856879609959at_nat Bool))) (= (@ tptp.collec7088162979684241874at_nat (lambda ((X4 tptp.produc859450856879609959at_nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat (@ tptp.collec7088162979684241874at_nat P))) (@ tptp.collec7088162979684241874at_nat Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.produc4166570645942440679at_nat Bool)) (Q (-> tptp.produc4166570645942440679at_nat Bool))) (= (@ tptp.collec5204685387357076818at_nat (lambda ((X4 tptp.produc4166570645942440679at_nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat (@ tptp.collec5204685387357076818at_nat P))) (@ tptp.collec5204685387357076818at_nat Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.produc3843707927480180839at_nat Bool)) (Q (-> tptp.produc3843707927480180839at_nat Bool))) (= (@ tptp.collec6321179662152712658at_nat (lambda ((X4 tptp.produc3843707927480180839at_nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat (@ tptp.collec6321179662152712658at_nat P))) (@ tptp.collec6321179662152712658at_nat Q)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (=> (@ P X4) (@ Q X4)))) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P))) (@ tptp.collect_nat Q)))))
% 6.81/7.13 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q6) R3)) (= (@ (@ tptp.divide_divide_int K) L) Q6))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (Q6 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R3 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q6))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q6) 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))))))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int) (Q6 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q6) R3)) (= (@ (@ tptp.modulo_modulo_int K) L) R3))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D2) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D2) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D2) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D2))))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.81/7.13 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.81/7.13 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (= tptp.minus_1356011639430497352at_nat (lambda ((X4 tptp.set_Pr1261947904930325089at_nat) (Y4 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.inf_in2572325071724192079at_nat X4) (@ tptp.uminus6524753893492686040at_nat Y4)))))
% 6.81/7.13 (assert (= tptp.minus_minus_set_nat (lambda ((X4 tptp.set_nat) (Y4 tptp.set_nat)) (@ (@ tptp.inf_inf_set_nat X4) (@ tptp.uminus5710092332889474511et_nat Y4)))))
% 6.81/7.13 (assert (= tptp.minus_minus_assn (lambda ((X4 tptp.assn) (Y4 tptp.assn)) (@ (@ tptp.inf_inf_assn X4) (@ tptp.uminus_uminus_assn Y4)))))
% 6.81/7.13 (assert (= tptp.minus_3524152463667985524t_unit (lambda ((X4 tptp.product_unit) (Y4 tptp.product_unit)) (@ (@ tptp.inf_inf_Product_unit X4) (@ tptp.uminus2952777764628376836t_unit Y4)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) A)) (@ (@ tptp.inf_in2572325071724192079at_nat X) B)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) A)) (@ (@ tptp.inf_inf_set_o X) B)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) A)) (@ (@ tptp.inf_inf_set_nat X) B)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) A)) (@ (@ tptp.inf_inf_set_int X) B)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) A)) (@ (@ tptp.inf_inf_assn X) B)) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) A)) (@ (@ tptp.inf_inf_Product_unit X) B)) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (A tptp.set_Pr1261947904930325089at_nat) (B tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) A)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat X)) B)) tptp.bot_bo2099793752762293965at_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (A tptp.set_o) (B tptp.set_o)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.inf_inf_set_o X) A)) (@ (@ tptp.inf_inf_set_o (@ tptp.uminus_uminus_set_o X)) B)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (A tptp.set_nat) (B tptp.set_nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.inf_inf_set_nat X) A)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat X)) B)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (A tptp.set_int) (B tptp.set_int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.inf_inf_set_int X) A)) (@ (@ tptp.inf_inf_set_int (@ tptp.uminus1532241313380277803et_int X)) B)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((X tptp.assn) (A tptp.assn) (B tptp.assn)) (= (@ (@ tptp.inf_inf_assn (@ (@ tptp.inf_inf_assn X) A)) (@ (@ tptp.inf_inf_assn (@ tptp.uminus_uminus_assn X)) B)) tptp.bot_bot_assn)))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (A tptp.product_unit) (B tptp.product_unit)) (= (@ (@ tptp.inf_inf_Product_unit (@ (@ tptp.inf_inf_Product_unit X) A)) (@ (@ tptp.inf_inf_Product_unit (@ tptp.uminus2952777764628376836t_unit X)) B)) tptp.bot_bot_Product_unit)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ tptp.uminus6524753893492686040at_nat A3)) (= A3 tptp.bot_bo2099793752762293965at_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.uminus_uminus_set_o A3)) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int A3)) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat A3)) (@ tptp.uminus4384627049435823934at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat A3)) (@ tptp.uminus2330091110623919550at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat A3)) (@ tptp.uminus935396558254630718at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.inf_inf_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.uminus6524753893492686040at_nat (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.inf_in2572325071724192079at_nat (@ tptp.uminus6524753893492686040at_nat A3)) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.uminus4384627049435823934at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.inf_in4302113700860409141at_nat (@ tptp.uminus4384627049435823934at_nat A3)) (@ tptp.uminus4384627049435823934at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.uminus2330091110623919550at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.inf_in1697001100524423349at_nat (@ tptp.uminus2330091110623919550at_nat A3)) (@ tptp.uminus2330091110623919550at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.uminus935396558254630718at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.inf_in7913087082777306421at_nat (@ tptp.uminus935396558254630718at_nat A3)) (@ tptp.uminus935396558254630718at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.inf_inf_set_nat (@ tptp.uminus5710092332889474511et_nat A3)) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D2)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D2)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D2)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D2))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.81/7.13 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.81/7.13 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.81/7.13 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.81/7.13 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((X tptp.set_o) (Y tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o X) Y) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o X) (@ tptp.uminus_uminus_set_o Y)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (= (@ (@ tptp.inf_inf_assn X) Y) tptp.bot_bot_assn) (@ (@ tptp.ord_less_eq_assn X) (@ tptp.uminus_uminus_assn Y)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ (@ tptp.inf_inf_Product_unit X) Y) tptp.bot_bot_Product_unit) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ tptp.uminus2952777764628376836t_unit Y)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_Pr1261947904930325089at_nat) (Q6 tptp.set_Pr1261947904930325089at_nat) (R3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat P3) (@ (@ tptp.sup_su6327502436637775413at_nat Q6) R3)) (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat P3) (@ tptp.uminus6524753893492686040at_nat Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_Pr8693737435421807431at_nat) (Q6 tptp.set_Pr8693737435421807431at_nat) (R3 tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat P3) (@ (@ tptp.sup_su718114333110466843at_nat Q6) R3)) (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat P3) (@ tptp.uminus4384627049435823934at_nat Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_Pr8551490117392284871at_nat) (Q6 tptp.set_Pr8551490117392284871at_nat) (R3 tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat P3) (@ (@ tptp.sup_su3035147773818789531at_nat Q6) R3)) (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat P3) (@ tptp.uminus2330091110623919550at_nat Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_Pr4329608150637261639at_nat) (Q6 tptp.set_Pr4329608150637261639at_nat) (R3 tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat P3) (@ (@ tptp.sup_su5525570899277871387at_nat Q6) R3)) (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat P3) (@ tptp.uminus935396558254630718at_nat Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_nat) (Q6 tptp.set_nat) (R3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat P3) (@ (@ tptp.sup_sup_set_nat Q6) R3)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat P3) (@ tptp.uminus5710092332889474511et_nat Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.assn) (Q6 tptp.assn) (R3 tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn P3) (@ (@ tptp.sup_sup_assn Q6) R3)) (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn P3) (@ tptp.uminus_uminus_assn Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.product_unit) (Q6 tptp.product_unit) (R3 tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit P3) (@ (@ tptp.sup_sup_Product_unit Q6) R3)) (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit P3) (@ tptp.uminus2952777764628376836t_unit Q6))) R3))))
% 6.81/7.13 (assert (forall ((P3 tptp.set_int) (Q6 tptp.set_int) (R3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int P3) (@ (@ tptp.sup_sup_set_int Q6) R3)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int P3) (@ tptp.uminus1532241313380277803et_int Q6))) R3))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) (@ tptp.uminus6524753893492686040at_nat Y))) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat X) (@ tptp.uminus4384627049435823934at_nat Y))) Z) (@ (@ tptp.ord_le3000389064537975527at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat X) (@ tptp.uminus2330091110623919550at_nat Y))) Z) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X) (@ tptp.uminus935396558254630718at_nat Y))) Z) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) (@ tptp.uminus5710092332889474511et_nat Y))) Z) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) (@ tptp.uminus_uminus_assn Y))) Z) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) (@ tptp.uminus2952777764628376836t_unit Y))) Z) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ (@ tptp.sup_sup_Product_unit Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) (@ tptp.uminus1532241313380277803et_int Y))) Z) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int Y) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr1261947904930325089at_nat) (Y tptp.set_Pr1261947904930325089at_nat) (Z tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ (@ tptp.inf_in2572325071724192079at_nat X) Y)) Z) (@ (@ tptp.ord_le3146513528884898305at_nat X) (@ (@ tptp.sup_su6327502436637775413at_nat (@ tptp.uminus6524753893492686040at_nat Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8693737435421807431at_nat) (Y tptp.set_Pr8693737435421807431at_nat) (Z tptp.set_Pr8693737435421807431at_nat)) (= (@ (@ tptp.ord_le3000389064537975527at_nat (@ (@ tptp.inf_in4302113700860409141at_nat X) Y)) Z) (@ (@ tptp.ord_le3000389064537975527at_nat X) (@ (@ tptp.sup_su718114333110466843at_nat (@ tptp.uminus4384627049435823934at_nat Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr8551490117392284871at_nat) (Y tptp.set_Pr8551490117392284871at_nat) (Z tptp.set_Pr8551490117392284871at_nat)) (= (@ (@ tptp.ord_le8081472938463900775at_nat (@ (@ tptp.inf_in1697001100524423349at_nat X) Y)) Z) (@ (@ tptp.ord_le8081472938463900775at_nat X) (@ (@ tptp.sup_su3035147773818789531at_nat (@ tptp.uminus2330091110623919550at_nat Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_Pr4329608150637261639at_nat) (Y tptp.set_Pr4329608150637261639at_nat) (Z tptp.set_Pr4329608150637261639at_nat)) (= (@ (@ tptp.ord_le1268244103169919719at_nat (@ (@ tptp.inf_in7913087082777306421at_nat X) Y)) Z) (@ (@ tptp.ord_le1268244103169919719at_nat X) (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.uminus935396558254630718at_nat Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat) (Z tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.inf_inf_set_nat X) Y)) Z) (@ (@ tptp.ord_less_eq_set_nat X) (@ (@ tptp.sup_sup_set_nat (@ tptp.uminus5710092332889474511et_nat Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.assn) (Y tptp.assn) (Z tptp.assn)) (= (@ (@ tptp.ord_less_eq_assn (@ (@ tptp.inf_inf_assn X) Y)) Z) (@ (@ tptp.ord_less_eq_assn X) (@ (@ tptp.sup_sup_assn (@ tptp.uminus_uminus_assn Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit) (Z tptp.product_unit)) (= (@ (@ tptp.ord_le3221252021190050221t_unit (@ (@ tptp.inf_inf_Product_unit X) Y)) Z) (@ (@ tptp.ord_le3221252021190050221t_unit X) (@ (@ tptp.sup_sup_Product_unit (@ tptp.uminus2952777764628376836t_unit Y)) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.inf_inf_set_int X) Y)) Z) (@ (@ tptp.ord_less_eq_set_int X) (@ (@ tptp.sup_sup_set_int (@ tptp.uminus1532241313380277803et_int Y)) Z)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A) N2)))))
% 6.81/7.13 (assert (forall ((L tptp.int) (K tptp.int) (Q6 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q6) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q6) tptp.zero_zero_int))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3) tptp.bot_bo2099793752762293965at_nat) (@ (@ tptp.ord_le3146513528884898305at_nat A3) (@ tptp.uminus6524753893492686040at_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o)) (= (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (@ (@ tptp.ord_less_eq_set_o A3) (@ tptp.uminus_uminus_set_o B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A3) (@ tptp.uminus5710092332889474511et_nat B3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A3) (@ tptp.uminus1532241313380277803et_int B3)))))
% 6.81/7.13 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))))
% 6.81/7.13 (assert (forall ((M tptp.int)) (=> (forall ((N5 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N5)))) (not (forall ((N5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5)))))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((W2 tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.81/7.13 (assert (= tptp.uminus_uminus_assn (lambda ((P4 tptp.assn)) (@ tptp.abs_assn (lambda ((H6 tptp.produc3658429121746597890et_nat)) (and (@ tptp.in_range H6) (not (@ (@ tptp.rep_assn P4) H6))))))))
% 6.81/7.13 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N5 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N5)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))) (not (forall ((N5 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5)))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (exists ((N5 tptp.nat)) (= X (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N5))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((A3 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A3) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N2)) (@ (@ tptp.divide_divide_int A3) N2))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.nO_MATCH_int_int tptp.one_one_int) X) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int X) N2))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.nO_MAT8252062027627875367nteger tptp.one_one_Code_integer) X) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger X) N2))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.nO_MATCH_rat_rat tptp.one_one_rat) X) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat X) N2))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.81/7.13 (assert (forall ((W2 tptp.num) (B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.81/7.13 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N5 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N5))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5))))))))
% 6.81/7.13 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (C tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W2)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.81/7.13 (assert (forall ((W2 tptp.num) (B tptp.rat) (C 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 C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_nat I3) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I3) (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K)))))))))
% 6.81/7.13 (assert (forall ((D2 tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D2))))))
% 6.81/7.13 (assert (forall ((D2 tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D2))) Z)))))
% 6.81/7.13 (assert (forall ((R3 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R3))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R3) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R3) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.81/7.13 (assert (forall ((R3 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R3) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R3) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.81/7.13 (assert (forall ((R3 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R3))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R3) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R3) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ F I3) K))))))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (K tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat B)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat B) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.81/7.13 (assert (forall ((B tptp.int) (K tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int B)) K) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) K)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int B) (@ tptp.semiri1314217659103216013at_int K))) tptp.one_one_int)) K)))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (K tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger B)) K) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger B) (@ tptp.semiri4939895301339042750nteger K))) tptp.one_one_Code_integer)) K)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.81/7.13 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I3) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I3) J2) (@ (@ P (@ (@ tptp.plus_plus_int I3) tptp.one_one_int)) J2)) (@ (@ P I3) J2)))) (@ (@ P A0) A1)))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.81/7.13 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.81/7.13 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus6524753893492686040at_nat A3))))))
% 6.81/7.13 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus_uminus_set_o A3))))))
% 6.81/7.13 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3))))))
% 6.81/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3))))))
% 6.81/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (not (@ _let_1 A3)) (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3))))))
% 6.81/7.13 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (= (@ _let_1 (@ tptp.uminus6524753893492686040at_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (= (@ _let_1 (@ tptp.uminus_uminus_set_o A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.81/7.13 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (= (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (not (@ P X4)))) (@ tptp.uminus6221592323253981072nt_int (@ tptp.collec213857154873943460nt_int P)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool))) (= (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ P X4)))) (@ tptp.uminus3195874150345416415st_nat (@ tptp.collect_list_nat P)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.set_nat Bool))) (= (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ P X4)))) (@ tptp.uminus613421341184616069et_nat (@ tptp.collect_set_nat P)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))) (@ tptp.uminus5710092332889474511et_nat (@ tptp.collect_nat P)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))) (@ tptp.uminus1532241313380277803et_int (@ tptp.collect_int P)))))
% 6.81/7.13 (assert (= tptp.uminus6524753893492686040at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (not (@ (@ tptp.member8440522571783428010at_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (lambda ((X4 Bool)) (not (@ (@ tptp.member_o X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (not (@ (@ tptp.member5262025264175285858nt_int X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ (@ tptp.member_list_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ (@ tptp.member_set_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ (@ tptp.member_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ (@ tptp.member_int X4) A6)))))))
% 6.81/7.13 (assert (forall ((C tptp.product_prod_nat_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat C))) (=> (@ _let_1 (@ tptp.uminus6524753893492686040at_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C Bool) (A3 tptp.set_o)) (let ((_let_1 (@ tptp.member_o C))) (=> (@ _let_1 (@ tptp.uminus_uminus_set_o A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.set_nat) (A3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ tptp.uminus613421341184616069et_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.nat) (A3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ tptp.uminus5710092332889474511et_nat A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (forall ((C tptp.int) (A3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ tptp.uminus1532241313380277803et_int A3)) (not (@ _let_1 A3))))))
% 6.81/7.13 (assert (= tptp.uminus6524753893492686040at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ tptp.uminus8676089048583255045_nat_o (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus_uminus_set_o (lambda ((A6 tptp.set_o)) (@ tptp.collect_o (@ tptp.uminus_uminus_o_o (lambda ((X4 Bool)) (@ (@ tptp.member_o X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus6221592323253981072nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ tptp.uminus7117520113953359693_int_o (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus3195874150345416415st_nat (lambda ((A6 tptp.set_list_nat)) (@ tptp.collect_list_nat (@ tptp.uminus5770388063884162150_nat_o (lambda ((X4 tptp.list_nat)) (@ (@ tptp.member_list_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus613421341184616069et_nat (lambda ((A6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ tptp.uminus6401447641752708672_nat_o (lambda ((X4 tptp.set_nat)) (@ (@ tptp.member_set_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus5710092332889474511et_nat (lambda ((A6 tptp.set_nat)) (@ tptp.collect_nat (@ tptp.uminus_uminus_nat_o (lambda ((X4 tptp.nat)) (@ (@ tptp.member_nat X4) A6)))))))
% 6.81/7.13 (assert (= tptp.uminus1532241313380277803et_int (lambda ((A6 tptp.set_int)) (@ tptp.collect_int (@ tptp.uminus_uminus_int_o (lambda ((X4 tptp.int)) (@ (@ tptp.member_int X4) A6)))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.81/7.13 (assert (forall ((X2 tptp.produc3260487557148687353it_nat)) (= (@ tptp.size_s2363601347547812957it_nat (@ tptp.some_P7913643980934408916it_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((X2 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((X2 tptp.produc8664842809031399944it_nat)) (= (@ tptp.size_s8766407808098229740it_nat (@ tptp.some_P1914260805536162275it_nat X2)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W2) Z))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W2) Z))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W2) Z))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.times_times_int W2) Z)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.ring_18347121197199848620nteger W2)) (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W2) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W2)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W2) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W2)) (@ tptp.ring_1_of_int_int Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W2) Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.81/7.13 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z)) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger Z)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger Z)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.ring_18347121197199848620nteger Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat V)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 Z)) (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.81/7.13 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.81/7.13 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.81/7.13 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (B tptp.int) (W2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W2)))))
% 6.81/7.13 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.81/7.13 (assert (forall ((B tptp.int) (W2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W2)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W2)) X))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((V tptp.num) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger X)) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((A tptp.int) (X tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)))))
% 6.81/7.13 (assert (forall ((X tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N2)) A))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X))) X)))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ring_18347121197199848620nteger X))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) Y) (@ (@ tptp.times_3573771949741848930nteger Y) _let_1)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys)) (@ tptp.size_size_list_o Xs2)) (@ P Ys))) (@ P Xs2))) (@ P Xs))))
% 6.81/7.13 (assert (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R3)))) R3))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X) Z))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (T5 tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T5)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T5) (@ (@ tptp.ord_less_rat T5) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I4)))))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) Z) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 6.81/7.13 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (forall ((X5 tptp.nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.nat Bool))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P4 (@ tptp.nat2 X4)))))))
% 6.81/7.13 (assert (= (lambda ((P5 (-> tptp.nat Bool))) (exists ((X5 tptp.nat)) (@ P5 X5))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((X4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ P4 (@ tptp.nat2 X4)))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim2889992004027027881ng_rat X))))
% 6.81/7.13 (assert (forall ((Q6 tptp.rat) (P3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q6) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P3) Q6)))) Q6)) P3))))
% 6.81/7.13 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 6.81/7.13 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 6.81/7.13 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 6.81/7.13 (assert (forall ((Q6 tptp.rat) (P3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q6) (@ (@ tptp.ord_less_rat P3) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P3) Q6)))) tptp.one_one_rat)) Q6)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (W2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W2) Z)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.81/7.13 (assert (forall ((X tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N2) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.81/7.13 (assert (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R3) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R3))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X))))
% 6.81/7.13 (assert (= tptp.plus_plus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.81/7.13 (assert (= tptp.times_times_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.81/7.13 (assert (= tptp.minus_minus_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.81/7.13 (assert (= tptp.divide_divide_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.81/7.13 (assert (= tptp.modulo_modulo_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A5)) (@ tptp.semiri1314217659103216013at_int B5))))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.ring_18347121197199848620nteger Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X3)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X3) tptp.one_one_int))) (forall ((Y6 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y6)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y6) tptp.one_one_int)))) (= Y6 X3)))))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W2) Z)))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W2)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W2) Z)))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= (@ tptp.nat2 W2) M) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (W2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2))) (= (= M (@ tptp.nat2 W2)) (and (=> _let_1 (= W2 (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.ring_18347121197199848620nteger X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.int)) (= (@ P (@ tptp.nat2 I2)) (and (forall ((N tptp.nat)) (=> (= I2 (@ tptp.semiri1314217659103216013at_int N)) (@ P N))) (=> (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.81/7.13 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.81/7.13 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.81/7.13 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X))) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X) Z))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X) (@ (@ tptp.ord_less_eq_rat X) _let_1))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (T5 tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T5)) (forall ((I4 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I4))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T5) (@ (@ tptp.ord_less_eq_rat T5) _let_1)) (@ P I4)))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X)) Z) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.81/7.13 (assert (forall ((W2 tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W2) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W2)) M) (@ (@ tptp.ord_less_int W2) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.81/7.13 (assert (forall ((Q6 tptp.rat) (P3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q6) (@ (@ tptp.ord_less_eq_rat P3) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P3) Q6)))) Q6)))))
% 6.81/7.13 (assert (forall ((Q6 tptp.rat) (P3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q6) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P3) Q6)))) tptp.one_one_rat)) Q6)) P3))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.81/7.13 (assert (= tptp.eucl_rel_int (lambda ((A12 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (or (exists ((K3 tptp.int)) (and (= A12 K3) (= A22 tptp.zero_zero_int) (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L2 tptp.int) (K3 tptp.int) (Q7 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q7) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q7) L2)))) (exists ((R4 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q7 tptp.int)) (and (= A12 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q7) R4)) (= (@ tptp.sgn_sgn_int R4) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R4)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q7) L2)) R4))))))))
% 6.81/7.13 (assert (forall ((A1 tptp.int) (A23 tptp.int) (A33 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A1) A23) A33) (=> (=> (= A23 tptp.zero_zero_int) (not (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A1 (@ (@ tptp.times_times_int Q5) A23)))))) (not (forall ((R2 tptp.int) (Q5 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q5) R2)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int A23)) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A23)) R2)))))))))))))
% 6.81/7.13 (assert (forall ((S tptp.multis2468970476368604999at_nat)) (= (not (= S tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s8510653225128441779at_nat S)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X)) (not (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat)))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((C3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat A3))) (=> (= (@ (@ tptp.minus_4286766774447292334at_nat C3) B3) tptp.zero_z1048942125864253310at_nat) (= (@ (@ tptp.minus_4286766774447292334at_nat (@ _let_1 B3)) C3) (@ _let_1 (@ (@ tptp.minus_4286766774447292334at_nat B3) C3)))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer B) tptp.ring_11222124179247155820nteger) (@ (@ tptp.member_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.ring_11222124179247155820nteger)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.times_times_rat A) B)) tptp.ring_1_Ints_rat)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.times_times_int A) B)) tptp.ring_1_Ints_int)))))
% 6.81/7.13 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 6.81/7.13 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 6.81/7.13 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 6.81/7.13 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X)) (@ tptp.abs_abs_Code_integer X)) X)))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X)) (@ tptp.abs_abs_rat X)) X)))
% 6.81/7.13 (assert (forall ((X tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X)) (@ tptp.abs_abs_int X)) X)))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X)) tptp.one_one_rat)))
% 6.81/7.13 (assert (forall ((X tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.81/7.13 (assert (= tptp.sgn_sgn_int (lambda ((I4 tptp.int)) (@ (@ (@ tptp.if_int (= I4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (= tptp.sgn_sgn_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (= X4 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.81/7.13 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X4 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X4)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.81/7.13 (assert (= tptp.sgn_sgn_rat (lambda ((X4 tptp.rat)) (@ (@ (@ tptp.if_rat (= X4 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A) tptp.ring_11222124179247155820nteger) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (not (= X tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X))))))
% 6.81/7.13 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (not (= X tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer) (= X tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat) (= X tptp.zero_zero_rat)))))
% 6.81/7.13 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int) (= X tptp.zero_zero_int)))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger) (= (= X Y) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Y))) tptp.one_one_Code_integer))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) Y))) tptp.one_one_rat))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Y))) tptp.one_one_int))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X) X) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (@ (@ tptp.ord_less_rat X) tptp.one_one_rat)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 6.81/7.13 (assert (forall ((R3 tptp.int) (L tptp.int) (K tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q6) L)) R3)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q6) R3)))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.81/7.13 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_nat Xs)) (= (@ tptp.size_size_list_nat (@ (@ (@ tptp.slice_nat From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))))
% 6.81/7.13 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_o Xs)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.slice_o From) To) Xs)) (@ (@ tptp.minus_minus_nat To) From))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri773545260158071498ct_rat N2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri3624122377584611663nteger N2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (= tptp.semiri773545260158071498ct_rat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M3)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (= tptp.semiri3624122377584611663nteger (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= M3 tptp.zero_zero_nat)) tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger M3)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M3)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_nat Xs) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (= (@ tptp.rotate1_o Xs) Xs))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 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) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X3 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X11 tptp.int)) (@ P X11)) (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) B3) (@ P (@ (@ tptp.plus_plus_int Y4) X4))))))))))))))
% 6.81/7.13 (assert (forall ((L tptp.set_int) (H tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (H tptp.code_integer) (L3 tptp.code_integer) (H3 tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger L) H) (@ (@ tptp.set_or189985376899183464nteger L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_le3102999989581377725nteger L) H)) (not (@ (@ tptp.ord_le3102999989581377725nteger L3) H3)))))))
% 6.81/7.13 (assert (forall ((I2 Bool) (L Bool) (U Bool)) (= (@ (@ tptp.member_o I2) (@ (@ tptp.set_or8904488021354931149Most_o L) U)) (and (@ (@ tptp.ord_less_eq_o L) I2) (@ (@ tptp.ord_less_eq_o I2) U)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((I2 tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.member_Code_integer I2) (@ (@ tptp.set_or189985376899183464nteger L) U)) (and (@ (@ tptp.ord_le3102999989581377725nteger L) I2) (@ (@ tptp.ord_le3102999989581377725nteger I2) U)))))
% 6.81/7.13 (assert (forall ((A Bool) (B Bool)) (= (= tptp.bot_bot_set_o (@ (@ tptp.set_or8904488021354931149Most_o A) B)) (not (@ (@ tptp.ord_less_eq_o A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 6.81/7.13 (assert (forall ((A Bool) (B Bool)) (= (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) tptp.bot_bot_set_o) (not (@ (@ tptp.ord_less_eq_o A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.set_or189985376899183464nteger A) B) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)))))
% 6.81/7.13 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.ord_less_o B) A) (= (@ (@ tptp.set_or8904488021354931149Most_o A) B) tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.ord_less_assn B) A) (= (@ (@ tptp.set_or7959216805967363635t_assn A) B) tptp.bot_bot_set_assn))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.set_or189985376899183464nteger A) B) tptp.bot_bo3990330152332043303nteger))))
% 6.81/7.13 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D2)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D2))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger C) D2)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (and (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le3102999989581377725nteger B) D2))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ (@ tptp.slice_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)) Xs) Xs)))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (= (@ (@ (@ tptp.slice_o tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)) Xs) Xs)))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri773545260158071498ct_rat _let_1) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri3624122377584611663nteger _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger _let_1)) (@ tptp.semiri3624122377584611663nteger N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.81/7.13 (assert (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (M6 tptp.multis2468970476368604999at_nat) (N7 tptp.multis2468970476368604999at_nat)) (=> (= (@ (@ tptp.plus_p7104986032573967614at_nat A3) B3) (@ (@ tptp.plus_p7104986032573967614at_nat M6) N7)) (not (forall ((Am tptp.multis2468970476368604999at_nat) (An tptp.multis2468970476368604999at_nat)) (=> (= A3 (@ (@ tptp.plus_p7104986032573967614at_nat Am) An)) (forall ((Bm tptp.multis2468970476368604999at_nat) (Bn tptp.multis2468970476368604999at_nat)) (=> (= B3 (@ (@ tptp.plus_p7104986032573967614at_nat Bm) Bn)) (=> (= M6 (@ (@ tptp.plus_p7104986032573967614at_nat Am) Bm)) (not (= N7 (@ (@ tptp.plus_p7104986032573967614at_nat An) Bn))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.81/7.13 (assert (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (let ((_let_1 (@ tptp.set_or633870826150836451st_rat L))) (=> (@ (@ tptp.ord_less_eq_rat L) M) (=> (@ (@ tptp.ord_less_eq_rat M) U) (= (@ (@ tptp.sup_sup_set_rat (@ _let_1 M)) (@ (@ tptp.set_or633870826150836451st_rat M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (let ((_let_1 (@ tptp.set_or7049704709247886629st_num L))) (=> (@ (@ tptp.ord_less_eq_num L) M) (=> (@ (@ tptp.ord_less_eq_num M) U) (= (@ (@ tptp.sup_sup_set_num (@ _let_1 M)) (@ (@ tptp.set_or7049704709247886629st_num M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int L))) (=> (@ (@ tptp.ord_less_eq_int L) M) (=> (@ (@ tptp.ord_less_eq_int M) U) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 M)) (@ (@ tptp.set_or1266510415728281911st_int M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat L))) (=> (@ (@ tptp.ord_less_eq_nat L) M) (=> (@ (@ tptp.ord_less_eq_nat M) U) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 M)) (@ (@ tptp.set_or1269000886237332187st_nat M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (let ((_let_1 (@ tptp.set_or189985376899183464nteger L))) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger M) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ _let_1 M)) (@ (@ tptp.set_or189985376899183464nteger M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri3624122377584611663nteger N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.semiri3624122377584611663nteger N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.semiri3624122377584611663nteger N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.semiri3624122377584611663nteger N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ _let_1 tptp.one_one_rat)) K))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat A) _let_3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_rat A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_rat _let_3) A) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat K)) _let_3)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat K))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) _let_1)) K)) (@ (@ tptp.gbinomial_rat A) K))))))
% 6.81/7.13 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (let ((_let_1 (@ tptp.ord_less_eq_assn C))) (= (@ (@ tptp.ord_less_set_assn (@ (@ tptp.set_or7959216805967363635t_assn A) B)) (@ (@ tptp.set_or7959216805967363635t_assn C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_assn A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_assn B) D2) (or (@ (@ tptp.ord_less_assn C) A) (@ (@ tptp.ord_less_assn B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D2) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D2) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D2) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D2) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D2)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D2) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger C) D2)) (and (or (not (@ (@ tptp.ord_le3102999989581377725nteger A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger B) D2) (or (@ (@ tptp.ord_le6747313008572928689nteger C) A) (@ (@ tptp.ord_le6747313008572928689nteger B) D2)))) (@ _let_1 D2))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo8411746178871703098atural (@ tptp.semiri2447717529341329178atural N2)) (@ tptp.semiri2447717529341329178atural M)) tptp.zero_z2226904508553997617atural))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.power_power_nat N2) N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_2)) (@ (@ tptp.gbinomial_rat _let_1) _let_2)) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ (@ tptp.gbinomial_rat A) _let_1)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) K))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat M)) K)) (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R3)))) (@ (@ tptp.power_power_nat N2) R3)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))) (= (@ (@ tptp.gbinomial_rat _let_2) _let_1) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat _let_2) (@ tptp.semiri681578069525770553at_rat _let_1))) (@ (@ tptp.gbinomial_rat A) K)))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (@ (@ tptp.times_times_rat (@ _let_1 K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))))
% 6.81/7.13 (assert (forall ((D2 tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D2) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P X3) (@ P (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D2))))) (= (exists ((X11 tptp.int)) (@ P X11)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D2)) (@ P X4))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (A3 tptp.set_int) (T5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D3)))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T5) A3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T5) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X7) D3)) T5))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T5) A3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X7 T5)) (not (= (@ (@ tptp.plus_plus_int X7) D3) T5)))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T5) tptp.one_one_int)) A3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X7 T5) (= (@ (@ tptp.plus_plus_int X7) D3) T5))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T5) B3) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D3))))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (B3 tptp.set_int) (T5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_int X7) T5) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X7) D3)) T5)))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int T5) B3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X7 T5)) (not (= (@ (@ tptp.minus_minus_int X7) D3) T5)))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T5) tptp.one_one_int)) B3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X7 T5) (= (@ (@ tptp.minus_minus_int X7) D3) T5))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.gbinomial_rat A) K) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (A3 tptp.set_int) (T5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.plus_plus_int X7) D3)))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T5) tptp.one_one_int)) A3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A3) (not (= X7 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X7) D3)) T5))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (T5 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T5) tptp.one_one_int)) B3) (forall ((X7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T5))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ _let_1 X7) (@ _let_1 (@ (@ tptp.minus_minus_int X7) D3))))))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (B3 tptp.set_int) (T5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D3) (forall ((X7 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X7 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X7) T5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X7) D3)) T5)))))))
% 6.81/7.13 (assert (forall ((D3 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A3 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) (= (@ P X3) (@ P6 X3))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D3)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A3) (not (= X3 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ P X3) (@ P (@ (@ tptp.plus_plus_int X3) D3))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (@ P6 X3) (@ P6 (@ (@ tptp.minus_minus_int X3) (@ (@ tptp.times_times_int K2) D3))))) (= (exists ((X11 tptp.int)) (@ P X11)) (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) A3) (@ P (@ (@ tptp.minus_minus_int Y4) X4))))))))))))))
% 6.81/7.13 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_int) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_int Xs)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_int (@ (@ (@ tptp.slice_int From) To) Xs)) I2) (@ (@ tptp.nth_int Xs) (@ (@ tptp.plus_plus_nat From) I2))))))))
% 6.81/7.13 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_nat Xs)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_nat (@ (@ (@ tptp.slice_nat From) To) Xs)) I2) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.plus_plus_nat From) I2))))))))
% 6.81/7.13 (assert (forall ((From tptp.nat) (To tptp.nat) (Xs tptp.list_o) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat From) To) (=> (@ (@ tptp.ord_less_eq_nat To) (@ tptp.size_size_list_o Xs)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat To) From)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.slice_o From) To) Xs)) I2) (@ (@ tptp.nth_o Xs) (@ (@ tptp.plus_plus_nat From) I2))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) M)) C))) (let ((_let_2 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat B) M)) C))) (let ((_let_3 (@ (@ tptp.set_or633870826150836451st_rat A) B))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) M))) (let ((_let_5 (= _let_3 tptp.bot_bot_set_rat))) (and (=> _let_5 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) tptp.bot_bot_set_rat)) (=> (not _let_5) (and (=> _let_4 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) (@ (@ tptp.set_or633870826150836451st_rat _let_1) _let_2))) (=> (not _let_4) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) (@ (@ tptp.set_or633870826150836451st_rat _let_2) _let_1)))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) M)) C))) (let ((_let_2 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat B) M)) C))) (let ((_let_3 (@ (@ tptp.set_or633870826150836451st_rat A) B))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) M))) (let ((_let_5 (= _let_3 tptp.bot_bot_set_rat))) (and (=> _let_5 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) tptp.bot_bot_set_rat)) (=> (not _let_5) (and (=> _let_4 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) (@ (@ tptp.set_or633870826150836451st_rat _let_1) _let_2))) (=> (not _let_4) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) M)) C))) _let_3) (@ (@ tptp.set_or633870826150836451st_rat _let_2) _let_1)))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat M))) (let ((_let_2 (@ (@ tptp.minus_minus_rat (@ _let_1 A)) C))) (let ((_let_3 (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C))) (let ((_let_4 (@ (@ tptp.set_or633870826150836451st_rat A) B))) (let ((_let_5 (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) M))) (let ((_let_6 (= _let_4 tptp.bot_bot_set_rat))) (and (=> _let_6 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) tptp.bot_bot_set_rat)) (=> (not _let_6) (and (=> _let_5 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) (@ (@ tptp.set_or633870826150836451st_rat _let_2) _let_3))) (=> (not _let_5) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) (@ (@ tptp.set_or633870826150836451st_rat _let_3) _let_2))))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (M tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat M))) (let ((_let_2 (@ (@ tptp.plus_plus_rat (@ _let_1 A)) C))) (let ((_let_3 (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C))) (let ((_let_4 (@ (@ tptp.set_or633870826150836451st_rat A) B))) (let ((_let_5 (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) M))) (let ((_let_6 (= _let_4 tptp.bot_bot_set_rat))) (and (=> _let_6 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) tptp.bot_bot_set_rat)) (=> (not _let_6) (and (=> _let_5 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) (@ (@ tptp.set_or633870826150836451st_rat _let_2) _let_3))) (=> (not _let_5) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat M) X4)) C))) _let_4) (@ (@ tptp.set_or633870826150836451st_rat _let_3) _let_2))))))))))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (Y tptp.rat) (C tptp.rat)) (let ((_let_1 (@ (@ tptp.set_or633870826150836451st_rat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat X) Y))) (let ((_let_3 (@ (@ tptp.times_times_rat X) C))) (let ((_let_4 (@ (@ tptp.times_times_rat Y) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (and (=> _let_2 (and (=> _let_5 (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.times_times_rat X4) C))) _let_1) (@ (@ tptp.set_or633870826150836451st_rat _let_3) _let_4))) (=> (not _let_5) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.times_times_rat X4) C))) _let_1) (@ (@ tptp.set_or633870826150836451st_rat _let_4) _let_3))))) (=> (not _let_2) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.times_times_rat X4) C))) _let_1) tptp.bot_bot_set_rat))))))))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> Bool Bool)) (X Bool) (A3 tptp.set_o)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> Bool tptp.nat)) (X Bool) (A3 tptp.set_o)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> Bool tptp.int)) (X Bool) (A3 tptp.set_o)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int F) A3))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> tptp.nat Bool)) (X tptp.nat) (A3 tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> tptp.nat tptp.nat)) (X tptp.nat) (A3 tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> tptp.nat tptp.int)) (X tptp.nat) (A3 tptp.set_nat)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int F) A3))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> tptp.int Bool)) (X tptp.int) (A3 tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> tptp.int tptp.nat)) (X tptp.int) (A3 tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> tptp.int tptp.int)) (X tptp.int) (A3 tptp.set_int)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int F) A3))))))
% 6.81/7.13 (assert (forall ((B tptp.set_nat) (F (-> Bool tptp.set_nat)) (X Bool) (A3 tptp.set_o)) (=> (= B (@ F X)) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_set_nat B) (@ (@ tptp.image_o_set_nat F) A3))))))
% 6.81/7.13 (assert (forall ((Y7 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (lambda ((X4 tptp.nat)) X4)) Y7) Y7)))
% 6.81/7.13 (assert (forall ((Y7 tptp.set_int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) X4)) Y7) Y7)))
% 6.81/7.13 (assert (forall ((F (-> Bool Bool))) (= (@ (@ tptp.image_o_o F) tptp.bot_bot_set_o) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.nat))) (= (@ (@ tptp.image_o_nat F) tptp.bot_bot_set_o) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.int))) (= (@ (@ tptp.image_o_int F) tptp.bot_bot_set_o) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat Bool))) (= (@ (@ tptp.image_nat_o F) tptp.bot_bot_set_nat) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat))) (= (@ (@ tptp.image_nat_nat F) tptp.bot_bot_set_nat) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int))) (= (@ (@ tptp.image_nat_int F) tptp.bot_bot_set_nat) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((F (-> tptp.int Bool))) (= (@ (@ tptp.image_int_o F) tptp.bot_bot_set_int) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat))) (= (@ (@ tptp.image_int_nat F) tptp.bot_bot_set_int) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int))) (= (@ (@ tptp.image_int_int F) tptp.bot_bot_set_int) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat))) (= (@ (@ tptp.image_nat_set_nat F) tptp.bot_bot_set_nat) tptp.bot_bot_set_set_nat)))
% 6.81/7.13 (assert (forall ((F (-> Bool Bool)) (A3 tptp.set_o)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_o_o F) A3)) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat Bool)) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_nat_o F) A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int Bool)) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_o (@ (@ tptp.image_int_o F) A3)) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.nat)) (A3 tptp.set_o)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.image_o_nat F) A3)) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.image_nat_nat F) A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.image_int_nat F) A3)) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.int)) (A3 tptp.set_o)) (= (= tptp.bot_bot_set_int (@ (@ tptp.image_o_int F) A3)) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_int (@ (@ tptp.image_nat_int F) A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.image_int_int F) A3)) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (= tptp.bot_bot_set_set_nat (@ (@ tptp.image_nat_set_nat F) A3)) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> Bool Bool)) (A3 tptp.set_o)) (= (= (@ (@ tptp.image_o_o F) A3) tptp.bot_bot_set_o) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat Bool)) (A3 tptp.set_nat)) (= (= (@ (@ tptp.image_nat_o F) A3) tptp.bot_bot_set_o) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int Bool)) (A3 tptp.set_int)) (= (= (@ (@ tptp.image_int_o F) A3) tptp.bot_bot_set_o) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.nat)) (A3 tptp.set_o)) (= (= (@ (@ tptp.image_o_nat F) A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (= (@ (@ tptp.image_nat_nat F) A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (= (@ (@ tptp.image_int_nat F) A3) tptp.bot_bot_set_nat) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.int)) (A3 tptp.set_o)) (= (= (@ (@ tptp.image_o_int F) A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (= (@ (@ tptp.image_nat_int F) A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (= (@ (@ tptp.image_int_int F) A3) tptp.bot_bot_set_int) (= A3 tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (= (@ (@ tptp.image_nat_set_nat F) A3) tptp.bot_bot_set_set_nat) (= A3 tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger)) S) S)))
% 6.81/7.13 (assert (forall ((S tptp.set_mu2057375006010111271at_nat)) (= (@ (@ tptp.image_2516384619306764229at_nat (@ tptp.plus_p7104986032573967614at_nat tptp.zero_z1048942125864253310at_nat)) S) S)))
% 6.81/7.13 (assert (forall ((S tptp.set_rat)) (= (@ (@ tptp.image_rat_rat (@ tptp.plus_plus_rat tptp.zero_zero_rat)) S) S)))
% 6.81/7.13 (assert (forall ((S tptp.set_nat)) (= (@ (@ tptp.image_nat_nat (@ tptp.plus_plus_nat tptp.zero_zero_nat)) S) S)))
% 6.81/7.13 (assert (forall ((S tptp.set_int)) (= (@ (@ tptp.image_int_int (@ tptp.plus_plus_int tptp.zero_zero_int)) S) S)))
% 6.81/7.13 (assert (forall ((K tptp.rat) (I2 tptp.rat) (J tptp.rat)) (= (@ (@ tptp.image_rat_rat (lambda ((N tptp.rat)) (@ (@ tptp.plus_plus_rat N) K))) (@ (@ tptp.set_or633870826150836451st_rat I2) J)) (@ (@ tptp.set_or633870826150836451st_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.int) (I2 tptp.int) (J tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((N tptp.int)) (@ (@ tptp.plus_plus_int N) K))) (@ (@ tptp.set_or1266510415728281911st_int I2) J)) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.code_integer) (I2 tptp.code_integer) (J tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((N tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger N) K))) (@ (@ tptp.set_or189985376899183464nteger I2) J)) (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) K)))))
% 6.81/7.13 (assert (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.image_rat_rat (lambda ((T3 tptp.rat)) (@ (@ tptp.minus_minus_rat T3) D2))) (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat (@ (@ tptp.minus_minus_rat A) D2)) (@ (@ tptp.minus_minus_rat B) D2)))))
% 6.81/7.13 (assert (forall ((D2 tptp.int) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((T3 tptp.int)) (@ (@ tptp.minus_minus_int T3) D2))) (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.minus_minus_int A) D2)) (@ (@ tptp.minus_minus_int B) D2)))))
% 6.81/7.13 (assert (forall ((D2 tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((T3 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger T3) D2))) (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.minus_8373710615458151222nteger A) D2)) (@ (@ tptp.minus_8373710615458151222nteger B) D2)))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (S tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int S))) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.image_int_int F) (@ _let_1 (@ tptp.collect_int P)))) (@ (@ tptp.image_int_int G) (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat S))) (= (@ (@ tptp.image_nat_int (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_int (@ (@ tptp.image_nat_int F) (@ _let_1 (@ tptp.collect_nat P)))) (@ (@ tptp.image_nat_int G) (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat)) (S tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int S))) (= (@ (@ tptp.image_int_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_int_nat F) (@ _let_1 (@ tptp.collect_int P)))) (@ (@ tptp.image_int_nat G) (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat S))) (= (@ (@ tptp.image_nat_nat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_nat_nat F) (@ _let_1 (@ tptp.collect_nat P)))) (@ (@ tptp.image_nat_nat G) (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.set_nat)) (G (-> tptp.nat tptp.set_nat)) (S tptp.set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_nat S))) (= (@ (@ tptp.image_nat_set_nat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_set_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_set_nat (@ (@ tptp.image_nat_set_nat F) (@ _let_1 (@ tptp.collect_nat P)))) (@ (@ tptp.image_nat_set_nat G) (@ _let_1 (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (F (-> tptp.list_nat tptp.nat)) (G (-> tptp.list_nat tptp.nat)) (S tptp.set_list_nat)) (let ((_let_1 (@ tptp.inf_inf_set_list_nat S))) (= (@ (@ tptp.image_list_nat_nat (lambda ((X4 tptp.list_nat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_list_nat_nat F) (@ _let_1 (@ tptp.collect_list_nat P)))) (@ (@ tptp.image_list_nat_nat G) (@ _let_1 (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.set_nat Bool)) (F (-> tptp.set_nat tptp.nat)) (G (-> tptp.set_nat tptp.nat)) (S tptp.set_set_nat)) (let ((_let_1 (@ tptp.inf_inf_set_set_nat S))) (= (@ (@ tptp.image_set_nat_nat (lambda ((X4 tptp.set_nat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_set_nat_nat F) (@ _let_1 (@ tptp.collect_set_nat P)))) (@ (@ tptp.image_set_nat_nat G) (@ _let_1 (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (F (-> tptp.product_prod_int_int tptp.nat)) (G (-> tptp.product_prod_int_int tptp.nat)) (S tptp.set_Pr958786334691620121nt_int)) (let ((_let_1 (@ tptp.inf_in2269163501485487111nt_int S))) (= (@ (@ tptp.image_5044651549707136836nt_nat (lambda ((X4 tptp.product_prod_int_int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_5044651549707136836nt_nat F) (@ _let_1 (@ tptp.collec213857154873943460nt_int P)))) (@ (@ tptp.image_5044651549707136836nt_nat G) (@ _let_1 (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (F (-> tptp.product_prod_nat_nat tptp.nat)) (G (-> tptp.product_prod_nat_nat tptp.nat)) (S tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.inf_in2572325071724192079at_nat S))) (= (@ (@ tptp.image_2486076414777270412at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.image_2486076414777270412at_nat F) (@ _let_1 (@ tptp.collec3392354462482085612at_nat P)))) (@ (@ tptp.image_2486076414777270412at_nat G) (@ _let_1 (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.produc859450856879609959at_nat)) (G (-> tptp.int tptp.produc859450856879609959at_nat)) (S tptp.set_int)) (let ((_let_1 (@ tptp.inf_inf_set_int S))) (= (@ (@ tptp.image_6031046145702598900at_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Pro4507677147265585453at_nat (@ P X4)) (@ F X4)) (@ G X4)))) S) (@ (@ tptp.sup_su718114333110466843at_nat (@ (@ tptp.image_6031046145702598900at_nat F) (@ _let_1 (@ tptp.collect_int P)))) (@ (@ tptp.image_6031046145702598900at_nat G) (@ _let_1 (@ tptp.collect_int (lambda ((X4 tptp.int)) (not (@ P X4)))))))))))
% 6.81/7.13 (assert (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat D2))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) D2) (= (@ (@ tptp.image_rat_rat _let_1) (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.81/7.13 (assert (forall ((D2 tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) D2) (= (@ (@ tptp.image_rat_rat (lambda ((C4 tptp.rat)) (@ (@ tptp.divide_divide_rat C4) D2))) (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat (@ (@ tptp.divide_divide_rat A) D2)) (@ (@ tptp.divide_divide_rat B) D2))))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (B Bool) (F (-> Bool Bool))) (=> (@ (@ tptp.member_o X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3))))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (B tptp.nat) (F (-> Bool tptp.nat))) (=> (@ (@ tptp.member_o X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat F) A3))))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (B tptp.int) (F (-> Bool tptp.int))) (=> (@ (@ tptp.member_o X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (B Bool) (F (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (B tptp.int) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member_nat X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (B Bool) (F (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (B tptp.nat) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat F) A3))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (B tptp.int) (F (-> tptp.int tptp.int))) (=> (@ (@ tptp.member_int X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int F) A3))))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (B tptp.set_nat) (F (-> Bool tptp.set_nat))) (=> (@ (@ tptp.member_o X) A3) (=> (= B (@ F X)) (@ (@ tptp.member_set_nat B) (@ (@ tptp.image_o_set_nat F) A3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) (@ (@ tptp.image_nat_set_nat F) A3)) (@ P X3))) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) A3) (@ P (@ F X7)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.image_nat_nat F) A3)) (@ P X3))) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) A3) (@ P (@ F X7)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.image_nat_int F) A3)) (@ P X3))) (forall ((X7 tptp.nat)) (=> (@ (@ tptp.member_nat X7) A3) (@ P (@ F X7)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.image_int_nat F) A3)) (@ P X3))) (forall ((X7 tptp.int)) (=> (@ (@ tptp.member_int X7) A3) (@ P (@ F X7)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.int Bool))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.image_int_int F) A3)) (@ P X3))) (forall ((X7 tptp.int)) (=> (@ (@ tptp.member_int X7) A3) (@ P (@ F X7)))))))
% 6.81/7.13 (assert (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (G (-> tptp.nat tptp.set_nat))) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_nat_set_nat F) M6) (@ (@ tptp.image_nat_set_nat G) N7))))))
% 6.81/7.13 (assert (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_nat_nat F) M6) (@ (@ tptp.image_nat_nat G) N7))))))
% 6.81/7.13 (assert (forall ((M6 tptp.set_nat) (N7 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (= M6 N7) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_nat_int F) M6) (@ (@ tptp.image_nat_int G) N7))))))
% 6.81/7.13 (assert (forall ((M6 tptp.set_int) (N7 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (= M6 N7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) N7) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_int_nat F) M6) (@ (@ tptp.image_int_nat G) N7))))))
% 6.81/7.13 (assert (forall ((M6 tptp.set_int) (N7 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (= M6 N7) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) N7) (= (@ F X3) (@ G X3)))) (= (@ (@ tptp.image_int_int F) M6) (@ (@ tptp.image_int_int G) N7))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (exists ((X7 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X7) (@ (@ tptp.image_nat_set_nat F) A3)) (@ P X7))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ P (@ F X3)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (=> (exists ((X7 tptp.nat)) (and (@ (@ tptp.member_nat X7) (@ (@ tptp.image_nat_nat F) A3)) (@ P X7))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ P (@ F X3)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.int Bool))) (=> (exists ((X7 tptp.int)) (and (@ (@ tptp.member_int X7) (@ (@ tptp.image_nat_int F) A3)) (@ P X7))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ P (@ F X3)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.nat Bool))) (=> (exists ((X7 tptp.nat)) (and (@ (@ tptp.member_nat X7) (@ (@ tptp.image_int_nat F) A3)) (@ P X7))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (@ P (@ F X3)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.int Bool))) (=> (exists ((X7 tptp.int)) (and (@ (@ tptp.member_int X7) (@ (@ tptp.image_int_int F) A3)) (@ P X7))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (@ P (@ F X3)))))))
% 6.81/7.13 (assert (forall ((Z tptp.set_nat) (F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.member_set_nat Z) (@ (@ tptp.image_nat_set_nat F) A3)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (= Z (@ F X4)))))))
% 6.81/7.13 (assert (forall ((Z tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.member_nat Z) (@ (@ tptp.image_nat_nat F) A3)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (= Z (@ F X4)))))))
% 6.81/7.13 (assert (forall ((Z tptp.nat) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.member_nat Z) (@ (@ tptp.image_int_nat F) A3)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (= Z (@ F X4)))))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.member_int Z) (@ (@ tptp.image_nat_int F) A3)) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (= Z (@ F X4)))))))
% 6.81/7.13 (assert (forall ((Z tptp.int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.member_int Z) (@ (@ tptp.image_int_int F) A3)) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (= Z (@ F X4)))))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (F (-> Bool Bool))) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_o_o F) A3)))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_o_nat F) A3)))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_o_int F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (F (-> tptp.nat Bool))) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_nat_o F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_nat_nat F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.member_nat X) A3) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_nat_int F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (F (-> tptp.int Bool))) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_o (@ F X)) (@ (@ tptp.image_int_o F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_nat (@ F X)) (@ (@ tptp.image_int_nat F) A3)))))
% 6.81/7.13 (assert (forall ((X tptp.int) (A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ (@ tptp.member_int X) A3) (@ (@ tptp.member_int (@ F X)) (@ (@ tptp.image_int_int F) A3)))))
% 6.81/7.13 (assert (forall ((X Bool) (A3 tptp.set_o) (F (-> Bool tptp.set_nat))) (=> (@ (@ tptp.member_o X) A3) (@ (@ tptp.member_set_nat (@ F X)) (@ (@ tptp.image_o_set_nat F) A3)))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> Bool Bool)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_o_o F) A3)) (not (forall ((X3 Bool)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_o X3) A3))))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> tptp.nat Bool)) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_nat_o F) A3)) (not (forall ((X3 tptp.nat)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_nat X3) A3))))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> tptp.int Bool)) (A3 tptp.set_int)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_int_o F) A3)) (not (forall ((X3 tptp.int)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_int X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> Bool tptp.nat)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_o_nat F) A3)) (not (forall ((X3 Bool)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_o X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_nat_nat F) A3)) (not (forall ((X3 tptp.nat)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_nat X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.image_int_nat F) A3)) (not (forall ((X3 tptp.int)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_int X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> Bool tptp.int)) (A3 tptp.set_o)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_o_int F) A3)) (not (forall ((X3 Bool)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_o X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_nat_int F) A3)) (not (forall ((X3 tptp.nat)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_nat X3) A3))))))))
% 6.81/7.13 (assert (forall ((B tptp.int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.image_int_int F) A3)) (not (forall ((X3 tptp.int)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_int X3) A3))))))))
% 6.81/7.13 (assert (forall ((B Bool) (F (-> tptp.set_nat Bool)) (A3 tptp.set_set_nat)) (=> (@ (@ tptp.member_o B) (@ (@ tptp.image_set_nat_o F) A3)) (not (forall ((X3 tptp.set_nat)) (=> (= B (@ F X3)) (not (@ (@ tptp.member_set_nat X3) A3))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_nat_nat F) (@ (@ tptp.image_nat_nat G) A3)) (@ (@ tptp.image_nat_nat (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.image_nat_nat F) (@ (@ tptp.image_int_nat G) A3)) (@ (@ tptp.image_int_nat (lambda ((X4 tptp.int)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_nat_int F) (@ (@ tptp.image_nat_nat G) A3)) (@ (@ tptp.image_nat_int (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.image_nat_int F) (@ (@ tptp.image_int_nat G) A3)) (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_int_nat F) (@ (@ tptp.image_nat_int G) A3)) (@ (@ tptp.image_nat_nat (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.image_int_nat F) (@ (@ tptp.image_int_int G) A3)) (@ (@ tptp.image_int_nat (lambda ((X4 tptp.int)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_int_int F) (@ (@ tptp.image_nat_int G) A3)) (@ (@ tptp.image_nat_int (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.image_int_int F) (@ (@ tptp.image_int_int G) A3)) (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.set_nat tptp.nat)) (G (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_set_nat_nat F) (@ (@ tptp.image_nat_set_nat G) A3)) (@ (@ tptp.image_nat_nat (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.set_nat tptp.int)) (G (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.image_set_nat_int F) (@ (@ tptp.image_nat_set_nat G) A3)) (@ (@ tptp.image_nat_int (lambda ((X4 tptp.nat)) (@ F (@ G X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> Bool Bool)) (A3 tptp.set_o) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) (@ (@ tptp.image_o_o F) A3)) (@ P X4)))) (@ (@ tptp.image_o_o F) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat Bool)) (A3 tptp.set_nat) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) (@ (@ tptp.image_nat_o F) A3)) (@ P X4)))) (@ (@ tptp.image_nat_o F) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int Bool)) (A3 tptp.set_int) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) (@ (@ tptp.image_int_o F) A3)) (@ P X4)))) (@ (@ tptp.image_int_o F) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.nat)) (A3 tptp.set_o) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.image_o_nat F) A3)) (@ P X4)))) (@ (@ tptp.image_o_nat F) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.image_nat_nat F) A3)) (@ P X4)))) (@ (@ tptp.image_nat_nat F) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.nat Bool))) (= (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.image_int_nat F) A3)) (@ P X4)))) (@ (@ tptp.image_int_nat F) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.int)) (A3 tptp.set_o) (P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.image_o_int F) A3)) (@ P X4)))) (@ (@ tptp.image_o_int F) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.image_nat_int F) A3)) (@ P X4)))) (@ (@ tptp.image_nat_int F) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.int Bool))) (= (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.image_int_int F) A3)) (@ P X4)))) (@ (@ tptp.image_int_int F) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.list_nat Bool)) (A3 tptp.set_list_nat) (P (-> Bool Bool))) (= (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) (@ (@ tptp.image_list_nat_o F) A3)) (@ P X4)))) (@ (@ tptp.image_list_nat_o F) (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ (@ tptp.member_list_nat X4) A3) (@ P (@ F X4)))))))))
% 6.81/7.13 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M5 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K2) M5)))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat B3) (@ (@ tptp.image_nat_set_nat F) A3)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A3) (= B3 (@ (@ tptp.image_nat_set_nat F) AA)))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_nat_nat F) A3)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A3) (= B3 (@ (@ tptp.image_nat_nat F) AA)))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_int_nat F) A3)) (exists ((AA tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int AA) A3) (= B3 (@ (@ tptp.image_int_nat F) AA)))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_int) (F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_nat_int F) A3)) (exists ((AA tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat AA) A3) (= B3 (@ (@ tptp.image_nat_int F) AA)))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_int_int F) A3)) (exists ((AA tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int AA) A3) (= B3 (@ (@ tptp.image_int_int F) AA)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (B3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_nat_set_nat F) A3)) B3) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (@ (@ tptp.member_set_nat (@ F X4)) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A3)) B3) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (@ (@ tptp.member_nat (@ F X4)) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat F) A3)) B3) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (@ (@ tptp.member_nat (@ F X4)) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int F) A3)) B3) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (@ (@ tptp.member_int (@ F X4)) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int F) A3)) B3) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (@ (@ tptp.member_int (@ F X4)) B3))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B3) (@ (@ tptp.image_nat_set_nat F) A3)) (not (forall ((C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C5) A3) (not (= B3 (@ (@ tptp.image_nat_set_nat F) C5)))))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_nat_nat F) A3)) (not (forall ((C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C5) A3) (not (= B3 (@ (@ tptp.image_nat_nat F) C5)))))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_int_nat F) A3)) (not (forall ((C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C5) A3) (not (= B3 (@ (@ tptp.image_int_nat F) C5)))))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_int) (F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_nat_int F) A3)) (not (forall ((C5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat C5) A3) (not (= B3 (@ (@ tptp.image_nat_int F) C5)))))))))
% 6.81/7.13 (assert (forall ((B3 tptp.set_int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_int_int F) A3)) (not (forall ((C5 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int C5) A3) (not (= B3 (@ (@ tptp.image_int_int F) C5)))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool Bool)) (B3 tptp.set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_o_o F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_o_nat F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_nat_o F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_int_o F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int)) (B3 tptp.set_int)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_int (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_o_int F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int)) (B3 tptp.set_int)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.member_int (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int)) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.member_int (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.set_nat)) (B3 tptp.set_set_nat)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.member_set_nat (@ F X3)) B3))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.image_o_set_nat F) A3)) B3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_le6893508408891458716et_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.image_nat_nat F))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.image_nat_int F))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.image_int_nat F))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.image_int_int F))) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.sup_sup_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_int F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_sup_set_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.produc859450856879609959at_nat tptp.nat)) (A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (let ((_let_1 (@ tptp.image_6160980552072806642at_nat F))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.produc859450856879609959at_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_3276603626957510736at_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_su718114333110466843at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.produc4166570645942440679at_nat tptp.nat)) (A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (let ((_let_1 (@ tptp.image_6009382790362589554at_nat F))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.produc3843707927480180839at_nat tptp.nat)) (A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (let ((_let_1 (@ tptp.image_3198525501578754290at_nat F))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.sup_sup_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.produc4166570645942440679at_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_5319605298250079696at_nat F))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.sup_su3035147773818789531at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_nat_o F) (@ tptp.collect_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat F) (@ tptp.collect_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_int_o F) (@ tptp.collect_int P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat F) (@ tptp.collect_int P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int)) (B3 tptp.set_int)) (=> (forall ((X3 tptp.nat)) (=> (@ P X3) (@ (@ tptp.member_int (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int F) (@ tptp.collect_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int Bool)) (F (-> tptp.int tptp.int)) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (@ P X3) (@ (@ tptp.member_int (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int F) (@ tptp.collect_int P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (F (-> tptp.list_nat Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.list_nat)) (=> (@ P X3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_list_nat_o F) (@ tptp.collect_list_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.list_nat Bool)) (F (-> tptp.list_nat tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.list_nat)) (=> (@ P X3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_list_nat_nat F) (@ tptp.collect_list_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.set_nat Bool)) (F (-> tptp.set_nat Bool)) (B3 tptp.set_o)) (=> (forall ((X3 tptp.set_nat)) (=> (@ P X3) (@ (@ tptp.member_o (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_o (@ (@ tptp.image_set_nat_o F) (@ tptp.collect_set_nat P))) B3))))
% 6.81/7.13 (assert (forall ((P (-> tptp.set_nat Bool)) (F (-> tptp.set_nat tptp.nat)) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (@ P X3) (@ (@ tptp.member_nat (@ F X3)) B3))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_set_nat_nat F) (@ tptp.collect_set_nat P))) B3))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.int tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li tptp.int)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_int)) (=> (= (@ tptp.size_size_list_int L4) N2) (not (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (@ (@ P (@ (@ tptp.nth_int L4) I)) I))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li tptp.nat)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat L4) N2) (not (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (@ (@ P (@ (@ tptp.nth_nat L4) I)) I))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> Bool tptp.nat Bool))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (exists ((Li Bool)) (@ (@ P Li) I3)))) (not (forall ((L4 tptp.list_o)) (=> (= (@ tptp.size_size_list_o L4) N2) (not (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N2) (@ (@ P (@ (@ tptp.nth_o L4) I)) I))))))))))
% 6.81/7.13 (assert (= (lambda ((Y5 tptp.list_int) (Z3 tptp.list_int)) (= Y5 Z3)) (lambda ((Xs3 tptp.list_int) (Ys2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I4) (@ (@ tptp.nth_int Ys2) I4))))))))
% 6.81/7.13 (assert (= (lambda ((Y5 tptp.list_nat) (Z3 tptp.list_nat)) (= Y5 Z3)) (lambda ((Xs3 tptp.list_nat) (Ys2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I4) (@ (@ tptp.nth_nat Ys2) I4))))))))
% 6.81/7.13 (assert (= (lambda ((Y5 tptp.list_o) (Z3 tptp.list_o)) (= Y5 Z3)) (lambda ((Xs3 tptp.list_o) (Ys2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys2)) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I4) (@ (@ tptp.nth_o Ys2) I4))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X11 tptp.int)) (@ (@ P I4) X11)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_int Xs3) I4)))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X11 tptp.nat)) (@ (@ P I4) X11)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_nat Xs3) I4)))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (exists ((X11 Bool)) (@ (@ P I4) X11)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) K) (@ (@ P I4) (@ (@ tptp.nth_o Xs3) I4)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int) (Ys3 tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys3)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I3) (@ (@ tptp.nth_int Ys3) I3)))) (= Xs Ys3)))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat) (Ys3 tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys3)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I3) (@ (@ tptp.nth_nat Ys3) I3)))) (= Xs Ys3)))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o) (Ys3 tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys3)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I3) (@ (@ tptp.nth_o Ys3) I3)))) (= Xs Ys3)))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat F))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.inf_inf_set_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat F))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.product_prod_nat_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_5846123807819985514at_nat F))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.nat)) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.image_2486076414777270412at_nat F))) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))) (@ (@ tptp.inf_inf_set_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.image_5168914502847457605at_nat F))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))) (@ (@ tptp.inf_in2572325071724192079at_nat (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int F))) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.inf_inf_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_int F))) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.inf_inf_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.int)) (A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.image_2483585944268220136at_int F))) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))) (@ (@ tptp.inf_inf_set_int (@ _let_1 A3)) (@ _let_1 B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_set_nat F))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_nat F))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_nat F))) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int F))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.image_nat_int F))) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (@ P M3))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N2) (@ P M3))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr7098220151150636591it_nat)) (not (@ (@ tptp.member1310632352865511136it_nat tptp.none_P2651198173097904984it_nat) (@ (@ tptp.image_2003495143432273353it_nat tptp.some_P7913643980934408916it_nat) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_num)) (not (@ (@ tptp.member_option_num tptp.none_num) (@ (@ tptp.image_num_option_num tptp.some_num) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1354866905816374718it_nat)) (not (@ (@ tptp.member5596548051065438575it_nat tptp.none_P9117596204409417319it_nat) (@ (@ tptp.image_3455408117458022631it_nat tptp.some_P1914260805536162275it_nat) A3)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_int (@ tptp.rotate1_int Xs)) N2) (@ (@ tptp.nth_int Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_nat (@ tptp.rotate1_nat Xs)) N2) (@ (@ tptp.nth_nat Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ (@ tptp.nth_o (@ tptp.rotate1_o Xs)) N2) (@ (@ tptp.nth_o Xs) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((C tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.image_rat_rat _let_1) (@ (@ tptp.set_or633870826150836451st_rat X) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_rat X) Y))) (let ((_let_4 (@ _let_1 X))) (let ((_let_5 (@ _let_1 Y))) (let ((_let_6 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (and (=> _let_6 (= _let_2 (@ (@ tptp.set_or633870826150836451st_rat _let_4) _let_5))) (=> (not _let_6) (and (=> _let_3 (= _let_2 (@ (@ tptp.set_or633870826150836451st_rat _let_5) _let_4))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_rat)))))))))))))
% 6.81/7.13 (assert (= tptp.nat_prod_decode_aux (lambda ((K3 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K3))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K3)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K3) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 6.81/7.13 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X) Xa)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4439495888332055232nt_int (@ (@ tptp.product_int_int Xs) Ys3)) N2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8617346907841251940nt_nat (@ (@ tptp.product_int_nat Xs) Ys3)) N2) (@ (@ tptp.product_Pair_int_nat (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_int Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7514405829937366042_int_o (@ (@ tptp.product_int_o Xs) Ys3)) N2) (@ (@ tptp.product_Pair_int_o (@ (@ tptp.nth_int Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.product_nat_int Xs) Ys3)) N2) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.product_nat_nat Xs) Ys3)) N2) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs) Ys3)) N2) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys3)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys3)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys3 tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys3)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (Xs tptp.list_a) (Ys3 tptp.list_P131111800688179804it_nat)) (let ((_let_1 (@ tptp.size_s341701280123345136it_nat Ys3))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_a Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8687047199098054322it_nat (@ (@ tptp.produc6966004487978991557it_nat Xs) Ys3)) N2) (@ (@ tptp.produc9178034014595674355it_nat (@ (@ tptp.nth_a Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_Pr4561283279332054789it_nat Ys3) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (T5 tptp.set_rat)) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) (@ tptp.uminus2201863774496077783et_rat T5)) (@ tptp.uminus2201863774496077783et_rat (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (T5 tptp.set_int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) (@ tptp.uminus1532241313380277803et_int T5)) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) (@ (@ tptp.minus_minus_set_rat S2) T5)) (@ (@ tptp.minus_minus_set_rat (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) S2)) (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) (@ (@ tptp.minus_minus_set_int S2) T5)) (@ (@ tptp.minus_minus_set_int (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) S2)) (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (= (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) (@ (@ tptp.inf_inf_set_rat S2) T5)) (@ (@ tptp.inf_inf_set_rat (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) S2)) (@ (@ tptp.image_rat_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.minus_minus_rat X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (= (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) (@ (@ tptp.inf_inf_set_int S2) T5)) (@ (@ tptp.inf_inf_set_int (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) S2)) (@ (@ tptp.image_int_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int X4) A))) T5)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups7501900531339628137nteger G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_z3403309356797280102nteger)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6857163185585827899at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A3)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) A))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) A))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) _let_1)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6857163185585827899at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.groups6857163185585827899at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G M)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ (@ tptp.groups7501900531339628137nteger _let_1) I5))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I5))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I4)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups7501900531339628137nteger F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ F A5)) __flatten_var_0))) A) B) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.multis2468970476368604999at_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6857163185585827899at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo4497565046347964853at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.multis2468970476368604999at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ F A5)) __flatten_var_0))) A) B) tptp.zero_z1048942125864253310at_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A5)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6857163185585827899at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X)))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (S2 tptp.set_rat) (T5 tptp.set_rat)) (let ((_let_1 (@ tptp.image_rat_rat (@ tptp.plus_plus_rat A)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_rat S2) T5)) (@ (@ tptp.inf_inf_set_rat (@ _let_1 S2)) (@ _let_1 T5))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (S2 tptp.set_int) (T5 tptp.set_int)) (let ((_let_1 (@ tptp.image_int_int (@ tptp.plus_plus_int A)))) (= (@ _let_1 (@ (@ tptp.inf_inf_set_int S2) T5)) (@ (@ tptp.inf_inf_set_int (@ _let_1 S2)) (@ _let_1 T5))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A3))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ tptp.abs_abs_int (@ F I4)))) A3))))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.code_integer))) (= (@ (@ tptp.groups4406642042086082107nteger G) tptp.bot_bot_set_o) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.rat))) (= (@ (@ tptp.groups7872700643590313910_o_rat G) tptp.bot_bot_set_o) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.nat))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) tptp.bot_bot_set_o) tptp.zero_zero_nat)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.int))) (= (@ (@ tptp.groups8505340233167759370_o_int G) tptp.bot_bot_set_o) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.code_integer))) (= (@ (@ tptp.groups7501900531339628137nteger G) tptp.bot_bot_set_nat) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.code_integer))) (= (@ (@ tptp.groups7873554091576472773nteger G) tptp.bot_bot_set_int) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.code_integer)) (A (-> Bool tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups4406642042086082107nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o 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.groups4406642042086082107nteger (lambda ((I4 Bool)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (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 ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (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 ((I4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (A (-> Bool tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o 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.groups7872700643590313910_o_rat (lambda ((I4 Bool)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (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 ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (A (-> tptp.int tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat X) I5) tptp.one_one_rat) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int 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.groups3906332499630173760nt_rat (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_rat (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.int)) (A (-> Bool tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I3)))) (=> (= (@ (@ tptp.groups8505340233167759370_o_int X) I5) tptp.one_one_int) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups8505340233167759370_o_int (lambda ((I4 Bool)) (@ (@ tptp.times_times_int (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.int)) (A (-> tptp.nat tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I3)))) (=> (= (@ (@ tptp.groups3539618377306564664at_int X) I5) tptp.one_one_int) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.int)) (A (-> tptp.int tptp.int)) (B tptp.int) (Delta tptp.int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ X I3)))) (=> (= (@ (@ tptp.groups4538972089207619220nt_int X) I5) tptp.one_one_int) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ A I3)) B))) Delta))) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.times_times_int (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_set_nat) (X (-> tptp.set_nat tptp.code_integer)) (A (-> tptp.set_nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I3)))) (=> (= (@ (@ tptp.groups9190459664516455967nteger X) I5) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.set_nat)) (=> (@ (@ tptp.member_set_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.groups9190459664516455967nteger (lambda ((I4 tptp.set_nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I4)) (@ X I4)))) I5)) B))) Delta))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A5 tptp.int)) (@ tptp.abs_abs_int (@ F A5)))) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((A5 tptp.int)) (@ tptp.abs_abs_int (@ F A5)))) A3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu2 tptp.nat)) tptp.zero_zero_nat)) A3) tptp.zero_zero_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu2 tptp.int)) tptp.zero_zero_int)) A3) tptp.zero_zero_int)))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A3) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A3)) (@ (@ tptp.groups977919841031483927at_nat G) A3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.nat)) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) (@ (@ tptp.groups8507830703676809646_o_nat G) A3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A3) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A3)) (@ (@ tptp.groups8294997508430121362at_nat G) A3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G) A3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat (@ G X3)) (@ F X3)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G) A3))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A3) (@ tptp.suc N2)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G I4)) B3))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B3 tptp.set_int) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (@ G I4)) B3))) A3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) K5)) (@ (@ tptp.groups7872700643590313910_o_rat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) K5)) (@ (@ tptp.groups8507830703676809646_o_nat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) K5)) (@ (@ tptp.groups8505340233167759370_o_int G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) K5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) K5)) (@ (@ tptp.groups3542108847815614940at_nat G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) K5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups4538972089207619220nt_int F) K5)) (@ (@ tptp.groups4538972089207619220nt_int G) K5)))))
% 6.81/7.13 (assert (forall ((K5 tptp.set_set_nat) (F (-> tptp.set_nat tptp.rat)) (G (-> tptp.set_nat tptp.rat))) (=> (forall ((I3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat I3) K5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7659867448343625626at_rat F) K5)) (@ (@ tptp.groups7659867448343625626at_rat G) K5)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X4)) (@ H X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A3)) (@ (@ tptp.groups3542108847815614940at_nat H) A3)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X4)) (@ H X4)))) A3) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A3)) (@ (@ tptp.groups4538972089207619220nt_int H) A3)))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I4)) (@ G J3)))) B3))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I4)) (@ G J3)))) B3))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (R3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) R3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F N)) R3))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (R3 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) R3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int (@ F N)) R3))) A3))))
% 6.81/7.13 (assert (forall ((R3 tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R3) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat R3) (@ F N)))) A3))))
% 6.81/7.13 (assert (forall ((R3 tptp.int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.times_times_int R3) (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N tptp.int)) (@ (@ tptp.times_times_int R3) (@ F N)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X4)) (@ G X4)))) A3) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int G) A3)))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.uminus_uminus_int (@ F X4)))) A3) (@ tptp.uminus_uminus_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups4406642042086082107nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7501900531339628137nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7873554091576472773nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups7872700643590313910_o_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups8507830703676809646_o_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups8505340233167759370_o_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups3539618377306564664at_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups4406642042086082107nteger F) A3)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) A3)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) A3)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) tptp.zero_zero_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_int (@ F X3)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups8505340233167759370_o_int F) A3)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_int (@ F X3)) tptp.zero_zero_int))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) A3)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat K3)) A)) tptp.one_one_rat)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (N2 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 N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X)))))))))))
% 6.81/7.13 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M3) N)) (@ (@ tptp.modulo_modulo_nat M3) N)))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_o) (X Bool)) (let ((_let_1 (@ tptp.nth_o L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o L)) (=> (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) L) (=> (@ (@ tptp.ord_less_eq_o (@ _let_1 I2)) X) (=> (@ (@ tptp.ord_less_o X) (@ _let_1 J)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.nth_o L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K2) (=> (@ (@ tptp.ord_less_nat K2) J) (=> (@ (@ tptp.ord_less_eq_o (@ _let_1 K2)) X) (not (@ (@ tptp.ord_less_o X) (@ _let_1 (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))))))))))))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_rat) (X tptp.rat)) (let ((_let_1 (@ tptp.nth_rat L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_rat L)) (=> (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) L) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 I2)) X) (=> (@ (@ tptp.ord_less_rat X) (@ _let_1 J)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.nth_rat L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K2) (=> (@ (@ tptp.ord_less_nat K2) J) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 K2)) X) (not (@ (@ tptp.ord_less_rat X) (@ _let_1 (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))))))))))))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_num) (X tptp.num)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num L)) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) L) (=> (@ (@ tptp.ord_less_eq_num (@ _let_1 I2)) X) (=> (@ (@ tptp.ord_less_num X) (@ _let_1 J)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.nth_num L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K2) (=> (@ (@ tptp.ord_less_nat K2) J) (=> (@ (@ tptp.ord_less_eq_num (@ _let_1 K2)) X) (not (@ (@ tptp.ord_less_num X) (@ _let_1 (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))))))))))))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat L)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) L) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) X) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 J)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K2) (=> (@ (@ tptp.ord_less_nat K2) J) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 K2)) X) (not (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))))))))))))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (L tptp.list_int) (X tptp.int)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int L)) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) L) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 I2)) X) (=> (@ (@ tptp.ord_less_int X) (@ _let_1 J)) (not (forall ((K2 tptp.nat)) (let ((_let_1 (@ tptp.nth_int L))) (=> (@ (@ tptp.ord_less_eq_nat I2) K2) (=> (@ (@ tptp.ord_less_nat K2) J) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 K2)) X) (not (@ (@ tptp.ord_less_int X) (@ _let_1 (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat)))))))))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_rat A) _let_1) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri773545260158071498ct_rat _let_1))))))
% 6.81/7.13 (assert (forall ((A tptp.code_natural) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinom7368847122466276068atural A) _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.groups2279045934846249631atural (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural A) (@ tptp.semiri3763490453095760265atural I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri2447717529341329178atural _let_1))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinom8545251970709558553nteger A) _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.semiri4939895301339042750nteger I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri3624122377584611663nteger _let_1))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_nat A) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1408675320244567234ct_nat _let_1))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.gbinomial_int A) _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K))) (@ tptp.semiri1406184849735516958ct_int _let_1))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) A)) K3)) (@ (@ tptp.power_power_rat X) K3))) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat (@ tptp.uminus_uminus_rat A)) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.81/7.13 (assert (forall ((I2 Bool) (K Bool)) (= (@ (@ tptp.member_o I2) (@ tptp.set_ord_atMost_o K)) (@ (@ tptp.ord_less_eq_o I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or4236626031148496127et_nat K)) (@ (@ tptp.ord_less_eq_set_nat I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ tptp.set_or58775011639299419et_int K)) (@ (@ tptp.ord_less_eq_set_int I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_atMost_rat K)) (@ (@ tptp.ord_less_eq_rat I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_atMost_num K)) (@ (@ tptp.ord_less_eq_num I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_atMost_nat K)) (@ (@ tptp.ord_less_eq_nat I2) K))))
% 6.81/7.13 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_atMost_int K)) (@ (@ tptp.ord_less_eq_int I2) K))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu2 tptp.nat)) tptp.one_one_nat)) A3) tptp.one_one_nat)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu2 tptp.nat)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu2 tptp.int)) tptp.one_one_int)) A3) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((X4 tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups705719431365010083at_int F) A3)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups705719431365010083at_int F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.ring_1_of_int_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.groups1705073143266064639nt_int F) A3)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_rat (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.ring_1_of_int_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.code_integer))) (= (@ (@ tptp.groups7694694392188491536nteger G) tptp.bot_bot_set_o) tptp.one_one_Code_integer)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.assn))) (= (@ (@ tptp.groups5301882518646026715o_assn G) tptp.bot_bot_set_o) tptp.one_one_assn)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.rat))) (= (@ (@ tptp.groups2869687844427037835_o_rat G) tptp.bot_bot_set_o) tptp.one_one_rat)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.nat))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) tptp.bot_bot_set_o) tptp.one_one_nat)))
% 6.81/7.13 (assert (forall ((G (-> Bool tptp.int))) (= (@ (@ tptp.groups3502327434004483295_o_int G) tptp.bot_bot_set_o) tptp.one_one_int)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.code_integer))) (= (@ (@ tptp.groups3455450783089532116nteger G) tptp.bot_bot_set_nat) tptp.one_one_Code_integer)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.assn))) (= (@ (@ tptp.groups6906906614972039071t_assn G) tptp.bot_bot_set_nat) tptp.one_one_assn)))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups73079841787564623at_rat G) tptp.bot_bot_set_nat) tptp.one_one_rat)))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.code_integer))) (= (@ (@ tptp.groups3827104343326376752nteger G) tptp.bot_bot_set_int) tptp.one_one_Code_integer)))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.assn))) (= (@ (@ tptp.groups7882442080178216443t_assn G) tptp.bot_bot_set_int) tptp.one_one_assn)))
% 6.81/7.13 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((L tptp.set_int) (H tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H)) (@ (@ tptp.ord_less_eq_set_int H) H3)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (H tptp.code_integer) (H3 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger L) H)) (@ tptp.set_or9101266186257409494nteger H3)) (or (not (@ (@ tptp.ord_le3102999989581377725nteger L) H)) (@ (@ tptp.ord_le3102999989581377725nteger H) H3)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_assn (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_rat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_Code_integer)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_assn)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_assn (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ G I4)) B3))) A3) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (B3 tptp.set_nat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ G I4)) B3))) A3) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int tptp.int)) (B3 tptp.set_int) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I4)) B3))) A3) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.nat tptp.int)) (B3 tptp.set_nat) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups705719431365010083at_int (@ G I4)) B3))) A3) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.int tptp.int)) (B3 tptp.set_int) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (@ G I4)) B3))) A3) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ G I4) J3))) A3))) B3))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (@ (@ tptp.sorted_wrt_nat (lambda ((Uu2 tptp.nat) (Uv tptp.nat)) true)) Xs)))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (@ (@ tptp.sorted_wrt_int (lambda ((Uu2 tptp.int) (Uv tptp.int)) true)) Xs)))
% 6.81/7.13 (assert (forall ((H Bool)) (not (= tptp.bot_bot_set_o (@ tptp.set_ord_atMost_o H)))))
% 6.81/7.13 (assert (forall ((H tptp.nat)) (not (= tptp.bot_bot_set_nat (@ tptp.set_ord_atMost_nat H)))))
% 6.81/7.13 (assert (forall ((H tptp.int)) (not (= tptp.bot_bot_set_int (@ tptp.set_ord_atMost_int H)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_nat (@ G X4)) (@ H X4)))) A3) (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) A3)) (@ (@ tptp.groups708209901874060359at_nat H) A3)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ G X4)) (@ H X4)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) A3)) (@ (@ tptp.groups705719431365010083at_int H) A3)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_int (@ G X4)) (@ H X4)))) A3) (@ (@ tptp.times_times_int (@ (@ tptp.groups1705073143266064639nt_int G) A3)) (@ (@ tptp.groups1705073143266064639nt_int H) A3)))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.power_power_nat (@ F X4)) N2))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A3)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.power_power_int (@ F X4)) N2))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ (@ tptp.power_power_int (@ F X4)) N2))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I4)) A))) A3)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) A))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (A3 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups705719431365010083at_int F) A3)) A))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int (lambda ((I4 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I4)) A))) A3)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups1705073143266064639nt_int F) A3)) A))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_3573771949741848930nteger (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_assn (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) U2))))))
% 6.81/7.13 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) U2))))))
% 6.81/7.13 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) U2))))))
% 6.81/7.13 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) U2))))))
% 6.81/7.13 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) U2))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat)) (=> (@ (@ tptp.sorted_wrt_rat tptp.ord_less_rat) Xs) (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num)) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_num) Xs) (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Xs) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) Xs) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A3)) (@ (@ tptp.groups7694694392188491536nteger G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A3)) (@ (@ tptp.groups3455450783089532116nteger G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) (@ G I3)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A3)) (@ (@ tptp.groups3827104343326376752nteger G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A3)) (@ (@ tptp.groups2869687844427037835_o_rat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A3)) (@ (@ tptp.groups73079841787564623at_rat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A3)) (@ (@ tptp.groups1072433553688619179nt_rat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A3)) (@ (@ tptp.groups3504817904513533571_o_nat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1707563613775114915nt_nat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3502327434004483295_o_int F) A3)) (@ (@ tptp.groups3502327434004483295_o_int G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) (@ G I3)))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat G) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups705719431365010083at_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.groups1705073143266064639nt_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups7694694392188491536nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F X3)))) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups2869687844427037835_o_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F X3)))) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups3504817904513533571_o_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F X3)))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ (@ tptp.groups3502327434004483295_o_int F) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ F X3)))) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((C tptp.nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_nat C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_nat C) (@ F A5)))) A3))))
% 6.81/7.13 (assert (forall ((C tptp.int) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((A5 tptp.nat)) (@ (@ tptp.power_power_int C) (@ F A5)))) A3))))
% 6.81/7.13 (assert (forall ((C tptp.int) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ (@ tptp.power_power_int C) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((A5 tptp.int)) (@ (@ tptp.power_power_int C) (@ F A5)))) A3))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7694694392188491536nteger F) A3)) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3455450783089532116nteger F) A3)) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le3102999989581377725nteger _let_1) tptp.one_one_Code_integer))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups3827104343326376752nteger F) A3)) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A3) (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.groups2869687844427037835_o_rat F) A3)) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups73079841787564623at_rat F) A3)) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A3)) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A3)) tptp.one_one_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X3 tptp.int)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_int X3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) tptp.one_one_nat))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (forall ((X3 Bool)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_o X3) A3) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) tptp.one_one_int))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3502327434004483295_o_int F) A3)) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (@ F X3))) (=> (@ (@ tptp.member_nat X3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_eq_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) tptp.one_one_nat))))
% 6.81/7.13 (assert (= tptp.sorted_wrt_int (lambda ((P4 (-> tptp.int tptp.int Bool)) (Xs3 tptp.list_int)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_int Xs3)) (@ (@ P4 (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (= tptp.sorted_wrt_nat (lambda ((P4 (-> tptp.nat tptp.nat Bool)) (Xs3 tptp.list_nat)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_nat Xs3)) (@ (@ P4 (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (= tptp.sorted_wrt_o (lambda ((P4 (-> Bool Bool Bool)) (Xs3 tptp.list_o)) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs3))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_o Xs3)) (@ (@ P4 (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.int tptp.int Bool)) (Xs tptp.list_int) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int P) Xs) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ P (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (Xs tptp.list_nat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat P) Xs) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ P (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((P (-> Bool Bool Bool)) (Xs tptp.list_o) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.sorted_wrt_o P) Xs) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (@ (@ P (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_int P) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_nat P) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool Bool))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_o P) Xs))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) _let_1)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) _let_1)))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_Code_integer (= J3 K)) tptp.one_one_Code_integer) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.assn)) (H (-> tptp.nat tptp.assn))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_assn (= J3 K)) tptp.one_one_assn) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_assn (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.one_one_rat) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.one_one_nat) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.one_one_int) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_rat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_num Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs)) tptp.one_one_nat) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3455450783089532116nteger G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6906906614972039071t_assn G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_assn (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_rat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_3573771949741848930nteger (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_assn (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.times_times_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_assn (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups3455450783089532116nteger G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_3573771949741848930nteger (@ G M)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_assn (@ (@ tptp.groups6906906614972039071t_assn G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_assn (@ G M)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G M)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups708209901874060359at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups705719431365010083at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) _let_1)))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I4)) (@ F (@ tptp.suc I4))))) (@ tptp.set_ord_atMost_nat I2)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F (@ tptp.suc I2))))))
% 6.81/7.13 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.81/7.13 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.81/7.13 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1084959871951514735nteger (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.assn)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1959793692361082170t_assn (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.assn)) (@ (@ tptp.times_times_assn (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_assn))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_nat))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A5 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ F A5)) __flatten_var_0))) A) B) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat)) (let ((_let_1 (@ tptp.suc I4))) (let ((_let_2 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_nat _let_1) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_2 I4)) (@ _let_2 _let_1)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int) (I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I2)) (@ _let_1 J))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_o)) (= (@ (@ tptp.sorted_wrt_o tptp.ord_less_eq_o) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.ord_less_eq_o (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_rat)) (= (@ (@ tptp.sorted_wrt_rat tptp.ord_less_eq_rat) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_rat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_rat Xs)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_num)) (= (@ (@ tptp.sorted_wrt_num tptp.ord_less_eq_num) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_num Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_num Xs)) (@ (@ tptp.ord_less_eq_num (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_nat)) (= (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_nat Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((Xs tptp.list_int)) (= (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) Xs) (forall ((I4 tptp.nat) (J3 tptp.nat)) (let ((_let_1 (@ tptp.nth_int Xs))) (=> (@ (@ tptp.ord_less_eq_nat I4) J3) (=> (@ (@ tptp.ord_less_nat J3) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.ord_less_eq_int (@ _let_1 I4)) (@ _let_1 J3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_assn (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_rat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_nat (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (let ((_let_2 (@ _let_1 P3))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups705719431365010083at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.times_times_int (@ _let_4 (@ _let_5 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (N2 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 N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((X tptp.rat) (N2 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 N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 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 M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.81/7.13 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.81/7.13 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.81/7.13 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.81/7.13 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat A) tptp.one_one_rat)) M)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger A) (@ tptp.suc N2)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N2) I4))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_Code_integer (= J3 K)) tptp.zero_z3403309356797280102nteger) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (H (-> tptp.nat tptp.multis2468970476368604999at_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups6857163185585827899at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (= J3 K)) tptp.zero_z1048942125864253310at_nat) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_mul8430962117462786573at_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_rat (= J3 K)) tptp.zero_zero_rat) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_int (= J3 K)) tptp.zero_zero_int) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((P3 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) P3) (=> (@ (@ tptp.ord_less_eq_nat K) P3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ (@ (@ tptp.if_nat (= J3 K)) tptp.zero_zero_nat) (@ H (@ (@ tptp.minus_minus_nat J3) (@ tptp.suc tptp.zero_zero_nat))))))) (@ tptp.set_ord_atMost_nat P3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat J3) K)) (@ G J3)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P3) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) I4)) (@ tptp.semiri681578069525770553at_rat I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) I4)) (@ tptp.semiri1314217659103216013at_int I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I4)) (@ tptp.semiri4939895301339042750nteger I4))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I4))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.comm_s4028243227959126397er_rat Z) _let_2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat _let_1)))) _let_2)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat K3)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D2 (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A3) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D2 tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4))) (@ D2 I4)))) A3) tptp.zero_zero_rat))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (Xs tptp.list_int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_Pr3440142176431000676at_int (@ (@ tptp.enumerate_int N2) Xs)) M) (@ (@ tptp.product_Pair_nat_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.nth_int Xs) M))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (Xs tptp.list_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_Pr7617993195940197384at_nat (@ (@ tptp.enumerate_nat N2) Xs)) M) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.nth_nat Xs) M))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (Xs tptp.list_o) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.enumerate_o N2) Xs)) M) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.nth_o Xs) M))))))
% 6.81/7.13 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri773545260158071498ct_rat K3)))))
% 6.81/7.13 (assert (= tptp.gbinom7368847122466276068atural (lambda ((A5 tptp.code_natural) (K3 tptp.nat)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.groups2279045934846249631atural (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_7197305767214868737atural A5) (@ tptp.semiri3763490453095760265atural I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri2447717529341329178atural K3)))))
% 6.81/7.13 (assert (= tptp.gbinom8545251970709558553nteger (lambda ((A5 tptp.code_integer) (K3 tptp.nat)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_8373710615458151222nteger A5) (@ tptp.semiri4939895301339042750nteger I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri3624122377584611663nteger K3)))))
% 6.81/7.13 (assert (= tptp.gbinomial_nat (lambda ((A5 tptp.nat) (K3 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat A5) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1408675320244567234ct_nat K3)))))
% 6.81/7.13 (assert (= tptp.gbinomial_int (lambda ((A5 tptp.int) (K3 tptp.nat)) (@ (@ tptp.divide_divide_int (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int A5) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3))) (@ tptp.semiri1406184849735516958ct_int K3)))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.13 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.81/7.13 (assert (forall ((I2 Bool) (L Bool) (U Bool)) (= (@ (@ tptp.member_o I2) (@ (@ tptp.set_or7139685690850216873Than_o L) U)) (and (@ (@ tptp.ord_less_eq_o L) I2) (@ (@ tptp.ord_less_o I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ (@ tptp.set_or3540276404033026485et_nat L) U)) (and (@ (@ tptp.ord_less_eq_set_nat L) I2) (@ (@ tptp.ord_less_set_nat I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.assn) (L tptp.assn) (U tptp.assn)) (= (@ (@ tptp.member_assn I2) (@ (@ tptp.set_or5523502641901747543n_assn L) U)) (and (@ (@ tptp.ord_less_eq_assn L) I2) (@ (@ tptp.ord_less_assn I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or8585797421378605585et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I2) (@ (@ tptp.ord_less_set_int I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or4029947393144176647an_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I2) (@ (@ tptp.ord_less_rat I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or1222409239386451017an_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I2) (@ (@ tptp.ord_less_num I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_nat I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or4662586982721622107an_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I2) (@ (@ tptp.ord_less_int I2) U)))))
% 6.81/7.13 (assert (forall ((I2 tptp.code_integer) (L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.member_Code_integer I2) (@ (@ tptp.set_or8404916559141939852nteger L) U)) (and (@ (@ tptp.ord_le3102999989581377725nteger L) I2) (@ (@ tptp.ord_le6747313008572928689nteger I2) U)))))
% 6.81/7.13 (assert (forall ((B Bool) (A Bool)) (=> (@ (@ tptp.ord_less_eq_o B) A) (= (@ (@ tptp.set_or7139685690850216873Than_o A) B) tptp.bot_bot_set_o))))
% 6.81/7.13 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= (@ (@ tptp.set_or8585797421378605585et_int A) B) tptp.bot_bot_set_set_int))))
% 6.81/7.13 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) tptp.bot_bot_set_rat))))
% 6.81/7.13 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.set_or1222409239386451017an_num A) B) tptp.bot_bot_set_num))))
% 6.81/7.13 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) tptp.bot_bot_set_nat))))
% 6.81/7.13 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.set_or4662586982721622107an_int A) B) tptp.bot_bot_set_int))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.set_or8404916559141939852nteger A) B) tptp.bot_bo3990330152332043303nteger))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A Bool) (B Bool)) (= (= tptp.bot_bot_set_o (@ (@ tptp.set_or7139685690850216873Than_o A) B)) (not (@ (@ tptp.ord_less_o A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= tptp.bot_bot_set_assn (@ (@ tptp.set_or5523502641901747543n_assn A) B)) (not (@ (@ tptp.ord_less_assn A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B)) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or1222409239386451017an_num A) B)) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or4662586982721622107an_int A) B)) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= tptp.bot_bo3990330152332043303nteger (@ (@ tptp.set_or8404916559141939852nteger A) B)) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 6.81/7.13 (assert (forall ((A Bool) (B Bool)) (= (= (@ (@ tptp.set_or7139685690850216873Than_o A) B) tptp.bot_bot_set_o) (not (@ (@ tptp.ord_less_o A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.assn) (B tptp.assn)) (= (= (@ (@ tptp.set_or5523502641901747543n_assn A) B) tptp.bot_bot_set_assn) (not (@ (@ tptp.ord_less_assn A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or1222409239386451017an_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or4662586982721622107an_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) tptp.bot_bo3990330152332043303nteger) (not (@ (@ tptp.ord_le6747313008572928689nteger A) B)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.81/7.13 (assert (forall ((I2 tptp.rat) (J tptp.rat) (M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat J))) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat I2) J)) (@ (@ tptp.set_or4029947393144176647an_rat M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_rat M) I2) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((I2 tptp.num) (J tptp.num) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num J))) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or1222409239386451017an_num I2) J)) (@ (@ tptp.set_or1222409239386451017an_num M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_num M) I2) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat J))) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_nat M) I2) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((I2 tptp.int) (J tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int J))) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or4662586982721622107an_int I2) J)) (@ (@ tptp.set_or4662586982721622107an_int M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_less_eq_int M) I2) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((I2 tptp.code_integer) (J tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger J))) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or8404916559141939852nteger I2) J)) (@ (@ tptp.set_or8404916559141939852nteger M) N2)) (or (@ _let_1 I2) (and (@ (@ tptp.ord_le3102999989581377725nteger M) I2) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((I2 tptp.rat) (N2 tptp.rat) (M tptp.rat)) (let ((_let_1 (@ tptp.set_or4029947393144176647an_rat I2))) (=> (@ (@ tptp.ord_less_eq_rat I2) N2) (= (@ (@ tptp.minus_minus_set_rat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.set_or4029947393144176647an_rat N2) M))))))
% 6.81/7.13 (assert (forall ((I2 tptp.num) (N2 tptp.num) (M tptp.num)) (let ((_let_1 (@ tptp.set_or1222409239386451017an_num I2))) (=> (@ (@ tptp.ord_less_eq_num I2) N2) (= (@ (@ tptp.minus_minus_set_num (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.set_or1222409239386451017an_num N2) M))))))
% 6.81/7.13 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ (@ tptp.minus_minus_set_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.set_or4665077453230672383an_nat N2) M))))))
% 6.81/7.13 (assert (forall ((I2 tptp.int) (N2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.set_or4662586982721622107an_int I2))) (=> (@ (@ tptp.ord_less_eq_int I2) N2) (= (@ (@ tptp.minus_minus_set_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.set_or4662586982721622107an_int N2) M))))))
% 6.81/7.13 (assert (forall ((I2 tptp.code_integer) (N2 tptp.code_integer) (M tptp.code_integer)) (let ((_let_1 (@ tptp.set_or8404916559141939852nteger I2))) (=> (@ (@ tptp.ord_le3102999989581377725nteger I2) N2) (= (@ (@ tptp.minus_2355218937544613996nteger (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.set_or8404916559141939852nteger N2) M))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups4406642042086082107nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4406642042086082107nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups879477027807139574nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S) tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= A K3)) (@ B K3)) tptp.zero_zero_nat))) S) tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups4406642042086082107nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4406642042086082107nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups879477027807139574nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.zero_z3403309356797280102nteger))) S) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.zero_zero_rat))) S) tptp.zero_zero_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.nat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S) tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_nat (= K3 A)) (@ B K3)) tptp.zero_zero_nat))) S) tptp.zero_zero_nat)))))))
% 6.81/7.13 (assert (forall ((K tptp.rat) (I2 tptp.rat) (J tptp.rat)) (= (@ (@ tptp.image_rat_rat (lambda ((N tptp.rat)) (@ (@ tptp.plus_plus_rat N) K))) (@ (@ tptp.set_or4029947393144176647an_rat I2) J)) (@ (@ tptp.set_or4029947393144176647an_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.int) (I2 tptp.int) (J tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((N tptp.int)) (@ (@ tptp.plus_plus_int N) K))) (@ (@ tptp.set_or4662586982721622107an_int I2) J)) (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) K)))))
% 6.81/7.13 (assert (forall ((K tptp.code_integer) (I2 tptp.code_integer) (J tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((N tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger N) K))) (@ (@ tptp.set_or8404916559141939852nteger I2) J)) (@ (@ tptp.set_or8404916559141939852nteger (@ (@ tptp.plus_p5714425477246183910nteger I2) K)) (@ (@ tptp.plus_p5714425477246183910nteger J) K)))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7694694392188491536nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7694694392188491536nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3827104343326376752nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3827104343326376752nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups3674199335183972705nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3674199335183972705nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= A K3)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.assn))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= A K3)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S) tptp.one_one_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K3)) (@ B K3)) tptp.one_one_rat))) S) tptp.one_one_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups7694694392188491536nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7694694392188491536nteger (lambda ((K3 Bool)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups3827104343326376752nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3827104343326376752nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups3674199335183972705nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3674199335183972705nteger (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 A)) (@ B K3)) tptp.one_one_Code_integer))) S) tptp.one_one_Code_integer)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.assn))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5301882518646026715o_assn (lambda ((K3 Bool)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.assn))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.assn))) (let ((_let_1 (@ (@ tptp.member_int A) S))) (=> (@ tptp.finite_finite_int S) (and (=> _let_1 (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (A tptp.code_integer) (B (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ (@ tptp.member_Code_integer A) S))) (=> (@ tptp.finite6017078050557962740nteger S) (and (=> _let_1 (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_assn (= K3 A)) (@ B K3)) tptp.one_one_assn))) S) tptp.one_one_assn)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (A Bool) (B (-> Bool tptp.rat))) (let ((_let_1 (@ (@ tptp.member_o A) S))) (=> (@ tptp.finite_finite_o S) (and (=> _let_1 (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((K3 Bool)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S) tptp.one_one_rat)))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S))) (=> (@ tptp.finite_finite_nat S) (and (=> _let_1 (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((K3 tptp.nat)) (@ (@ (@ tptp.if_rat (= K3 A)) (@ B K3)) tptp.one_one_rat))) S) tptp.one_one_rat)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups3190895334310489300er_nat F) A3)) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4077766827762148844at_nat F) A3)) (forall ((X4 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups708209901874060359at_nat F) A3)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X4))))))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger N2)) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.numera5444537566228673987atural N2)) tptp.one_one_Code_natural) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le5570908160329646204atural tptp.one_one_Code_natural) (@ tptp.numera5444537566228673987atural N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (= X Y))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.zero_z3403309356797280102nteger)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.zero_zero_rat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.one_one_Code_integer)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.one_one_assn)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.one_one_rat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.one_one_nat)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (let ((_let_3 (@ _let_2 (@ _let_1 (@ tptp.suc N2))))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_3 tptp.one_one_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A3) (@ (@ tptp.member_nat tptp.zero_zero_nat) A3)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A3) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I4)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I4)))) A3) tptp.zero_zero_rat))))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.81/7.13 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ F X4)))) A3))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (S4 tptp.set_int)) (=> (@ tptp.finite_finite_int S) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((S6 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int S6) S) (@ (@ tptp.minus_minus_set_int S4) S))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (S4 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((S6 tptp.set_Code_integer)) (= (@ (@ tptp.minus_2355218937544613996nteger S6) S) (@ (@ tptp.minus_2355218937544613996nteger S4) S))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (S4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat S) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((S6 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.minus_1356011639430497352at_nat S6) S) (@ (@ tptp.minus_1356011639430497352at_nat S4) S))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (S4 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((S6 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat S6) S) (@ (@ tptp.minus_minus_set_nat S4) S))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (and (= A C) (= B D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (and (= A C) (= B D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (and (= A C) (= B D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (and (= A C) (= B D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (and (= A C) (= B D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= A C))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= A C))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= A C))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= A C))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= A C))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (= (@ (@ tptp.set_or4029947393144176647an_rat A) B) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D2) (= B D2))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (=> (= (@ (@ tptp.set_or1222409239386451017an_num A) B) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_num C) D2) (= B D2))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (= (@ (@ tptp.set_or4665077453230672383an_nat A) B) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D2) (= B D2))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (= (@ (@ tptp.set_or4662586982721622107an_int A) B) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D2) (= B D2))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (= (@ (@ tptp.set_or8404916559141939852nteger A) B) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger C) D2) (= B D2))))))
% 6.81/7.13 (assert (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N7))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.13 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N8) (@ (@ tptp.ord_less_nat X4) M3)))))))
% 6.81/7.13 (assert (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N7) (@ (@ tptp.ord_less_nat X3) N2))) (@ tptp.finite_finite_nat N7))))
% 6.81/7.13 (assert (= tptp.finite_finite_nat (lambda ((N8 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) N8) (@ (@ tptp.ord_less_eq_nat X4) M3)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 6.81/7.13 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p4538020629002901425atural Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p5714425477246183910nteger Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.81/7.13 (assert (forall ((Z tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural Z) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p4538020629002901425atural Z) Z))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.plus_p4538020629002901425atural A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.81/7.13 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger X) X)) X)) X))))
% 6.81/7.13 (assert (forall ((X tptp.assn)) (= (@ (@ tptp.power_power_assn X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn X) X)) X)) X))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger A) A))))
% 6.81/7.13 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_assn A) A))))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.81/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.81/7.13 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N5) (@ F N5))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_nat) (G (-> Bool tptp.nat tptp.nat)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ G X4) Y4))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y4))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.nat)) (R (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ G X4) Y4))) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_int) (G (-> Bool tptp.int tptp.int)) (R (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X4 Bool)) (@ (@ G X4) Y4))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.int)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (G (-> tptp.code_integer tptp.int tptp.int)) (R (-> tptp.code_integer tptp.int Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.groups4538972089207619220nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ G X4) Y4))) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_o) (G (-> tptp.nat Bool tptp.nat)) (R (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_o B3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat (@ G X4)) (@ tptp.collect_o (lambda ((Y4 Bool)) (and (@ (@ tptp.member_o Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((Y4 Bool)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.nat)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer tptp.nat)) (R (-> tptp.nat tptp.code_integer Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups7237345082560585321er_nat (@ G X4)) (@ tptp.collect_Code_integer (lambda ((Y4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups7237345082560585321er_nat (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.nat tptp.nat)) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_nat) (G (-> Bool tptp.nat tptp.nat)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X4 Bool)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X4 Bool)) (@ (@ G X4) Y4))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (G (-> tptp.int tptp.nat tptp.nat)) (R (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ G X4) Y4))) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.nat)) (R (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups3190895334310489300er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.groups708209901874060359at_nat (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3190895334310489300er_nat (lambda ((X4 tptp.code_integer)) (@ (@ G X4) Y4))) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_nat) (G (-> Bool tptp.nat tptp.int)) (R (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ G X4) Y4))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (G (-> tptp.code_integer tptp.nat tptp.int)) (R (-> tptp.code_integer tptp.nat Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.groups705719431365010083at_int (@ G X4)) (@ tptp.collect_nat (lambda ((Y4 tptp.nat)) (and (@ (@ tptp.member_nat Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3188404863801439024er_int (lambda ((X4 tptp.code_integer)) (@ (@ G X4) Y4))) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_int) (G (-> Bool tptp.int tptp.int)) (R (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3502327434004483295_o_int (lambda ((X4 Bool)) (@ (@ G X4) Y4))) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (G (-> tptp.code_integer tptp.int tptp.int)) (R (-> tptp.code_integer tptp.int Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.groups1705073143266064639nt_int (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3188404863801439024er_int (lambda ((X4 tptp.code_integer)) (@ (@ G X4) Y4))) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_o) (G (-> tptp.nat Bool tptp.nat)) (R (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_o B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat (@ G X4)) (@ tptp.collect_o (lambda ((Y4 Bool)) (and (@ (@ tptp.member_o Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((Y4 Bool)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (G (-> tptp.nat tptp.int tptp.nat)) (R (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat (@ G X4)) (@ tptp.collect_int (lambda ((Y4 tptp.int)) (and (@ (@ tptp.member_int Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer tptp.nat)) (R (-> tptp.nat tptp.code_integer Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.groups3190895334310489300er_nat (@ G X4)) (@ tptp.collect_Code_integer (lambda ((Y4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Y4) B3) (@ (@ R X4) Y4))))))) A3) (@ (@ tptp.groups3190895334310489300er_nat (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) (@ (@ G X4) Y4))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ (@ R X4) Y4))))))) B3))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.13 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B)) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ _let_1 D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num B))) (=> (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or1222409239386451017an_num A) B)) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_num C) A) (@ _let_1 D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ _let_1 D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or4662586982721622107an_int A) B)) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_less_eq_int C) A) (@ _let_1 D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger B))) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or8404916559141939852nteger A) B)) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (or (@ _let_1 A) (and (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ _let_1 D2)))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_8256067586552552935nteger X) _let_2) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (@ (@ tptp.ord_le3102999989581377725nteger X) Y))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.81/7.13 (assert (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (let ((_let_1 (@ tptp.set_or4029947393144176647an_rat L))) (=> (@ (@ tptp.ord_less_eq_rat L) M) (=> (@ (@ tptp.ord_less_eq_rat M) U) (= (@ (@ tptp.sup_sup_set_rat (@ _let_1 M)) (@ (@ tptp.set_or4029947393144176647an_rat M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (let ((_let_1 (@ tptp.set_or1222409239386451017an_num L))) (=> (@ (@ tptp.ord_less_eq_num L) M) (=> (@ (@ tptp.ord_less_eq_num M) U) (= (@ (@ tptp.sup_sup_set_num (@ _let_1 M)) (@ (@ tptp.set_or1222409239386451017an_num M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat L))) (=> (@ (@ tptp.ord_less_eq_nat L) M) (=> (@ (@ tptp.ord_less_eq_nat M) U) (= (@ (@ tptp.sup_sup_set_nat (@ _let_1 M)) (@ (@ tptp.set_or4665077453230672383an_nat M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (let ((_let_1 (@ tptp.set_or4662586982721622107an_int L))) (=> (@ (@ tptp.ord_less_eq_int L) M) (=> (@ (@ tptp.ord_less_eq_int M) U) (= (@ (@ tptp.sup_sup_set_int (@ _let_1 M)) (@ (@ tptp.set_or4662586982721622107an_int M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (let ((_let_1 (@ tptp.set_or8404916559141939852nteger L))) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger M) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ _let_1 M)) (@ (@ tptp.set_or8404916559141939852nteger M) U)) (@ _let_1 U)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (@ P M3))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (@ P M3))) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X4))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.81/7.13 (assert (forall ((L Bool) (M Bool) (U Bool)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.set_or7139685690850216873Than_o L) M)) (@ (@ tptp.set_or7139685690850216873Than_o M) U)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.set_or4665077453230672383an_nat L) M)) (@ (@ tptp.set_or4665077453230672383an_nat M) U)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.set_or4662586982721622107an_int L) M)) (@ (@ tptp.set_or4662586982721622107an_int M) U)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.set_or8404916559141939852nteger L) M)) (@ (@ tptp.set_or8404916559141939852nteger M) U)) tptp.bot_bo3990330152332043303nteger)))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (not (= S tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) S) (not (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) S) (@ (@ tptp.ord_le6747313008572928689nteger Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o)) (=> (@ tptp.finite_finite_o S) (=> (not (= S tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) S) (not (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) S) (@ (@ tptp.ord_less_o Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_assn)) (=> (@ tptp.finite_finite_assn S) (=> (not (= S tptp.bot_bot_set_assn)) (exists ((X3 tptp.assn)) (and (@ (@ tptp.member_assn X3) S) (not (exists ((Xa2 tptp.assn)) (and (@ (@ tptp.member_assn Xa2) S) (@ (@ tptp.ord_less_assn Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_rat)) (=> (@ tptp.finite_finite_rat S) (=> (not (= S tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) S) (not (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) S) (@ (@ tptp.ord_less_rat Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_num)) (=> (@ tptp.finite_finite_num S) (=> (not (= S tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) S) (not (exists ((Xa2 tptp.num)) (and (@ (@ tptp.member_num Xa2) S) (@ (@ tptp.ord_less_num Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (=> (not (= S tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) S) (not (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) S) (@ (@ tptp.ord_less_nat Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int)) (=> (@ tptp.finite_finite_int S) (=> (not (= S tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) S) (not (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) S) (@ (@ tptp.ord_less_int Xa2) X3))))))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_Code_integer)) (=> (not (= X6 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) X6) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) X6) (@ (@ tptp.ord_le6747313008572928689nteger X3) Xa2))))) (not (@ tptp.finite6017078050557962740nteger X6))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_o)) (=> (not (= X6 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) X6) (exists ((Xa2 Bool)) (and (@ (@ tptp.member_o Xa2) X6) (@ (@ tptp.ord_less_o X3) Xa2))))) (not (@ tptp.finite_finite_o X6))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_rat)) (=> (not (= X6 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (@ (@ tptp.member_rat X3) X6) (exists ((Xa2 tptp.rat)) (and (@ (@ tptp.member_rat Xa2) X6) (@ (@ tptp.ord_less_rat X3) Xa2))))) (not (@ tptp.finite_finite_rat X6))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_num)) (=> (not (= X6 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (@ (@ tptp.member_num X3) X6) (exists ((Xa2 tptp.num)) (and (@ (@ tptp.member_num Xa2) X6) (@ (@ tptp.ord_less_num X3) Xa2))))) (not (@ tptp.finite_finite_num X6))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_nat)) (=> (not (= X6 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) X6) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) X6) (@ (@ tptp.ord_less_nat X3) Xa2))))) (not (@ tptp.finite_finite_nat X6))))))
% 6.81/7.13 (assert (forall ((X6 tptp.set_int)) (=> (not (= X6 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) X6) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) X6) (@ (@ tptp.ord_less_int X3) Xa2))))) (not (@ tptp.finite_finite_int X6))))))
% 6.81/7.13 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R3)) (@ (@ tptp.power_power_nat N2) R3)))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 6.81/7.13 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.81/7.13 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_nat I4) (@ (@ tptp.binomial N2) I4)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.rat)) (I5 tptp.set_o) (G (-> Bool tptp.rat)) (I2 Bool)) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) I5) (@ (@ tptp.groups7872700643590313910_o_rat G) I5)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_o I2) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.rat)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I5) (@ (@ tptp.groups2906978787729119204at_rat G) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.rat)) (I5 tptp.set_int) (G (-> tptp.int tptp.rat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I5) (@ (@ tptp.groups3906332499630173760nt_rat G) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.code_integer tptp.rat)) (I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (I2 tptp.code_integer)) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) I5) (@ (@ tptp.groups6602215022474089585er_rat G) I5)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_rat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.nat)) (I5 tptp.set_o) (G (-> Bool tptp.nat)) (I2 Bool)) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) I5) (@ (@ tptp.groups8507830703676809646_o_nat G) I5)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_o I2) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.int tptp.nat)) (I5 tptp.set_int) (G (-> tptp.int tptp.nat)) (I2 tptp.int)) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) I5) (@ (@ tptp.groups4541462559716669496nt_nat G) I5)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_int I2) I5) (=> (@ tptp.finite_finite_int I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (I2 tptp.code_integer)) (=> (= (@ (@ tptp.groups7237345082560585321er_nat F) I5) (@ (@ tptp.groups7237345082560585321er_nat G) I5)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_nat (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> Bool tptp.int)) (I5 tptp.set_o) (G (-> Bool tptp.int)) (I2 Bool)) (=> (= (@ (@ tptp.groups8505340233167759370_o_int F) I5) (@ (@ tptp.groups8505340233167759370_o_int G) I5)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_o I2) I5) (=> (@ tptp.finite_finite_o I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.nat tptp.int)) (I5 tptp.set_nat) (G (-> tptp.nat tptp.int)) (I2 tptp.nat)) (=> (= (@ (@ tptp.groups3539618377306564664at_int F) I5) (@ (@ tptp.groups3539618377306564664at_int G) I5)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ tptp.finite_finite_nat I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (assert (forall ((F (-> tptp.code_integer tptp.int)) (I5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (I2 tptp.code_integer)) (=> (= (@ (@ tptp.groups7234854612051535045er_int F) I5) (@ (@ tptp.groups7234854612051535045er_int G) I5)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_int (@ F I3)) (@ G I3)))) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ tptp.finite6017078050557962740nteger I5) (= (@ F I2) (@ G I2))))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.numera6620942414471956472nteger tptp.one)) A)))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.81/7.13 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural A) (@ tptp.numera5444537566228673987atural tptp.one)) A)))
% 6.81/7.13 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.81/7.13 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.81/7.13 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger tptp.one)) A) A)))
% 6.81/7.13 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.81/7.13 (assert (forall ((A tptp.code_natural)) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural tptp.one)) A) A)))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.code_integer)) (Y (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I4)) (@ Y I4)) tptp.zero_z3403309356797280102nteger))))))))))
% 6.81/7.13 (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 ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I4)) (@ Y I4)) tptp.zero_z3403309356797280102nteger))))))))))
% 6.81/7.13 (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 ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y I4) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I4)) (@ Y I4)) tptp.zero_z3403309356797280102nteger))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ X I4) tptp.zero_z3403309356797280102nteger)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ Y I4) tptp.zero_z3403309356797280102nteger)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ (@ tptp.plus_p5714425477246183910nteger (@ X I4)) (@ Y I4)) tptp.zero_z3403309356797280102nteger))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (Y (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.rat)) (Y (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.rat)) (Y (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ X I4) tptp.zero_zero_rat)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ Y I4) tptp.zero_zero_rat)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ (@ tptp.plus_plus_rat (@ X I4)) (@ Y I4)) tptp.zero_zero_rat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.nat)) (Y (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.plus_plus_nat (@ X I4)) (@ Y I4)) tptp.zero_zero_nat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.zero_zero_nat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.zero_zero_nat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.plus_plus_nat (@ X I4)) (@ Y I4)) tptp.zero_zero_nat))))))))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I4) K)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (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))))))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.code_integer)) (Y (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I4)) (@ Y I4)) tptp.one_one_Code_integer))))))))))
% 6.81/7.13 (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 ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I4)) (@ Y I4)) tptp.one_one_Code_integer))))))))))
% 6.81/7.13 (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 ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y I4) tptp.one_one_Code_integer)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I4)) (@ Y I4)) tptp.one_one_Code_integer))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.code_integer)) (Y (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ X I4) tptp.one_one_Code_integer)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ Y I4) tptp.one_one_Code_integer)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ (@ tptp.times_3573771949741848930nteger (@ X I4)) (@ Y I4)) tptp.one_one_Code_integer))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.assn)) (Y (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.times_times_assn (@ X I4)) (@ Y I4)) tptp.one_one_assn))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.assn)) (Y (-> tptp.nat tptp.assn))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_assn (@ X I4)) (@ Y I4)) tptp.one_one_assn))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_int) (X (-> tptp.int tptp.assn)) (Y (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ X I4) tptp.one_one_assn)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ Y I4) tptp.one_one_assn)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) I5) (not (= (@ (@ tptp.times_times_assn (@ X I4)) (@ Y I4)) tptp.one_one_assn))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_Code_integer) (X (-> tptp.code_integer tptp.assn)) (Y (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ X I4) tptp.one_one_assn)))))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ Y I4) tptp.one_one_assn)))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) I5) (not (= (@ (@ tptp.times_times_assn (@ X I4)) (@ Y I4)) tptp.one_one_assn))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_o) (X (-> Bool tptp.rat)) (Y (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ X I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ Y I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X I4)) (@ Y I4)) tptp.one_one_rat))))))))))
% 6.81/7.13 (assert (forall ((I5 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ X I4) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ Y I4) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (and (@ (@ tptp.member_nat I4) I5) (not (= (@ (@ tptp.times_times_rat (@ X I4)) (@ Y I4)) tptp.one_one_rat))))))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger) (and (= X tptp.zero_z3403309356797280102nteger) (= Y tptp.zero_z3403309356797280102nteger))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) (or (not (= X tptp.zero_z3403309356797280102nteger)) (not (= Y tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.81/7.13 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural N2))) (= (@ tptp.numera5444537566228673987atural (@ tptp.bit0 N2)) (@ (@ tptp.plus_p4538020629002901425atural _let_1) _let_1)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.code_integer)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups4406642042086082107nteger G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups4406642042086082107nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups7501900531339628137nteger G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7873554091576472773nteger G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups879477027807139574nteger G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ P X4))))) (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.rat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7872700643590313910_o_rat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups6602215022474089585er_rat G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ P X4))))) (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.nat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups8507830703676809646_o_nat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ G X4)) tptp.zero_zero_nat))) A3)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger X) Y)) _let_2) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_7079662738309270450atural (@ (@ tptp.plus_p4538020629002901425atural X) Y)) _let_2) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.power_7079662738309270450atural X) _let_2)) (@ (@ tptp.power_7079662738309270450atural Y) _let_2))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural _let_1)) X)) Y)))))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (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)))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.product_prod_int_int tptp.nat)) (P (-> tptp.product_prod_int_int Bool))) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.list_nat tptp.nat)) (P (-> tptp.list_nat Bool))) (=> (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.set_nat tptp.nat)) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.nat tptp.nat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.code_integer tptp.nat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((M6 (-> tptp.product_prod_nat_nat tptp.nat)) (P (-> tptp.product_prod_nat_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ P X4)) (@ M6 X4)) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (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))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (= (@ (@ tptp.groups8507830703676809646_o_nat H) S) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_o_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (= (@ (@ tptp.groups4541462559716669496nt_nat H) S) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_int_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (= (@ (@ tptp.groups7237345082560585321er_nat H) S) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups7237345082560585321er_nat H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_951025933927791156er_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o S) (= (@ (@ tptp.groups8505340233167759370_o_int H) S) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups8505340233167759370_o_int H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_o_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups3539618377306564664at_int H) S) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger S) (= (@ (@ tptp.groups7234854612051535045er_int H) S) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups7234854612051535045er_int H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_948535463418740880er_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups3542108847815614940at_nat H) S) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups3542108847815614940at_nat H) S) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (H (-> tptp.int tptp.int)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (= (@ (@ tptp.groups4538972089207619220nt_int H) S) (@ (@ tptp.groups3539618377306564664at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_int_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (H (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int S) (= (@ (@ tptp.groups4538972089207619220nt_int H) S) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_int_int G) S))))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (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))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.81/7.13 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.81/7.13 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.code_integer)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7694694392188491536nteger G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups7694694392188491536nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (@ (@ tptp.groups3455450783089532116nteger (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3827104343326376752nteger G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (@ (@ tptp.groups3827104343326376752nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ P X4))))) (@ (@ tptp.groups3674199335183972705nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.assn)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups5301882518646026715o_assn G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups5301882518646026715o_assn (lambda ((X4 Bool)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.assn)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A3) (@ P X4))))) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) A3) (@ P X4))))) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.rat)) (P (-> Bool Bool))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups2869687844427037835_o_rat G) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) A3) (@ P X4))))) (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.one_one_rat))) A3)))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A3) (@ P X4))))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ G X4)) tptp.one_one_rat))) A3)))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (= (@ (@ tptp.groups3504817904513533571_o_nat H) S) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_o_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_int) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (= (@ (@ tptp.groups1707563613775114915nt_nat H) S) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_int_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (= (@ (@ tptp.groups3190895334310489300er_nat H) S) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3190895334310489300er_nat H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_951025933927791156er_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (= (@ (@ tptp.groups3502327434004483295_o_int H) S) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3502327434004483295_o_int H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_o_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (= (@ (@ tptp.groups3188404863801439024er_int H) S) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3188404863801439024er_int H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_951025933927791156er_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o S) (= (@ (@ tptp.groups3502327434004483295_o_int H) S) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3502327434004483295_o_int H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_o_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger S) (= (@ (@ tptp.groups3188404863801439024er_int H) S) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3188404863801439024er_int H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_948535463418740880er_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups708209901874060359at_nat H) S) (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_int G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups708209901874060359at_nat H) S) (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_nat G) S))))))
% 6.81/7.13 (assert (forall ((S tptp.set_nat) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (= (@ (@ tptp.groups705719431365010083at_int H) S) (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) (@ (@ tptp.image_nat_nat G) S))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.power_8256067586552552935nteger (@ _let_2 N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((A tptp.assn) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_assn A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_assn A) (@ (@ tptp.power_power_assn (@ _let_2 N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 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) N2))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.81/7.13 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ tptp.finite_finite_rat (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (and (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat A) X4) (@ (@ tptp.ord_less_eq_rat X4) B)))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (=> (@ (@ tptp.ord_less_nat X3) D2) (= (@ G X3) (@ H X3))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ (@ tptp.set_or4665077453230672383an_nat C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) X3) (=> (@ (@ tptp.ord_less_int X3) D2) (= (@ G X3) (@ H X3))))) (= (@ (@ tptp.groups4538972089207619220nt_int G) (@ (@ tptp.set_or4662586982721622107an_int A) B)) (@ (@ tptp.groups4538972089207619220nt_int H) (@ (@ tptp.set_or4662586982721622107an_int C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (=> (@ (@ tptp.ord_less_nat X3) D2) (= (@ G X3) (@ H X3))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.groups708209901874060359at_nat H) (@ (@ tptp.set_or4665077453230672383an_nat C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (=> (@ (@ tptp.ord_less_nat X3) D2) (= (@ G X3) (@ H X3))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.groups705719431365010083at_int H) (@ (@ tptp.set_or4665077453230672383an_nat C) D2))))))))
% 6.81/7.13 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int) (G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int))) (=> (= A C) (=> (= B D2) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) X3) (=> (@ (@ tptp.ord_less_int X3) D2) (= (@ G X3) (@ H X3))))) (= (@ (@ tptp.groups1705073143266064639nt_int G) (@ (@ tptp.set_or4662586982721622107an_int A) B)) (@ (@ tptp.groups1705073143266064639nt_int H) (@ (@ tptp.set_or4662586982721622107an_int C) D2))))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.81/7.13 (assert (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat L) M) (=> (@ (@ tptp.ord_less_eq_rat M) U) (= (@ (@ tptp.sup_sup_set_rat (@ (@ tptp.set_or4029947393144176647an_rat L) M)) (@ (@ tptp.set_or633870826150836451st_rat M) U)) (@ (@ tptp.set_or633870826150836451st_rat L) U))))))
% 6.81/7.13 (assert (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (@ (@ tptp.ord_less_eq_num L) M) (=> (@ (@ tptp.ord_less_eq_num M) U) (= (@ (@ tptp.sup_sup_set_num (@ (@ tptp.set_or1222409239386451017an_num L) M)) (@ (@ tptp.set_or7049704709247886629st_num M) U)) (@ (@ tptp.set_or7049704709247886629st_num L) U))))))
% 6.81/7.13 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat L) M) (=> (@ (@ tptp.ord_less_eq_nat M) U) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.set_or4665077453230672383an_nat L) M)) (@ (@ tptp.set_or1269000886237332187st_nat M) U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))))
% 6.81/7.13 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int L) M) (=> (@ (@ tptp.ord_less_eq_int M) U) (= (@ (@ tptp.sup_sup_set_int (@ (@ tptp.set_or4662586982721622107an_int L) M)) (@ (@ tptp.set_or1266510415728281911st_int M) U)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger M) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ (@ tptp.set_or8404916559141939852nteger L) M)) (@ (@ tptp.set_or189985376899183464nteger M) U)) (@ (@ tptp.set_or189985376899183464nteger L) U))))))
% 6.81/7.13 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat N2) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K))))))
% 6.81/7.13 (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)))))))))
% 6.81/7.13 (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)))))))))
% 6.81/7.13 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.81/7.13 (assert (forall ((L Bool) (M Bool) (U Bool)) (= (@ (@ tptp.inf_inf_set_o (@ (@ tptp.set_or7139685690850216873Than_o L) M)) (@ (@ tptp.set_or8904488021354931149Most_o M) U)) tptp.bot_bot_set_o)))
% 6.81/7.13 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ (@ tptp.set_or4665077453230672383an_nat L) M)) (@ (@ tptp.set_or1269000886237332187st_nat M) U)) tptp.bot_bot_set_nat)))
% 6.81/7.13 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ (@ tptp.set_or4662586982721622107an_int L) M)) (@ (@ tptp.set_or1266510415728281911st_int M) U)) tptp.bot_bot_set_int)))
% 6.81/7.13 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ (@ tptp.set_or8404916559141939852nteger L) M)) (@ (@ tptp.set_or189985376899183464nteger M) U)) tptp.bot_bo3990330152332043303nteger)))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.minus_minus_rat (@ _let_1 (@ _let_2 P3))) (@ _let_1 (@ _let_2 N2))) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.minus_minus_int (@ _let_1 (@ _let_2 P3))) (@ _let_1 (@ _let_2 N2))) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3)))))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) _let_2) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_2)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) X)) Y)))))))
% 6.81/7.13 (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)))))))
% 6.81/7.13 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K3))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P3 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) P3) (= (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N2))) (@ _let_2 (@ (@ tptp.set_or4665077453230672383an_nat N2) P3))) (@ _let_2 (@ _let_1 P3)))))))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.81/7.13 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.13 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_rat))))
% 6.81/7.13 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups4406642042086082107nteger F) A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A3) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups7501900531339628137nteger F) A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups7873554091576472773nteger F) A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (= (= (@ (@ tptp.groups879477027807139574nteger F) A3) tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A3) (= (@ F X4) tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups7872700643590313910_o_rat F) A3) tptp.zero_zero_rat) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A3) (= (@ F X4) tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A3) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A3) (= (@ F X4) tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A3) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (= (@ F X4) tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (= (= (@ (@ tptp.groups6602215022474089585er_rat F) A3) tptp.zero_zero_rat) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) A3) (= (@ F X4) tptp.zero_zero_rat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups8507830703676809646_o_nat F) A3) tptp.zero_zero_nat) (forall ((X4 Bool)) (=> (@ (@ tptp.member_o X4) A3) (= (@ F X4) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A3) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A3) (= (@ F X4) tptp.zero_zero_nat))))))))
% 6.81/7.13 (assert (forall ((S2 tptp.set_nat) (T5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (T5 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (I2 (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (T5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.nat)) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7501900531339628137nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (I2 (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (I2 (-> tptp.int tptp.int)) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.int)) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups7873554091576472773nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (I2 (-> tptp.nat tptp.code_integer)) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups7501900531339628137nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (I2 (-> tptp.int tptp.code_integer)) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups7873554091576472773nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (I2 (-> tptp.code_integer tptp.code_integer)) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ G X3)))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S2) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_le3102999989581377725nteger (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.groups879477027807139574nteger F) S2)) (@ (@ tptp.groups879477027807139574nteger G) T5))))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (T5 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I2 (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X3)))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S2) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) T5) (= (@ I2 Xa2) X3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G Xa2)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) T5))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.nat)) (and (@ (@ tptp.member_nat X7) A3) (@ (@ tptp.ord_less_rat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.groups2906978787729119204at_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.int)) (and (@ (@ tptp.member_int X7) A3) (@ (@ tptp.ord_less_rat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) (@ (@ tptp.groups3906332499630173760nt_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X7) A3) (@ (@ tptp.ord_less_rat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A3)) (@ (@ tptp.groups6602215022474089585er_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.int)) (and (@ (@ tptp.member_int X7) A3) (@ (@ tptp.ord_less_nat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X7) A3) (@ (@ tptp.ord_less_nat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A3)) (@ (@ tptp.groups7237345082560585321er_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.nat)) (and (@ (@ tptp.member_nat X7) A3) (@ (@ tptp.ord_less_int (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A3)) (@ (@ tptp.groups3539618377306564664at_int G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X7) A3) (@ (@ tptp.ord_less_int (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups7234854612051535045er_int F) A3)) (@ (@ tptp.groups7234854612051535045er_int G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.nat)) (and (@ (@ tptp.member_nat X7) A3) (@ (@ tptp.ord_less_nat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ (@ tptp.groups3542108847815614940at_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_int (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.int)) (and (@ (@ tptp.member_int X7) A3) (@ (@ tptp.ord_less_int (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A3)) (@ (@ tptp.groups4538972089207619220nt_int G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat)) (G (-> tptp.product_prod_nat_nat tptp.rat))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A3) (@ (@ tptp.ord_less_eq_rat (@ F X3)) (@ G X3)))) (=> (exists ((X7 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X7) A3) (@ (@ tptp.ord_less_rat (@ F X7)) (@ G X7)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups342789780944988191at_rat F) A3)) (@ (@ tptp.groups342789780944988191at_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups6602215022474089585er_rat F) A3)) (@ (@ tptp.groups6602215022474089585er_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups7872700643590313910_o_rat F) A3)) (@ (@ tptp.groups7872700643590313910_o_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A3)) (@ (@ tptp.groups2906978787729119204at_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_rat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A3)) (@ (@ tptp.groups3906332499630173760nt_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups7237345082560585321er_nat F) A3)) (@ (@ tptp.groups7237345082560585321er_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) (@ (@ tptp.groups8507830703676809646_o_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_nat (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ (@ tptp.groups4541462559716669496nt_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups7234854612051535045er_int F) A3)) (@ (@ tptp.groups7234854612051535045er_int G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups8505340233167759370_o_int F) A3)) (@ (@ tptp.groups8505340233167759370_o_int G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_int (@ F X3)) (@ G X3)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A3)) (@ (@ tptp.groups3539618377306564664at_int G) A3)))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ (@ R tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_3573771949741848930nteger X12) Y12)) (@ (@ tptp.times_3573771949741848930nteger X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3455450783089532116nteger H) S)) (@ (@ tptp.groups3455450783089532116nteger G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ (@ R tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_3573771949741848930nteger X12) Y12)) (@ (@ tptp.times_3573771949741848930nteger X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3827104343326376752nteger H) S)) (@ (@ tptp.groups3827104343326376752nteger G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.code_integer tptp.code_integer Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ (@ R tptp.one_one_Code_integer) tptp.one_one_Code_integer) (=> (forall ((X12 tptp.code_integer) (Y12 tptp.code_integer) (X22 tptp.code_integer) (Y22 tptp.code_integer)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_3573771949741848930nteger X12) Y12)) (@ (@ tptp.times_3573771949741848930nteger X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups3674199335183972705nteger H) S)) (@ (@ tptp.groups3674199335183972705nteger G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X12) Y12)) (@ (@ tptp.times_times_assn X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups6906906614972039071t_assn H) S)) (@ (@ tptp.groups6906906614972039071t_assn G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_int) (H (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X12) Y12)) (@ (@ tptp.times_times_assn X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups7882442080178216443t_assn H) S)) (@ (@ tptp.groups7882442080178216443t_assn G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.assn tptp.assn Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ (@ R tptp.one_one_assn) tptp.one_one_assn) (=> (forall ((X12 tptp.assn) (Y12 tptp.assn) (X22 tptp.assn) (Y22 tptp.assn)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_assn X12) Y12)) (@ (@ tptp.times_times_assn X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1304777262505850412r_assn H) S)) (@ (@ tptp.groups1304777262505850412r_assn G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_rat X12) Y12)) (@ (@ tptp.times_times_rat X22) Y22)))) (=> (@ tptp.finite_finite_nat S) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups73079841787564623at_rat H) S)) (@ (@ tptp.groups73079841787564623at_rat G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_int) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_rat X12) Y12)) (@ (@ tptp.times_times_rat X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1072433553688619179nt_rat H) S)) (@ (@ tptp.groups1072433553688619179nt_rat G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.rat tptp.rat Bool)) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ (@ R tptp.one_one_rat) tptp.one_one_rat) (=> (forall ((X12 tptp.rat) (Y12 tptp.rat) (X22 tptp.rat) (Y22 tptp.rat)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_rat X12) Y12)) (@ (@ tptp.times_times_rat X22) Y22)))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups2555765274223993564er_rat H) S)) (@ (@ tptp.groups2555765274223993564er_rat G) S))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.nat tptp.nat Bool)) (S tptp.set_int) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R tptp.one_one_nat) tptp.one_one_nat) (=> (forall ((X12 tptp.nat) (Y12 tptp.nat) (X22 tptp.nat) (Y22 tptp.nat)) (=> (and (@ (@ R X12) X22) (@ (@ R Y12) Y22)) (@ (@ R (@ (@ tptp.times_times_nat X12) Y12)) (@ (@ tptp.times_times_nat X22) Y22)))) (=> (@ tptp.finite_finite_int S) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) S) (@ (@ R (@ H X3)) (@ G X3)))) (@ (@ R (@ (@ tptp.groups1707563613775114915nt_nat H) S)) (@ (@ tptp.groups1707563613775114915nt_nat G) S))))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N5)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat))))))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N5)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N5) tptp.one_one_nat)))))))))))
% 6.81/7.14 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q7 tptp.nat)) (@ (@ tptp.ord_less_nat Q7) N2))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N2)) tptp.one_one_Code_integer) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.collect_nat (lambda ((Q7 tptp.nat)) (@ (@ tptp.ord_less_nat Q7) N2))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_7197305767214868737atural (@ _let_1 N2)) tptp.one_one_Code_natural) (@ (@ tptp.groups6325495683096345652atural _let_1) (@ tptp.collect_nat (lambda ((Q7 tptp.nat)) (@ (@ tptp.ord_less_nat Q7) N2))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q7 tptp.nat)) (@ (@ tptp.ord_less_nat Q7) N2))))))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q7 tptp.nat)) (@ (@ tptp.ord_less_nat Q7) N2))))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_3573771949741848930nteger (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_assn (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_3573771949741848930nteger (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_assn (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ (@ tptp.times_times_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R3) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R3) N2))) N2))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.code_integer)) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups4406642042086082107nteger F) S2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.member_o I2) S2) (= (@ F I2) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger F) S2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F I2) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger F) S2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (I2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups879477027807139574nteger F) S2) tptp.zero_z3403309356797280102nteger) (=> (@ (@ tptp.member_Code_integer I2) S2) (= (@ F I2) tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat)) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_o I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (F (-> 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) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> 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) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (I2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) S2) tptp.zero_zero_rat) (=> (@ (@ tptp.member_Code_integer I2) S2) (= (@ F I2) tptp.zero_zero_rat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.nat)) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_o I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> 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) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I2) S2) (= (@ F I2) tptp.zero_zero_nat)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.code_integer)) (B3 tptp.code_integer) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups4406642042086082107nteger F) S2) B3) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (B3 tptp.code_integer) (I2 tptp.nat)) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger F) S2) B3) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (B3 tptp.code_integer) (I2 tptp.int)) (=> (@ tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (B3 tptp.code_integer) (I2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) S2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (=> (= (@ (@ tptp.groups879477027807139574nteger F) S2) B3) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_le3102999989581377725nteger (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.rat)) (B3 tptp.rat) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups7872700643590313910_o_rat F) S2) B3) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B3 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) (@ F I3)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S2) B3) (=> (@ (@ tptp.member_nat I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.rat)) (B3 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) (@ F I3)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (B3 tptp.rat) (I2 tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) S2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (=> (= (@ (@ tptp.groups6602215022474089585er_rat F) S2) B3) (=> (@ (@ tptp.member_Code_integer I2) S2) (@ (@ tptp.ord_less_eq_rat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_o) (F (-> Bool tptp.nat)) (B3 tptp.nat) (I2 Bool)) (=> (@ tptp.finite_finite_o S2) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) S2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (=> (= (@ (@ tptp.groups8507830703676809646_o_nat F) S2) B3) (=> (@ (@ tptp.member_o I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 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) (@ F I3)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S2) B3) (=> (@ (@ tptp.member_int I2) S2) (@ (@ tptp.ord_less_eq_nat (@ F I2)) B3)))))))
% 6.81/7.14 (assert (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.81/7.14 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.product_prod_int_int tptp.nat)) (A tptp.product_prod_int_int)) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.list_nat tptp.nat)) (A tptp.list_nat)) (=> (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.set_nat tptp.nat)) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.nat tptp.nat)) (A tptp.nat)) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.int tptp.nat)) (A tptp.int)) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.code_integer tptp.nat)) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.product_prod_nat_nat tptp.nat)) (A tptp.product_prod_nat_nat)) (=> (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ M6 X4))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (= X4 A)) (@ tptp.suc _let_1)) _let_1)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.code_integer)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups4406642042086082107nteger G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups4406642042086082107nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7873554091576472773nteger G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups879477027807139574nteger G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.zero_z3403309356797280102nteger))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.rat)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7872700643590313910_o_rat G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups7872700643590313910_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups6602215022474089585er_rat G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.zero_zero_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.nat)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups8507830703676809646_o_nat G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.zero_zero_nat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.zero_zero_nat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7237345082560585321er_nat G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.zero_zero_nat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.int)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups8505340233167759370_o_int G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups8505340233167759370_o_int (lambda ((X4 Bool)) (@ (@ (@ tptp.if_int (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.zero_zero_int))) A3)))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger G) S)) T) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3542108847815614940at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int G) S)) T) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3542108847815614940at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.int tptp.nat)) (H (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat G) S)) T) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups4538972089207619220nt_int H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups4538972089207619220nt_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_Code_integer) (G (-> tptp.int tptp.code_integer)) (H (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1587234942943678608nteger G) S)) T) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups4538972089207619220nt_int H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups4538972089207619220nt_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_o) (T tptp.set_nat) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_o_nat G) S)) T) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups8507830703676809646_o_nat H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups8507830703676809646_o_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.int tptp.nat)) (H (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat G) S)) T) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups4541462559716669496nt_nat H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups4541462559716669496nt_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_951025933927791156er_nat G) S)) T) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups7237345082560585321er_nat H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups7237345082560585321er_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat G) S)) T) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3542108847815614940at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_o) (T tptp.set_int) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_o_int G) S)) T) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups8505340233167759370_o_int H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups8505340233167759370_o_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int G) S)) T) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Y4 tptp.int)) (@ (@ tptp.groups3539618377306564664at_int H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3539618377306564664at_int H) S)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_nat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_z3403309356797280102nteger))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_zero_rat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.zero_zero_int))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.product_prod_int_int tptp.nat)) (N7 (-> tptp.product_prod_int_int tptp.nat))) (=> (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.list_nat tptp.nat)) (N7 (-> tptp.list_nat tptp.nat))) (=> (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.set_nat tptp.nat)) (N7 (-> tptp.set_nat tptp.nat))) (=> (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.nat tptp.nat)) (N7 (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.int tptp.nat)) (N7 (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.code_integer tptp.nat)) (N7 (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((M6 (-> tptp.product_prod_nat_nat tptp.nat)) (N7 (-> tptp.product_prod_nat_nat tptp.nat))) (=> (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ M6 X4))))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ M6 X4)) (@ N7 X4)))))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger G) S)) T) (= (@ (@ tptp.groups3190895334310489300er_nat (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups708209901874060359at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups708209901874060359at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.nat tptp.int)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_nat_int G) S)) T) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((Y4 tptp.int)) (@ (@ tptp.groups708209901874060359at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups708209901874060359at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_Code_integer) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1215581382706833972nteger G) S)) T) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups705719431365010083at_int H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups705719431365010083at_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_Code_integer) (G (-> tptp.int tptp.code_integer)) (H (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.image_1587234942943678608nteger G) S)) T) (= (@ (@ tptp.groups3188404863801439024er_int (lambda ((Y4 tptp.code_integer)) (@ (@ tptp.groups1705073143266064639nt_int H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups1705073143266064639nt_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_o) (T tptp.set_nat) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_o_nat G) S)) T) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3504817904513533571_o_nat H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3504817904513533571_o_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.int tptp.nat)) (H (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_int_nat G) S)) T) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups1707563613775114915nt_nat H) (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups1707563613775114915nt_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_951025933927791156er_nat G) S)) T) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3190895334310489300er_nat H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3190895334310489300er_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_nat_nat G) S)) T) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat H) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups708209901874060359at_nat H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_o) (T tptp.set_nat) (G (-> Bool tptp.nat)) (H (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_o_nat G) S)) T) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3502327434004483295_o_int H) (@ tptp.collect_o (lambda ((X4 Bool)) (and (@ (@ tptp.member_o X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3502327434004483295_o_int H) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.image_951025933927791156er_nat G) S)) T) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Y4 tptp.nat)) (@ (@ tptp.groups3188404863801439024er_int H) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X4) S) (= (@ G X4) Y4))))))) T) (@ (@ tptp.groups3188404863801439024er_int H) S)))))))
% 6.81/7.14 (assert (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N7))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.code_integer)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups7694694392188491536nteger G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups7694694392188491536nteger (lambda ((X4 Bool)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3827104343326376752nteger G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups3827104343326376752nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups3674199335183972705nteger G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups3674199335183972705nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.one_one_Code_integer))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.assn)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups5301882518646026715o_assn G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups5301882518646026715o_assn (lambda ((X4 Bool)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.assn)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7882442080178216443t_assn G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups1304777262505850412r_assn G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.one_one_assn))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.rat)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups2869687844427037835_o_rat G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups2869687844427037835_o_rat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.one_one_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat)) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups1072433553688619179nt_rat G) (@ (@ tptp.inf_inf_set_int A3) B3)) (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_int X4) B3)) (@ G X4)) tptp.one_one_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups2555765274223993564er_rat G) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (@ (@ tptp.groups2555765274223993564er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ (@ tptp.member_Code_integer X4) B3)) (@ G X4)) tptp.one_one_rat))) A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (G (-> Bool tptp.nat)) (B3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.groups3504817904513533571_o_nat G) (@ (@ tptp.inf_inf_set_o A3) B3)) (@ (@ tptp.groups3504817904513533571_o_nat (lambda ((X4 Bool)) (@ (@ (@ tptp.if_nat (@ (@ tptp.member_o X4) B3)) (@ G X4)) tptp.one_one_nat))) A3)))))
% 6.81/7.14 (assert (forall ((Z tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.assn) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W2))) (@ (@ tptp.times_times_assn _let_2) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (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))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (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))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (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))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_assn))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_assn))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_rat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_rat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) (@ tptp.collect_int (lambda ((X4 tptp.int)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_nat))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (= (@ G X4) tptp.one_one_int))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (= (@ G X4) tptp.one_one_Code_integer))))) (@ _let_1 A3))))))
% 6.81/7.14 (assert (forall ((A tptp.rat)) (@ tptp.finite_finite_rat (@ tptp.collect_rat (lambda ((K3 tptp.rat)) (and (@ (@ tptp.member_rat K3) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat K3)) A)))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I4) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D2)))) _let_1)))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (= (@ (@ tptp.ord_less_eq_set_assn (@ (@ tptp.set_or7959216805967363635t_assn A) B)) (@ (@ tptp.set_or5523502641901747543n_assn C) D2)) (=> (@ (@ tptp.ord_less_eq_assn A) B) (and (@ (@ tptp.ord_less_eq_assn C) A) (@ (@ tptp.ord_less_assn B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D2 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or8585797421378605585et_int C) D2)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_set_int B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or4029947393144176647an_rat C) D2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_rat B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D2 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or1222409239386451017an_num C) D2)) (=> (@ (@ tptp.ord_less_eq_num A) B) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_num B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or4665077453230672383an_nat C) D2)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or4662586982721622107an_int C) D2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_int B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ (@ tptp.set_or189985376899183464nteger A) B)) (@ (@ tptp.set_or8404916559141939852nteger C) D2)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le6747313008572928689nteger B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or4029947393144176647an_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D2)) (=> (@ (@ tptp.ord_less_rat A) B) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D2))))))
% 6.81/7.14 (assert (forall ((L tptp.rat) (M tptp.rat) (U tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat L) M) (=> (@ (@ tptp.ord_less_rat M) U) (= (@ (@ tptp.sup_sup_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) M)) (@ (@ tptp.set_or4029947393144176647an_rat M) U)) (@ (@ tptp.set_or4029947393144176647an_rat L) U))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (M tptp.num) (U tptp.num)) (=> (@ (@ tptp.ord_less_eq_num L) M) (=> (@ (@ tptp.ord_less_num M) U) (= (@ (@ tptp.sup_sup_set_num (@ (@ tptp.set_or7049704709247886629st_num L) M)) (@ (@ tptp.set_or1222409239386451017an_num M) U)) (@ (@ tptp.set_or1222409239386451017an_num L) U))))))
% 6.81/7.14 (assert (forall ((L tptp.nat) (M tptp.nat) (U tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat L) M) (=> (@ (@ tptp.ord_less_nat M) U) (= (@ (@ tptp.sup_sup_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) M)) (@ (@ tptp.set_or4665077453230672383an_nat M) U)) (@ (@ tptp.set_or4665077453230672383an_nat L) U))))))
% 6.81/7.14 (assert (forall ((L tptp.int) (M tptp.int) (U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int L) M) (=> (@ (@ tptp.ord_less_int M) U) (= (@ (@ tptp.sup_sup_set_int (@ (@ tptp.set_or1266510415728281911st_int L) M)) (@ (@ tptp.set_or4662586982721622107an_int M) U)) (@ (@ tptp.set_or4662586982721622107an_int L) U))))))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (M tptp.code_integer) (U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) M) (=> (@ (@ tptp.ord_le6747313008572928689nteger M) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ (@ tptp.set_or189985376899183464nteger L) M)) (@ (@ tptp.set_or8404916559141939852nteger M) U)) (@ (@ tptp.set_or8404916559141939852nteger L) U))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6857163185585827899at_nat G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups6857163185585827899at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.plus_plus_rat (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ _let_1 (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 N2))) (@ G N2)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.times_times_assn (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.times_times_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.times_times_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.times_times_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc M)) N2))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.times_times_assn (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.times_times_rat (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.times_times_nat (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat A))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_2 (@ _let_1 (@ tptp.suc B))) (@ (@ tptp.times_times_int (@ _let_2 (@ _let_1 B))) (@ G B))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6857163185585827899at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_assn (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_rat (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_nat (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ G N2)) (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4406642042086082107nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ tptp.finite_finite_nat I5) (=> (@ (@ tptp.member_nat I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups7501900531339628137nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups7873554091576472773nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups879477027807139574nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups7872700643590313910_o_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups6602215022474089585er_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups8507830703676809646_o_nat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups879477027807139574nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups4406642042086082107nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7501900531339628137nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.groups7873554091576472773nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups6602215022474089585er_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups7872700643590313910_o_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (F (-> 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) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (F (-> 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) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups7237345082560585321er_nat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups8507830703676809646_o_nat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups7694694392188491536nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3455450783089532116nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3827104343326376752nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3674199335183972705nteger F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2869687844427037835_o_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (I2 tptp.nat) (F (-> 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 (@ F I2)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (I2 tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite_finite_int I5) (=> (@ (@ tptp.member_int I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups2555765274223993564er_rat F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (I2 Bool) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite_finite_o I5) (=> (@ (@ tptp.member_o I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3502327434004483295_o_int F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (I2 tptp.code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (@ (@ tptp.member_Code_integer I2) I5) (=> (@ _let_1 (@ F I2)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F I3)))) (@ _let_1 (@ (@ tptp.groups3188404863801439024er_int F) I5)))))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3674199335183972705nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups7694694392188491536nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat I5) (=> (not (= I5 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3455450783089532116nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int I5) (=> (not (= I5 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) I5) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ F I3)))) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ (@ tptp.groups3827104343326376752nteger F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2555765274223993564er_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups2869687844427037835_o_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_nat) (F (-> 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.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups73079841787564623at_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_int) (F (-> 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.one_one_rat) (@ F I3)))) (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.groups1072433553688619179nt_rat F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger I5) (=> (not (= I5 tptp.bot_bo3990330152332043303nteger)) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups3188404863801439024er_int F) I5)))))))
% 6.81/7.14 (assert (forall ((I5 tptp.set_o) (F (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o I5) (=> (not (= I5 tptp.bot_bot_set_o)) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) I5) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ F I3)))) (@ (@ tptp.ord_less_int tptp.one_one_int) (@ (@ tptp.groups3502327434004483295_o_int F) I5)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger H))) (let ((_let_2 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger H))) (let ((_let_2 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat H))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat H))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat H))) (let ((_let_2 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat H))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_nat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int H))) (let ((_let_2 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_int))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int H))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_int))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger H))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat C3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) (@ (@ tptp.minus_minus_set_nat C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat H))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat C3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) (@ (@ tptp.minus_minus_set_nat C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger H))) (let ((_let_2 (@ tptp.groups4406642042086082107nteger G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger H))) (let ((_let_2 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat H))) (let ((_let_2 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat H))) (let ((_let_2 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat H))) (let ((_let_2 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat H))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_nat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int H))) (let ((_let_2 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int H))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.zero_zero_int))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.zero_zero_int))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger H))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat C3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) (@ (@ tptp.minus_minus_set_nat C3) A3)) (= (@ G A4) tptp.zero_z3403309356797280102nteger))) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat C3) B3)) (= (@ H B4) tptp.zero_z3403309356797280102nteger))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_nat) (A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat H))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat C3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) C3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) (@ (@ tptp.minus_minus_set_nat C3) A3)) (= (@ G A4) tptp.zero_zero_rat))) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat C3) B3)) (= (@ H B4) tptp.zero_zero_rat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4406642042086082107nteger G) S) (@ (@ tptp.groups4406642042086082107nteger H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups879477027807139574nteger G) S) (@ (@ tptp.groups879477027807139574nteger H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G) S) (@ (@ tptp.groups7872700643590313910_o_rat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6602215022474089585er_rat G) S) (@ (@ tptp.groups6602215022474089585er_rat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.zero_zero_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) S) (@ (@ tptp.groups8507830703676809646_o_nat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat G) S) (@ (@ tptp.groups7237345082560585321er_nat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.zero_zero_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8505340233167759370_o_int G) S) (@ (@ tptp.groups8505340233167759370_o_int H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7234854612051535045er_int G) S) (@ (@ tptp.groups7234854612051535045er_int H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ H X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7501900531339628137nteger G) S) (@ (@ tptp.groups7501900531339628137nteger H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2906978787729119204at_rat G) S) (@ (@ tptp.groups2906978787729119204at_rat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4406642042086082107nteger G) T) (@ (@ tptp.groups4406642042086082107nteger H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups879477027807139574nteger G) T) (@ (@ tptp.groups879477027807139574nteger H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G) T) (@ (@ tptp.groups7872700643590313910_o_rat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6602215022474089585er_rat G) T) (@ (@ tptp.groups6602215022474089585er_rat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) T) (@ (@ tptp.groups8507830703676809646_o_nat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat G) T) (@ (@ tptp.groups7237345082560585321er_nat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8505340233167759370_o_int G) T) (@ (@ tptp.groups8505340233167759370_o_int H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7234854612051535045er_int G) T) (@ (@ tptp.groups7234854612051535045er_int H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (H (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7501900531339628137nteger G) T) (@ (@ tptp.groups7501900531339628137nteger H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat)) (H (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2906978787729119204at_rat G) T) (@ (@ tptp.groups2906978787729119204at_rat H) S))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups975429370522433651at_int F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4406642042086082107nteger G) S) (@ (@ tptp.groups4406642042086082107nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7873554091576472773nteger G) S) (@ (@ tptp.groups7873554091576472773nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.zero_z3403309356797280102nteger))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups879477027807139574nteger G) S) (@ (@ tptp.groups879477027807139574nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.zero_zero_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7872700643590313910_o_rat G) S) (@ (@ tptp.groups7872700643590313910_o_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) S) (@ (@ tptp.groups3906332499630173760nt_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.zero_zero_rat))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups6602215022474089585er_rat G) S) (@ (@ tptp.groups6602215022474089585er_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.zero_zero_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat G) S) (@ (@ tptp.groups8507830703676809646_o_nat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) S) (@ (@ tptp.groups4541462559716669496nt_nat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.zero_zero_nat))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat G) S) (@ (@ tptp.groups7237345082560585321er_nat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.zero_zero_int))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.zero_zero_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups8505340233167759370_o_int G) S) (@ (@ tptp.groups8505340233167759370_o_int H) T)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger H))) (let ((_let_2 (@ tptp.groups7694694392188491536nteger G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_Code_integer))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger H))) (let ((_let_2 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_Code_integer))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.assn)) (H (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn H))) (let ((_let_2 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_assn))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_assn))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat H))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_rat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_rat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat H))) (let ((_let_2 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_rat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_nat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat H))) (let ((_let_2 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_nat))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int H))) (let ((_let_2 (@ tptp.groups3502327434004483295_o_int G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_int))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int H))) (let ((_let_2 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_int))) (= (= (@ _let_2 A3) (@ _let_1 B3)) (= (@ _let_2 C3) (@ _let_1 C3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger H))) (let ((_let_2 (@ tptp.groups7694694392188491536nteger G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_Code_integer))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger H))) (let ((_let_2 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_Code_integer))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_Code_integer))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.assn)) (H (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn H))) (let ((_let_2 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_assn))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn H))) (let ((_let_2 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_assn))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_assn))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat H))) (let ((_let_2 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_rat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_rat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat H))) (let ((_let_2 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_rat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_rat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups3504817904513533571_o_nat H))) (let ((_let_2 (@ tptp.groups3504817904513533571_o_nat G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_nat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat H))) (let ((_let_2 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_nat))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_nat))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_o) (A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int H))) (let ((_let_2 (@ tptp.groups3502327434004483295_o_int G))) (=> (@ tptp.finite_finite_o C3) (=> (@ (@ tptp.ord_less_eq_set_o A3) C3) (=> (@ (@ tptp.ord_less_eq_set_o B3) C3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) (@ (@ tptp.minus_minus_set_o C3) A3)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o C3) B3)) (= (@ H B4) tptp.one_one_int))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((C3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int H))) (let ((_let_2 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) C3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) C3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) (@ (@ tptp.minus_2355218937544613996nteger C3) A3)) (= (@ G A4) tptp.one_one_int))) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger C3) B3)) (= (@ H B4) tptp.one_one_int))) (=> (= (@ _let_2 C3) (@ _let_1 C3)) (= (@ _let_2 A3) (@ _let_1 B3))))))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 S) (@ _let_1 T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int G))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_int))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_nat) (S tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat T) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.minus_minus_set_nat T) S)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int T) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 T) (@ _let_1 S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.one_one_Code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7694694392188491536nteger G) S) (@ (@ tptp.groups7694694392188491536nteger H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3674199335183972705nteger G) S) (@ (@ tptp.groups3674199335183972705nteger H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.assn)) (G (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.one_one_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G) S) (@ (@ tptp.groups2869687844427037835_o_rat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2555765274223993564er_rat G) S) (@ (@ tptp.groups2555765274223993564er_rat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) S) (@ (@ tptp.groups3504817904513533571_o_nat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3190895334310489300er_nat G) S) (@ (@ tptp.groups3190895334310489300er_nat H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H X3) tptp.one_one_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3502327434004483295_o_int G) S) (@ (@ tptp.groups3502327434004483295_o_int H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H X3) tptp.one_one_int))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3188404863801439024er_int G) S) (@ (@ tptp.groups3188404863801439024er_int H) T))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.code_integer)) (H (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7694694392188491536nteger G) T) (@ (@ tptp.groups7694694392188491536nteger H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (H (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3674199335183972705nteger G) T) (@ (@ tptp.groups3674199335183972705nteger H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.assn)) (H (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) T) (@ (@ tptp.groups5301882518646026715o_assn H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (H (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) T) (@ (@ tptp.groups1304777262505850412r_assn H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.rat)) (H (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G) T) (@ (@ tptp.groups2869687844427037835_o_rat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (H (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2555765274223993564er_rat G) T) (@ (@ tptp.groups2555765274223993564er_rat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.nat)) (H (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) T) (@ (@ tptp.groups3504817904513533571_o_nat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (H (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_nat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3190895334310489300er_nat G) T) (@ (@ tptp.groups3190895334310489300er_nat H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (G (-> Bool tptp.int)) (H (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o T) (=> (@ (@ tptp.ord_less_eq_set_o S) T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3502327434004483295_o_int G) T) (@ (@ tptp.groups3502327434004483295_o_int H) S))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (H (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ G X3) tptp.one_one_int))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) S) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3188404863801439024er_int G) T) (@ (@ tptp.groups3188404863801439024er_int H) S))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.int)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat)) (B3 tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ _let_1 A3) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ (@ tptp.times_times_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.code_integer)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.assn)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.assn)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.rat)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat)) (B3 tptp.set_Code_integer)) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (G (-> tptp.int tptp.nat)) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 A3) (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7694694392188491536nteger G) S) (@ (@ tptp.groups7694694392188491536nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3827104343326376752nteger G) S) (@ (@ tptp.groups3827104343326376752nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.one_one_Code_integer))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.one_one_Code_integer))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3674199335183972705nteger G) S) (@ (@ tptp.groups3674199335183972705nteger H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.assn)) (G (-> Bool tptp.assn))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.one_one_assn))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups5301882518646026715o_assn G) S) (@ (@ tptp.groups5301882518646026715o_assn H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups7882442080178216443t_assn G) S) (@ (@ tptp.groups7882442080178216443t_assn H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.one_one_assn))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.one_one_assn))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1304777262505850412r_assn G) S) (@ (@ tptp.groups1304777262505850412r_assn H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.one_one_rat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.one_one_rat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2869687844427037835_o_rat G) S) (@ (@ tptp.groups2869687844427037835_o_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_int) (S tptp.set_int) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int T) (=> (@ tptp.finite_finite_int S) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int T) S)) (= (@ H I3) tptp.one_one_rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) (@ (@ tptp.minus_minus_set_int S) T)) (= (@ G I3) tptp.one_one_rat))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups1072433553688619179nt_rat G) S) (@ (@ tptp.groups1072433553688619179nt_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_Code_integer) (S tptp.set_Code_integer) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger T) (=> (@ tptp.finite6017078050557962740nteger S) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger T) S)) (= (@ H I3) tptp.one_one_rat))) (=> (forall ((I3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer I3) (@ (@ tptp.minus_2355218937544613996nteger S) T)) (= (@ G I3) tptp.one_one_rat))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups2555765274223993564er_rat G) S) (@ (@ tptp.groups2555765274223993564er_rat H) T)))))))))
% 6.81/7.14 (assert (forall ((T tptp.set_o) (S tptp.set_o) (H (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o T) (=> (@ tptp.finite_finite_o S) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o T) S)) (= (@ H I3) tptp.one_one_nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) (@ (@ tptp.minus_minus_set_o S) T)) (= (@ G I3) tptp.one_one_nat))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ (@ tptp.inf_inf_set_o S) T)) (= (@ G X3) (@ H X3)))) (= (@ (@ tptp.groups3504817904513533571_o_nat G) S) (@ (@ tptp.groups3504817904513533571_o_nat H) T)))))))))
% 6.81/7.14 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (D2 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D2))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (D2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (let ((_let_2 (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6325495683096345652atural (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural (@ tptp.semiri3763490453095760265atural I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural)) (@ (@ tptp.plus_p4538020629002901425atural (@ _let_2 A)) (@ (@ tptp.times_2397367101498566445atural _let_1) D2))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (D2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D2))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (D2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 A)) (@ (@ tptp.times_3573771949741848930nteger _let_1) D2))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D2))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) A3) (= (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A3) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R3) K3))))) (@ tptp.set_ord_atMost_nat R3)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R3))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I4))))) _let_1)))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (Q6 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 Q6))) (=> (@ (@ 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)))))))))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N2) M))) (= (@ (@ tptp.groups708209901874060359at_nat G) _let_1) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I4))))) _let_1)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat N2) M))) (= (@ (@ tptp.groups705719431365010083at_int G) _let_1) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ tptp.suc I4))))) _let_1)))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I4)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat (@ tptp.minus_minus_nat N)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))))))
% 6.81/7.14 (assert (= tptp.semiri3624122377584611663nteger (lambda ((N tptp.nat)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat (@ tptp.minus_minus_nat N)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))))))
% 6.81/7.14 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat (@ tptp.minus_minus_nat N)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))))))
% 6.81/7.14 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.gbinomial_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) K3))) K3)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) M))))
% 6.81/7.14 (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))))))))))
% 6.81/7.14 (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))))))))))
% 6.81/7.14 (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))))))))))
% 6.81/7.14 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) X4)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3906332499630173760nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3906332499630173760nt_rat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups6602215022474089585er_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups6602215022474089585er_rat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups4541462559716669496nt_nat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups7237345082560585321er_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups7237345082560585321er_nat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups7234854612051535045er_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups7234854612051535045er_int G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups2906978787729119204at_rat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_int (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups3539618377306564664at_int G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_int (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int H) (@ _let_2 _let_1))) (@ (@ tptp.groups4538972089207619220nt_int G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_list_nat) (P (-> tptp.list_nat Bool)) (H (-> tptp.list_nat tptp.rat)) (G (-> tptp.list_nat tptp.rat))) (let ((_let_1 (@ tptp.collect_list_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_list_nat A3))) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (@ (@ tptp.groups3760926236672600436at_rat (lambda ((X4 tptp.list_nat)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups3760926236672600436at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups3760926236672600436at_rat G) (@ _let_2 (@ tptp.uminus3195874150345416415st_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3827104343326376752nteger (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups3827104343326376752nteger H) (@ _let_2 _let_1))) (@ (@ tptp.groups3827104343326376752nteger G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups3674199335183972705nteger (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups3674199335183972705nteger H) (@ _let_2 _let_1))) (@ (@ tptp.groups3674199335183972705nteger G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3455450783089532116nteger (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.groups3455450783089532116nteger H) (@ _let_2 _let_1))) (@ (@ tptp.groups3455450783089532116nteger G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.assn)) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7882442080178216443t_assn (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_assn (@ (@ tptp.groups7882442080178216443t_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups7882442080178216443t_assn G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.assn)) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups1304777262505850412r_assn (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_assn (@ (@ tptp.groups1304777262505850412r_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups1304777262505850412r_assn G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.assn)) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups6906906614972039071t_assn (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_assn (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_assn (@ (@ tptp.groups6906906614972039071t_assn H) (@ _let_2 _let_1))) (@ (@ tptp.groups6906906614972039071t_assn G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups1072433553688619179nt_rat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_rat (@ (@ tptp.groups1072433553688619179nt_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1072433553688619179nt_rat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (H (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.collect_Code_integer P))) (let ((_let_2 (@ tptp.inf_in1364745209274528805nteger A3))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups2555765274223993564er_rat (lambda ((X4 tptp.code_integer)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_rat (@ (@ tptp.groups2555765274223993564er_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups2555765274223993564er_rat G) (@ _let_2 (@ tptp.uminus804700908173204444nteger _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (H (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.collect_nat P))) (let ((_let_2 (@ tptp.inf_inf_set_nat A3))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups73079841787564623at_rat (lambda ((X4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_rat (@ (@ tptp.groups73079841787564623at_rat H) (@ _let_2 _let_1))) (@ (@ tptp.groups73079841787564623at_rat G) (@ _let_2 (@ tptp.uminus5710092332889474511et_nat _let_1))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (H (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.collect_int P))) (let ((_let_2 (@ tptp.inf_inf_set_int A3))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups1707563613775114915nt_nat (lambda ((X4 tptp.int)) (@ (@ (@ tptp.if_nat (@ P X4)) (@ H X4)) (@ G X4)))) A3) (@ (@ tptp.times_times_nat (@ (@ tptp.groups1707563613775114915nt_nat H) (@ _let_2 _let_1))) (@ (@ tptp.groups1707563613775114915nt_nat G) (@ _let_2 (@ tptp.uminus1532241313380277803et_int _let_1))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri773545260158071498ct_rat _let_3) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat _let_2) _let_3)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N2))) (@ tptp.semiri773545260158071498ct_rat N2))))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (= (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (D2 tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri3763490453095760265atural N2))) (= (@ (@ tptp.groups6325495683096345652atural (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p4538020629002901425atural A) (@ (@ tptp.times_2397367101498566445atural (@ tptp.semiri3763490453095760265atural I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.plus_p4538020629002901425atural _let_2) tptp.one_one_Code_natural)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural _let_1) A)) (@ (@ tptp.times_2397367101498566445atural _let_2) D2)))) _let_1))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (D2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D2)))) _let_1))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (D2 tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D2)))) _let_1))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (D2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I4)) D2)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D2)))) _let_1))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (= (@ (@ tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.multis2468970476368604999at_nat))) (let ((_let_1 (@ tptp.groups6857163185585827899at_nat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.zero_z1048942125864253310at_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_p7104986032573967614at_nat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (Q6 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 Q6))) (=> (@ (@ 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)))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.one_one_assn)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (let ((_let_2 (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.set_or4665077453230672383an_nat M) N2))) (@ G N2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3674199335183972705nteger F) A3)) (@ (@ tptp.groups3674199335183972705nteger G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_o)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups7694694392188491536nteger F) A3)) (@ (@ tptp.groups7694694392188491536nteger G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3455450783089532116nteger F) A3)) (@ (@ tptp.groups3455450783089532116nteger G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A3) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) _let_1) (@ (@ tptp.ord_le6747313008572928689nteger _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_int)) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.groups3827104343326376752nteger F) A3)) (@ (@ tptp.groups3827104343326376752nteger G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (G (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2555765274223993564er_rat F) A3)) (@ (@ tptp.groups2555765274223993564er_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.rat)) (G (-> Bool tptp.rat))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2869687844427037835_o_rat F) A3)) (@ (@ tptp.groups2869687844427037835_o_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((I3 tptp.nat)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_nat I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups73079841787564623at_rat F) A3)) (@ (@ tptp.groups73079841787564623at_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((I3 tptp.int)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_int I3) A3) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_rat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1072433553688619179nt_rat F) A3)) (@ (@ tptp.groups1072433553688619179nt_rat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((I3 tptp.code_integer)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_Code_integer I3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3190895334310489300er_nat F) A3)) (@ (@ tptp.groups3190895334310489300er_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((I3 Bool)) (let ((_let_1 (@ F I3))) (=> (@ (@ tptp.member_o I3) A3) (and (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) _let_1) (@ (@ tptp.ord_less_nat _let_1) (@ G I3)))))) (=> (not (= A3 tptp.bot_bot_set_o)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A3)) (@ (@ tptp.groups3504817904513533571_o_nat G) A3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F B4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B4)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A3)) (@ _let_1 B3))))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups7873554091576472773nteger G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.int))) (let ((_let_1 (@ tptp.groups975429370522433651at_int F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F (-> tptp.produc859450856879609959at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups1265588324298845189at_rat F))) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F (-> tptp.produc859450856879609959at_nat tptp.int))) (let ((_let_1 (@ tptp.groups1898227913876290649at_int F))) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.one_one_assn))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (= (@ G X3) tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (= (@ G X3) tptp.one_one_nat))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_nat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.assn))) (let ((_let_1 (@ tptp.groups5301882518646026715o_assn G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (= (@ (@ tptp.inf_inf_set_nat A3) B3) tptp.bot_bot_set_nat) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (= (@ (@ tptp.inf_inf_set_int A3) B3) tptp.bot_bot_set_int) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_assn (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (= (@ (@ tptp.inf_in1364745209274528805nteger A3) B3) tptp.bot_bo3990330152332043303nteger) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_o) (G (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat G))) (=> (@ tptp.finite_finite_o A3) (=> (@ tptp.finite_finite_o B3) (=> (= (@ (@ tptp.inf_inf_set_o A3) B3) tptp.bot_bot_set_o) (= (@ _let_1 (@ (@ tptp.sup_sup_set_o A3) B3)) (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B3))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B3))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (let ((_let_2 (@ (@ tptp.sup_su848401254843788991nteger A3) B3))) (=> (@ tptp.finite6017078050557962740nteger _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A3) B3))) (=> (@ tptp.finite_finite_nat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A3) B3))) (=> (@ tptp.finite_finite_nat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_nat A3) B3))) (=> (@ tptp.finite_finite_nat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int F))) (let ((_let_2 (@ (@ tptp.sup_sup_set_int A3) B3))) (=> (@ tptp.finite_finite_int _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat F))) (let ((_let_2 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3))) (=> (@ tptp.finite6177210948735845034at_nat _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups342789780944988191at_rat G))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_1356011639430497352at_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.assn))) (let ((_let_1 (@ tptp.groups7882442080178216443t_assn G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.assn))) (let ((_let_1 (@ tptp.groups1304777262505850412r_assn G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.assn))) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (G (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat G))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ _let_1 (@ (@ tptp.minus_2355218937544613996nteger B3) A3)))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_nat B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat G))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A3) B3))) (@ _let_1 (@ (@ tptp.minus_minus_set_int B3) A3)))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.times_times_rat _let_2) Z)) _let_4) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s4028243227959126397er_rat Z) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri3763490453095760265atural N2))) (= (@ (@ tptp.groups6325495683096345652atural tptp.semiri3763490453095760265atural) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.plus_p4538020629002901425atural _let_1) tptp.one_one_Code_natural))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups977919841031483927at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F (-> tptp.produc859450856879609959at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups1900718384385340925at_nat F))) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (F (-> tptp.produc4166570645942440679at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups7059897769266147197at_nat F))) (=> (@ tptp.finite1918287321285529104at_nat A3) (=> (@ tptp.finite1918287321285529104at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.nat))) (let ((_let_1 (@ tptp.groups3860910324918113789at_nat F))) (=> (@ tptp.finite4343798906461161616at_nat A3) (=> (@ tptp.finite4343798906461161616at_nat B3) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3)))))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat N2) M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat N2) M)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat N2) M)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I4)))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))
% 6.81/7.14 (assert (forall ((R3 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat R3) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R3) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat _let_1)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat R3) _let_1))))))
% 6.81/7.14 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A5 tptp.rat) (N tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_rat A5) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.81/7.14 (assert (= tptp.comm_s8582702949713902594nteger (lambda ((A5 tptp.code_integer) (N tptp.nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A5) (@ tptp.semiri4939895301339042750nteger I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.81/7.14 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A5 tptp.nat) (N tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat A5) (@ tptp.semiri1316708129612266289at_nat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.81/7.14 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A5 tptp.int) (N tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_int A5) (@ tptp.semiri1314217659103216013at_int I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri773545260158071498ct_rat N2) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) N2)))) (@ tptp.semiri773545260158071498ct_rat _let_1)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) N2)))) (@ tptp.semiri1406184849735516958ct_int _let_1)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri3624122377584611663nteger N2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) N2)))) (@ tptp.semiri3624122377584611663nteger _let_1)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) N2)))) (@ tptp.semiri1408675320244567234ct_nat _let_1)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_rat _let_1))) (= (@ (@ tptp.groups2906978787729119204at_rat (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat _let_2) (@ tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_rat _let_2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (B Bool) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups4406642042086082107nteger F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B3) A3)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups879477027807139574nteger F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups7501900531339628137nteger F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A3)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F X3)))) (@ (@ tptp.ord_le6747313008572928689nteger (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (B Bool) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups7872700643590313910_o_rat F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B3) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups6602215022474089585er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A3)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X3)))) (@ (@ tptp.ord_less_rat (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (B Bool) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.groups8507830703676809646_o_nat F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B3) A3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X3)))) (@ (@ tptp.ord_less_nat (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (B Bool) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups8505340233167759370_o_int F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (@ (@ tptp.member_o B) (@ (@ tptp.minus_minus_set_o B3) A3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (B tptp.code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ (@ tptp.member_Code_integer B) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X3)))) (@ (@ tptp.ord_less_int (@ _let_1 A3)) (@ _let_1 B3))))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.groups7694694392188491536nteger F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B4)))) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.rat))) (let ((_let_1 (@ tptp.groups2869687844427037835_o_rat F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B4)))) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((B4 tptp.nat)) (=> (@ (@ tptp.member_nat B4) (@ (@ tptp.minus_minus_set_nat B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B4)))) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.groups3502327434004483295_o_int F))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((B4 Bool)) (=> (@ (@ tptp.member_o B4) (@ (@ tptp.minus_minus_set_o B3) A3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((B4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer B4) (@ (@ tptp.minus_2355218937544613996nteger B3) A3)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ F B4)))) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F A4)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B3) A3)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ F A4)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((B4 tptp.int)) (=> (@ (@ tptp.member_int B4) (@ (@ tptp.minus_minus_set_int B3) A3)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ F B4)))) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F A4)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A3)) (@ _let_1 B3)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups1072433553688619179nt_rat F))) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ (@ tptp.inf_inf_set_int A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_int A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_int A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat))) (let ((_let_1 (@ tptp.groups2555765274223993564er_rat F))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) (@ (@ tptp.inf_in1364745209274528805nteger A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su848401254843788991nteger A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1364745209274528805nteger A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.rat))) (let ((_let_1 (@ tptp.groups3442636767675653108at_rat F))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su6327502436637775413at_nat A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in2572325071724192079at_nat A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat) (F (-> tptp.produc859450856879609959at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups7136053025338371162at_rat F))) (=> (@ tptp.finite4392333629123659920at_nat A3) (=> (@ tptp.finite4392333629123659920at_nat B3) (=> (forall ((X3 tptp.produc859450856879609959at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat X3) (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su718114333110466843at_nat A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in4302113700860409141at_nat A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat) (F (-> tptp.produc4166570645942440679at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups5938585286922990810at_rat F))) (=> (@ tptp.finite1918287321285529104at_nat A3) (=> (@ tptp.finite1918287321285529104at_nat B3) (=> (forall ((X3 tptp.produc4166570645942440679at_nat)) (=> (@ (@ tptp.member6689249552917799696at_nat X3) (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in1697001100524423349at_nat A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat) (F (-> tptp.produc3843707927480180839at_nat tptp.rat))) (let ((_let_1 (@ tptp.groups8874911130973611098at_rat F))) (=> (@ tptp.finite4343798906461161616at_nat A3) (=> (@ tptp.finite4343798906461161616at_nat B3) (=> (forall ((X3 tptp.produc3843707927480180839at_nat)) (=> (@ (@ tptp.member8757157785044589968at_nat X3) (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_in7913087082777306421at_nat A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups73079841787564623at_rat F))) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.inf_inf_set_nat A3) B3)) (not (= (@ F X3) tptp.zero_zero_rat)))) (= (@ _let_1 (@ (@ tptp.sup_sup_set_nat A3) B3)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_1 A3)) (@ _let_1 B3))) (@ _let_1 (@ (@ tptp.inf_inf_set_nat A3) B3))))))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.semiri681578069525770553at_rat K3))))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.gbinomial_rat A) (@ (@ tptp.plus_plus_nat M) tptp.one_one_nat))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_8256067586552552935nteger A) K3))) (@ (@ tptp.power_8256067586552552935nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) N2) (@ (@ tptp.groups7501900531339628137nteger (lambda ((K3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s8582702949713902594nteger A) K3))) (@ (@ tptp.comm_s8582702949713902594nteger B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (= tptp.gbinomial_rat (lambda ((A5 tptp.rat) (K3 tptp.nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A5) (@ tptp.semiri681578069525770553at_rat I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat K3) I4))))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K3)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (K tptp.nat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.gbinomial_rat A) K)) (@ tptp.semiri773545260158071498ct_rat K)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ (@ tptp.gbinomial_rat A) K)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_rat A) (@ tptp.semiri681578069525770553at_rat I4)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)))))
% 6.81/7.14 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 6.81/7.14 (assert (forall ((L tptp.num) (R3 tptp.nat) (Q6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q6) 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))))))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (R3 tptp.int) (Q6 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q6) 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))))))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (R3 tptp.code_integer) (Q6 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q6))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q6) 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))))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo8411746178871703098atural (@ (@ tptp.times_2397367101498566445atural A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.modulo8411746178871703098atural A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (=> (forall ((N5 tptp.nat)) (=> (@ P N5) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N5))))) (@ P N2))))))
% 6.81/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (or (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (=> (or (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (or (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (or (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (or (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool))) (=> (or (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q))) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (=> (or (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q))) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (and (@ P X4) (@ Q X4))))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X4 tptp.product_prod_int_int)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.list_nat Bool)) (Q (-> tptp.list_nat Bool))) (= (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((X4 tptp.list_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P)) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (= (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((X4 tptp.set_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P)) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_nat (@ tptp.collect_nat P)) (@ tptp.finite_finite_nat (@ tptp.collect_nat Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((X4 tptp.int)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite_finite_int (@ tptp.collect_int P)) (@ tptp.finite_finite_int (@ tptp.collect_int Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_integer Bool)) (Q (-> tptp.code_integer Bool))) (= (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((X4 tptp.code_integer)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P)) (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer Q))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool)) (Q (-> tptp.product_prod_nat_nat Bool))) (= (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X4 tptp.product_prod_nat_nat)) (or (@ P X4) (@ Q X4))))) (and (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P)) (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat Q))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.81/7.14 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 6.81/7.14 (assert (forall ((F4 tptp.set_int) (G2 tptp.set_int)) (=> (or (@ tptp.finite_finite_int F4) (@ tptp.finite_finite_int G2)) (@ tptp.finite_finite_int (@ (@ tptp.inf_inf_set_int F4) G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (=> (or (@ tptp.finite6017078050557962740nteger F4) (@ tptp.finite6017078050557962740nteger G2)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.inf_in1364745209274528805nteger F4) G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_nat) (G2 tptp.set_nat)) (=> (or (@ tptp.finite_finite_nat F4) (@ tptp.finite_finite_nat G2)) (@ tptp.finite_finite_nat (@ (@ tptp.inf_inf_set_nat F4) G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (or (@ tptp.finite6177210948735845034at_nat F4) (@ tptp.finite6177210948735845034at_nat G2)) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.inf_in2572325071724192079at_nat F4) G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_int) (G2 tptp.set_int)) (= (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F4) G2)) (and (@ tptp.finite_finite_int F4) (@ tptp.finite_finite_int G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (= (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger F4) G2)) (and (@ tptp.finite6017078050557962740nteger F4) (@ tptp.finite6017078050557962740nteger G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F4) G2)) (and (@ tptp.finite6177210948735845034at_nat F4) (@ tptp.finite6177210948735845034at_nat G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (= (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat F4) G2)) (and (@ tptp.finite4392333629123659920at_nat F4) (@ tptp.finite4392333629123659920at_nat G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr8551490117392284871at_nat) (G2 tptp.set_Pr8551490117392284871at_nat)) (= (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat F4) G2)) (and (@ tptp.finite1918287321285529104at_nat F4) (@ tptp.finite1918287321285529104at_nat G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (= (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F4) G2)) (and (@ tptp.finite4343798906461161616at_nat F4) (@ tptp.finite4343798906461161616at_nat G2)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_nat) (G2 tptp.set_nat)) (= (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F4) G2)) (and (@ tptp.finite_finite_nat F4) (@ tptp.finite_finite_nat G2)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_int A) I4) (@ (@ tptp.ord_less_eq_int I4) B)))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I4) (@ (@ tptp.ord_less_int I4) B)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (@ tptp.finite6931041176100689706nteger (@ tptp.collec574505750873337192nteger (lambda ((B6 tptp.set_Code_integer)) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (@ tptp.finite9047747110432174090at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le3146513528884898305at_nat B6) A3)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A3)))))))
% 6.81/7.14 (assert (forall ((M6 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M6) (exists ((N5 tptp.nat)) (forall ((X7 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X7) M6) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X7)) N5)))))))
% 6.81/7.14 (assert (forall ((M6 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M6) (exists ((N5 tptp.nat)) (forall ((X7 tptp.list_o)) (=> (@ (@ tptp.member_list_o X7) M6) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X7)) N5)))))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_int_int Bool))) (=> (not (@ tptp.finite2998713641127702882nt_int (@ tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.list_nat Bool))) (=> (not (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat P))) (exists ((X_1 tptp.list_nat)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.set_nat Bool))) (=> (not (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat P))) (exists ((X_1 tptp.set_nat)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat (@ tptp.collect_nat P))) (exists ((X_1 tptp.nat)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.int Bool))) (=> (not (@ tptp.finite_finite_int (@ tptp.collect_int P))) (exists ((X_1 tptp.int)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_integer Bool))) (=> (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer P))) (exists ((X_1 tptp.code_integer)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (=> (not (@ tptp.finite6177210948735845034at_nat (@ tptp.collec3392354462482085612at_nat P))) (exists ((X_1 tptp.product_prod_nat_nat)) (@ P X_1)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_nat) (R (-> Bool tptp.nat Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_int) (R (-> Bool tptp.int Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (B3 tptp.set_Code_integer) (R (-> Bool tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (R (-> tptp.nat tptp.int Bool))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (R (-> tptp.nat tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (R (-> tptp.int tptp.nat Bool))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (exists ((Xa2 tptp.int)) (and (@ (@ tptp.member_int Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_Code_integer) (R (-> tptp.int tptp.code_integer Bool))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (exists ((Xa2 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) B3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (R (-> tptp.code_integer tptp.nat Bool))) (=> (not (@ tptp.finite6017078050557962740nteger A3)) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (exists ((Xa2 tptp.nat)) (and (@ (@ tptp.member_nat Xa2) B3) (@ (@ R X3) Xa2))))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) B3) (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A3) (@ (@ R A5) X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o A) A3) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_o A) X3) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A3) (=> (@ (@ tptp.ord_less_eq_o X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat A) A3) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A3) (@ (@ tptp.ord_less_eq_set_nat A) X3) (forall ((Xa2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_nat X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.member_Code_integer A) A3) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger A) X3) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A3) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (@ (@ tptp.member_set_int A) A3) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A3) (@ (@ tptp.ord_less_eq_set_int A) X3) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A3) (=> (@ (@ tptp.member_rat A) A3) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A3) (@ (@ tptp.ord_less_eq_rat A) X3) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A3) (=> (@ (@ tptp.member_num A) A3) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A3) (@ (@ tptp.ord_less_eq_num A) X3) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A3) (=> (@ (@ tptp.ord_less_eq_num X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat A) A3) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat A) X3) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int A) A3) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_int A) X3) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_int X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (A Bool)) (=> (@ tptp.finite_finite_o A3) (=> (@ (@ tptp.member_o A) A3) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (@ (@ tptp.ord_less_eq_o X3) A) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A3) (=> (@ (@ tptp.ord_less_eq_o Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ (@ tptp.member_set_nat A) A3) (exists ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A3) (@ (@ tptp.ord_less_eq_set_nat X3) A) (forall ((Xa2 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_nat Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (A tptp.code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.member_Code_integer A) A3) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A3) (@ (@ tptp.ord_le3102999989581377725nteger X3) A) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A3) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (@ (@ tptp.member_set_int A) A3) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A3) (@ (@ tptp.ord_less_eq_set_int X3) A) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_int Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A3) (=> (@ (@ tptp.member_rat A) A3) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A3) (@ (@ tptp.ord_less_eq_rat X3) A) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_rat Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A3) (=> (@ (@ tptp.member_num A) A3) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A3) (@ (@ tptp.ord_less_eq_num X3) A) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A3) (=> (@ (@ tptp.ord_less_eq_num Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.member_nat A) A3) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (@ (@ tptp.ord_less_eq_nat X3) A) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_nat Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.member_int A) A3) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (@ (@ tptp.ord_less_eq_int X3) A) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_int Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (@ tptp.finite6017078050557962740nteger tptp.bot_bo3990330152332043303nteger))
% 6.81/7.14 (assert (@ tptp.finite6177210948735845034at_nat tptp.bot_bo2099793752762293965at_nat))
% 6.81/7.14 (assert (@ tptp.finite_finite_o tptp.bot_bot_set_o))
% 6.81/7.14 (assert (@ tptp.finite_finite_nat tptp.bot_bot_set_nat))
% 6.81/7.14 (assert (@ tptp.finite_finite_int tptp.bot_bot_set_int))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (= S tptp.bot_bo3990330152332043303nteger)))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (= S tptp.bot_bo2099793752762293965at_nat)))))
% 6.81/7.14 (assert (forall ((S tptp.set_o)) (=> (not (@ tptp.finite_finite_o S)) (not (= S tptp.bot_bot_set_o)))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (= S tptp.bot_bot_set_nat)))))
% 6.81/7.14 (assert (forall ((S tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (= S tptp.bot_bot_set_int)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (P (-> tptp.set_set_nat Bool))) (= (forall ((B6 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B6) (@ (@ tptp.image_nat_set_nat F) A3)) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_set_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F) A3)) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_int_nat F) A3)) (@ P B6))) (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B6) A3) (@ P (@ (@ tptp.image_int_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.set_int Bool))) (= (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_nat_int F) A3)) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.set_int Bool))) (= (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_int_int F) A3)) (@ P B6))) (forall ((B6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B6) A3) (@ P (@ (@ tptp.image_int_int F) B6)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ tptp.finite_finite_nat B3) (@ tptp.finite_finite_nat A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ tptp.finite6017078050557962740nteger B3) (@ tptp.finite6017078050557962740nteger A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (@ tptp.finite6177210948735845034at_nat B3) (@ tptp.finite6177210948735845034at_nat A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ tptp.finite_finite_int B3) (@ tptp.finite_finite_int A3)))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat S) T) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger S) T) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat S) T) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int S) T) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ tptp.finite_finite_nat A3)))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (@ tptp.finite6017078050557962740nteger A3)))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (@ tptp.finite6177210948735845034at_nat A3)))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ tptp.finite_finite_int A3)))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_int) (G2 tptp.set_int)) (=> (@ tptp.finite_finite_int F4) (=> (@ tptp.finite_finite_int G2) (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Code_integer) (G2 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger F4) (=> (@ tptp.finite6017078050557962740nteger G2) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr1261947904930325089at_nat) (G2 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat F4) (=> (@ tptp.finite6177210948735845034at_nat G2) (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr8693737435421807431at_nat) (G2 tptp.set_Pr8693737435421807431at_nat)) (=> (@ tptp.finite4392333629123659920at_nat F4) (=> (@ tptp.finite4392333629123659920at_nat G2) (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr8551490117392284871at_nat) (G2 tptp.set_Pr8551490117392284871at_nat)) (=> (@ tptp.finite1918287321285529104at_nat F4) (=> (@ tptp.finite1918287321285529104at_nat G2) (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_Pr4329608150637261639at_nat) (G2 tptp.set_Pr4329608150637261639at_nat)) (=> (@ tptp.finite4343798906461161616at_nat F4) (=> (@ tptp.finite4343798906461161616at_nat G2) (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat F4) G2))))))
% 6.81/7.14 (assert (forall ((F4 tptp.set_nat) (G2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat F4) (=> (@ tptp.finite_finite_nat G2) (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat F4) G2))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_int)) (=> (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (=> (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (=> (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (=> (not (@ tptp.finite4392333629123659920at_nat S)) (not (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (=> (not (@ tptp.finite1918287321285529104at_nat S)) (not (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (=> (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int) (T tptp.set_int)) (= (not (@ tptp.finite_finite_int (@ (@ tptp.sup_sup_set_int S) T))) (or (not (@ tptp.finite_finite_int S)) (not (@ tptp.finite_finite_int T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_Code_integer)) (= (not (@ tptp.finite6017078050557962740nteger (@ (@ tptp.sup_su848401254843788991nteger S) T))) (or (not (@ tptp.finite6017078050557962740nteger S)) (not (@ tptp.finite6017078050557962740nteger T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr1261947904930325089at_nat) (T tptp.set_Pr1261947904930325089at_nat)) (= (not (@ tptp.finite6177210948735845034at_nat (@ (@ tptp.sup_su6327502436637775413at_nat S) T))) (or (not (@ tptp.finite6177210948735845034at_nat S)) (not (@ tptp.finite6177210948735845034at_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr8693737435421807431at_nat) (T tptp.set_Pr8693737435421807431at_nat)) (= (not (@ tptp.finite4392333629123659920at_nat (@ (@ tptp.sup_su718114333110466843at_nat S) T))) (or (not (@ tptp.finite4392333629123659920at_nat S)) (not (@ tptp.finite4392333629123659920at_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr8551490117392284871at_nat) (T tptp.set_Pr8551490117392284871at_nat)) (= (not (@ tptp.finite1918287321285529104at_nat (@ (@ tptp.sup_su3035147773818789531at_nat S) T))) (or (not (@ tptp.finite1918287321285529104at_nat S)) (not (@ tptp.finite1918287321285529104at_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_Pr4329608150637261639at_nat) (T tptp.set_Pr4329608150637261639at_nat)) (= (not (@ tptp.finite4343798906461161616at_nat (@ (@ tptp.sup_su5525570899277871387at_nat S) T))) (or (not (@ tptp.finite4343798906461161616at_nat S)) (not (@ tptp.finite4343798906461161616at_nat T))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat) (T tptp.set_nat)) (= (not (@ tptp.finite_finite_nat (@ (@ tptp.sup_sup_set_nat S) T))) (or (not (@ tptp.finite_finite_nat S)) (not (@ tptp.finite_finite_nat T))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((A8 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A8) (=> (forall ((B8 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat B8) A8) (@ P B8))) (@ P A8)))) (@ P A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((A8 tptp.set_int)) (=> (@ tptp.finite_finite_int A8) (=> (forall ((B8 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B8) A8) (@ P B8))) (@ P A8)))) (@ P A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((A8 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A8) (=> (forall ((B8 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le1307284697595431911nteger B8) A8) (@ P B8))) (@ P A8)))) (@ P A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.set_Pr1261947904930325089at_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((A8 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A8) (=> (forall ((B8 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat B8) A8) (@ P B8))) (@ P A8)))) (@ P A3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_o_nat F) A3)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_o_int F) A3)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (=> (not (@ tptp.finite_finite_o A3)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_o_Code_integer F) A3)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (not (@ tptp.finite_finite_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_nat_nat F) A3)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_nat_int F) A3)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (=> (not (@ tptp.finite_finite_nat A3)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1215581382706833972nteger F) A3)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (not (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_int_nat F) A3)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite_finite_int (@ (@ tptp.image_int_int F) A3)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (=> (not (@ tptp.finite_finite_int A3)) (=> (@ tptp.finite6017078050557962740nteger (@ (@ tptp.image_1587234942943678608nteger F) A3)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (not (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (not (@ tptp.finite6017078050557962740nteger A3)) (=> (@ tptp.finite_finite_nat (@ (@ tptp.image_951025933927791156er_nat F) A3)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A3) (not (@ tptp.finite6017078050557962740nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A3) (= (@ F A5) (@ F X3)))))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (N2 tptp.nat)) (=> (= A3 (@ (@ tptp.image_nat_set_nat F) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2))))) (@ tptp.finite1152437895449049373et_nat A3))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (= A3 (@ (@ tptp.image_nat_nat F) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2))))) (@ tptp.finite_finite_nat A3))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (= A3 (@ (@ tptp.image_nat_int F) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2))))) (@ tptp.finite_finite_int A3))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (=> (= A3 (@ (@ tptp.image_1215581382706833972nteger F) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2))))) (@ tptp.finite6017078050557962740nteger A3))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.product_prod_nat_nat)) (N2 tptp.nat)) (=> (= A3 (@ (@ tptp.image_5846123807819985514at_nat F) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2))))) (@ tptp.finite6177210948735845034at_nat A3))))
% 6.81/7.14 (assert (= tptp.finite1152437895449049373et_nat (lambda ((A6 tptp.set_set_nat)) (exists ((N tptp.nat) (F3 (-> tptp.nat tptp.set_nat))) (= A6 (@ (@ tptp.image_nat_set_nat F3) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))))))))
% 6.81/7.14 (assert (= tptp.finite_finite_nat (lambda ((A6 tptp.set_nat)) (exists ((N tptp.nat) (F3 (-> tptp.nat tptp.nat))) (= A6 (@ (@ tptp.image_nat_nat F3) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))))))))
% 6.81/7.14 (assert (= tptp.finite_finite_int (lambda ((A6 tptp.set_int)) (exists ((N tptp.nat) (F3 (-> tptp.nat tptp.int))) (= A6 (@ (@ tptp.image_nat_int F3) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))))))))
% 6.81/7.14 (assert (= tptp.finite6017078050557962740nteger (lambda ((A6 tptp.set_Code_integer)) (exists ((N tptp.nat) (F3 (-> tptp.nat tptp.code_integer))) (= A6 (@ (@ tptp.image_1215581382706833972nteger F3) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))))))))
% 6.81/7.14 (assert (= tptp.finite6177210948735845034at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat)) (exists ((N tptp.nat) (F3 (-> tptp.nat tptp.product_prod_nat_nat))) (= A6 (@ (@ tptp.image_5846123807819985514at_nat F3) (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N)))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A3) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A3) (=> (@ (@ tptp.ord_le3102999989581377725nteger Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A3) (=> (@ (@ tptp.ord_less_eq_o Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A3) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_int Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A3) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_rat Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A3) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A3) (=> (@ (@ tptp.ord_less_eq_num Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_nat Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_int Xa2) X3) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (not (= A3 tptp.bot_bo3990330152332043303nteger)) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer X3) A3) (forall ((Xa2 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer Xa2) A3) (=> (@ (@ tptp.ord_le3102999989581377725nteger X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (=> (not (= A3 tptp.bot_bot_set_o)) (exists ((X3 Bool)) (and (@ (@ tptp.member_o X3) A3) (forall ((Xa2 Bool)) (=> (@ (@ tptp.member_o Xa2) A3) (=> (@ (@ tptp.ord_less_eq_o X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A3) (=> (not (= A3 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (@ (@ tptp.member_set_int X3) A3) (forall ((Xa2 tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_set_int X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A3) (=> (not (= A3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (@ (@ tptp.member_rat X3) A3) (forall ((Xa2 tptp.rat)) (=> (@ (@ tptp.member_rat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_rat X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_num)) (=> (@ tptp.finite_finite_num A3) (=> (not (= A3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (@ (@ tptp.member_num X3) A3) (forall ((Xa2 tptp.num)) (=> (@ (@ tptp.member_num Xa2) A3) (=> (@ (@ tptp.ord_less_eq_num X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (not (= A3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A3) (forall ((Xa2 tptp.nat)) (=> (@ (@ tptp.member_nat Xa2) A3) (=> (@ (@ tptp.ord_less_eq_nat X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (not (= A3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A3) (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) A3) (=> (@ (@ tptp.ord_less_eq_int X3) Xa2) (= X3 Xa2))))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_nat_nat F) A3)) (@ tptp.finite_finite_nat B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_Code_integer) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_1215581382706833972nteger F) A3)) (@ tptp.finite6017078050557962740nteger B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_nat) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_int_nat F) A3)) (@ tptp.finite_finite_nat B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_Code_integer) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_1587234942943678608nteger F) A3)) (@ tptp.finite6017078050557962740nteger B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_nat) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_951025933927791156er_nat F) A3)) (@ tptp.finite_finite_nat B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_4470545334726330049nteger F) A3)) (@ tptp.finite6017078050557962740nteger B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_int) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_nat_int F) A3)) (@ tptp.finite_finite_int B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_int_int F) A3)) (@ tptp.finite_finite_int B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_int) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_948535463418740880er_int F) A3)) (@ tptp.finite_finite_int B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat))) (=> (@ tptp.finite_finite_nat A3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B3) (@ (@ tptp.image_nat_set_nat F) A3)) (@ tptp.finite1152437895449049373et_nat B3)))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_nat_nat F) A3)) (exists ((C5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C5) A3) (@ tptp.finite_finite_nat C5) (= B3 (@ (@ tptp.image_nat_nat F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.code_integer tptp.nat)) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_951025933927791156er_nat F) A3)) (exists ((C5 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger C5) A3) (@ tptp.finite6017078050557962740nteger C5) (= B3 (@ (@ tptp.image_951025933927791156er_nat F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (F (-> tptp.nat tptp.code_integer)) (A3 tptp.set_nat)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_1215581382706833972nteger F) A3)) (exists ((C5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C5) A3) (@ tptp.finite_finite_nat C5) (= B3 (@ (@ tptp.image_1215581382706833972nteger F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_4470545334726330049nteger F) A3)) (exists ((C5 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger C5) A3) (@ tptp.finite6017078050557962740nteger C5) (= B3 (@ (@ tptp.image_4470545334726330049nteger F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (F (-> tptp.int tptp.nat)) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.image_int_nat F) A3)) (exists ((C5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int C5) A3) (@ tptp.finite_finite_int C5) (= B3 (@ (@ tptp.image_int_nat F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (F (-> tptp.int tptp.code_integer)) (A3 tptp.set_int)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger B3) (@ (@ tptp.image_1587234942943678608nteger F) A3)) (exists ((C5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int C5) A3) (@ tptp.finite_finite_int C5) (= B3 (@ (@ tptp.image_1587234942943678608nteger F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (F (-> tptp.nat tptp.int)) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_nat_int F) A3)) (exists ((C5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C5) A3) (@ tptp.finite_finite_nat C5) (= B3 (@ (@ tptp.image_nat_int F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (F (-> tptp.code_integer tptp.int)) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_948535463418740880er_int F) A3)) (exists ((C5 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger C5) A3) (@ tptp.finite6017078050557962740nteger C5) (= B3 (@ (@ tptp.image_948535463418740880er_int F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (F (-> tptp.int tptp.int)) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.image_int_int F) A3)) (exists ((C5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int C5) A3) (@ tptp.finite_finite_int C5) (= B3 (@ (@ tptp.image_int_int F) C5))))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_set_nat) (F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat B3) (@ (@ tptp.image_nat_set_nat F) A3)) (exists ((C5 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat C5) A3) (@ tptp.finite_finite_nat C5) (= B3 (@ (@ tptp.image_nat_set_nat F) C5))))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F) A3)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A3 tptp.set_Code_integer) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_951025933927791156er_nat F) A3)) (@ P B6))) (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3) (@ P (@ (@ tptp.image_951025933927791156er_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A3 tptp.set_nat) (P (-> tptp.set_Code_integer Bool))) (= (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_1215581382706833972nteger F) A3)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_1215581382706833972nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A3 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (= (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_4470545334726330049nteger F) A3)) (@ P B6))) (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3) (@ P (@ (@ tptp.image_4470545334726330049nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.set_nat Bool))) (= (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_int_nat F) A3)) (@ P B6))) (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3) (@ P (@ (@ tptp.image_int_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.code_integer)) (A3 tptp.set_int) (P (-> tptp.set_Code_integer Bool))) (= (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_1587234942943678608nteger F) A3)) (@ P B6))) (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3) (@ P (@ (@ tptp.image_1587234942943678608nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.set_int Bool))) (= (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_nat_int F) A3)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A3 tptp.set_Code_integer) (P (-> tptp.set_int Bool))) (= (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_948535463418740880er_int F) A3)) (@ P B6))) (exists ((B6 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3) (@ P (@ (@ tptp.image_948535463418740880er_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.set_int Bool))) (= (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_int_int F) A3)) (@ P B6))) (exists ((B6 tptp.set_int)) (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3) (@ P (@ (@ tptp.image_int_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (P (-> tptp.set_set_nat Bool))) (= (exists ((B6 tptp.set_set_nat)) (and (@ tptp.finite1152437895449049373et_nat B6) (@ (@ tptp.ord_le6893508408891458716et_nat B6) (@ (@ tptp.image_nat_set_nat F) A3)) (@ P B6))) (exists ((B6 tptp.set_nat)) (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3) (@ P (@ (@ tptp.image_nat_set_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_nat_nat F) A3))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3)) (@ P (@ (@ tptp.image_nat_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.nat)) (A3 tptp.set_Code_integer) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_951025933927791156er_nat F) A3))) (@ P B6))) (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3)) (@ P (@ (@ tptp.image_951025933927791156er_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.code_integer)) (A3 tptp.set_nat) (P (-> tptp.set_Code_integer Bool))) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_1215581382706833972nteger F) A3))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3)) (@ P (@ (@ tptp.image_1215581382706833972nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.code_integer)) (A3 tptp.set_Code_integer) (P (-> tptp.set_Code_integer Bool))) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_4470545334726330049nteger F) A3))) (@ P B6))) (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3)) (@ P (@ (@ tptp.image_4470545334726330049nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.nat)) (A3 tptp.set_int) (P (-> tptp.set_nat Bool))) (= (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) (@ (@ tptp.image_int_nat F) A3))) (@ P B6))) (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3)) (@ P (@ (@ tptp.image_int_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.code_integer)) (A3 tptp.set_int) (P (-> tptp.set_Code_integer Bool))) (= (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) (@ (@ tptp.image_1587234942943678608nteger F) A3))) (@ P B6))) (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3)) (@ P (@ (@ tptp.image_1587234942943678608nteger F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (A3 tptp.set_nat) (P (-> tptp.set_int Bool))) (= (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_nat_int F) A3))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3)) (@ P (@ (@ tptp.image_nat_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.code_integer tptp.int)) (A3 tptp.set_Code_integer) (P (-> tptp.set_int Bool))) (= (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_948535463418740880er_int F) A3))) (@ P B6))) (forall ((B6 tptp.set_Code_integer)) (=> (and (@ tptp.finite6017078050557962740nteger B6) (@ (@ tptp.ord_le7084787975880047091nteger B6) A3)) (@ P (@ (@ tptp.image_948535463418740880er_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int)) (A3 tptp.set_int) (P (-> tptp.set_int Bool))) (= (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) (@ (@ tptp.image_int_int F) A3))) (@ P B6))) (forall ((B6 tptp.set_int)) (=> (and (@ tptp.finite_finite_int B6) (@ (@ tptp.ord_less_eq_set_int B6) A3)) (@ P (@ (@ tptp.image_int_int F) B6)))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.set_nat)) (A3 tptp.set_nat) (P (-> tptp.set_set_nat Bool))) (= (forall ((B6 tptp.set_set_nat)) (=> (and (@ tptp.finite1152437895449049373et_nat B6) (@ (@ tptp.ord_le6893508408891458716et_nat B6) (@ (@ tptp.image_nat_set_nat F) A3))) (@ P B6))) (forall ((B6 tptp.set_nat)) (=> (and (@ tptp.finite_finite_nat B6) (@ (@ tptp.ord_less_eq_set_nat B6) A3)) (@ P (@ (@ tptp.image_nat_set_nat F) B6)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural tptp.zero_zero_nat) A) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)))))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural tptp.zero_zero_nat) A) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1617098188084679374atural (@ tptp.suc N2)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se1617098188084679374atural N2) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural (@ tptp.suc N2)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se168947363167071951atural N2) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7083795435491715335atural (@ tptp.suc N2)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.modulo8411746178871703098atural A) _let_1)) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.bit_se7083795435491715335atural N2) (@ (@ tptp.divide5121882707175180666atural A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.81/7.14 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A5) _let_1))))))))))
% 6.81/7.14 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y)))))))
% 6.81/7.14 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4))) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I4))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) I4))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I4))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I4)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I4))) tptp.zero_z3403309356797280102nteger))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))))))
% 6.81/7.14 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X4 tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X4))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim3151403230148437115or_rat X4)))))
% 6.81/7.14 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K3))))))
% 6.81/7.14 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 6.81/7.14 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.times_2397367101498566445atural A) (@ (@ tptp.divide5121882707175180666atural B) A)) B))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) A)) A) B))))
% 6.81/7.14 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.81/7.14 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) A)) A) B))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural B) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) A)) (@ (@ tptp.divide5121882707175180666atural B) A)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_7079662738309270450atural A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (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_8256067586552552935nteger A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W2))) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.zero_z3403309356797280102nteger) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger)))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_natural _let_1) A)) (= (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1))) tptp.one_one_Code_natural) A)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (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_8256067586552552935nteger A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (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_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) _let_1)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (and _let_2 (= A tptp.zero_z3403309356797280102nteger)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (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)))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) A)) _let_2) (@ (@ tptp.divide5121882707175180666atural A) _let_2))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_7079662738309270450atural _let_1) N2))) (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) N2) (= (@ (@ tptp.modulo8411746178871703098atural (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo8411746178871703098atural A) _let_2))))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B9 tptp.nat) (C6 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B9) C6)) (@ (@ tptp.dvd_dvd_nat B9) B) (@ (@ tptp.dvd_dvd_nat C6) C))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B9 tptp.int) (C6 tptp.int)) (and (= A (@ (@ tptp.times_times_int B9) C6)) (@ (@ tptp.dvd_dvd_int B9) B) (@ (@ tptp.dvd_dvd_int C6) C))))))
% 6.81/7.14 (assert (forall ((P3 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P3) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P3 (@ (@ tptp.times_times_nat X3) Y3)) (=> (@ (@ tptp.dvd_dvd_nat X3) A) (not (@ (@ tptp.dvd_dvd_nat Y3) B)))))))))
% 6.81/7.14 (assert (forall ((P3 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P3) (@ (@ tptp.times_times_int A) B)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.times_times_int X3) Y3)) (=> (@ (@ tptp.dvd_dvd_int X3) A) (not (@ (@ tptp.dvd_dvd_int Y3) B)))))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))))
% 6.81/7.14 (assert (forall ((B tptp.assn) (A tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn B) A) (not (forall ((K2 tptp.assn)) (not (= A (@ (@ tptp.times_times_assn B) K2))))))))
% 6.81/7.14 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K2 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K2))))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (K tptp.assn)) (=> (= A (@ (@ tptp.times_times_assn B) K)) (@ (@ tptp.dvd_dvd_assn B) A))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.81/7.14 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B5 tptp.code_integer) (A5 tptp.code_integer)) (exists ((K3 tptp.code_integer)) (= A5 (@ (@ tptp.times_3573771949741848930nteger B5) K3))))))
% 6.81/7.14 (assert (= tptp.dvd_dvd_assn (lambda ((B5 tptp.assn) (A5 tptp.assn)) (exists ((K3 tptp.assn)) (= A5 (@ (@ tptp.times_times_assn B5) K3))))))
% 6.81/7.14 (assert (= tptp.dvd_dvd_rat (lambda ((B5 tptp.rat) (A5 tptp.rat)) (exists ((K3 tptp.rat)) (= A5 (@ (@ tptp.times_times_rat B5) K3))))))
% 6.81/7.14 (assert (= tptp.dvd_dvd_nat (lambda ((B5 tptp.nat) (A5 tptp.nat)) (exists ((K3 tptp.nat)) (= A5 (@ (@ tptp.times_times_nat B5) K3))))))
% 6.81/7.14 (assert (= tptp.dvd_dvd_int (lambda ((B5 tptp.int) (A5 tptp.int)) (exists ((K3 tptp.int)) (= A5 (@ (@ tptp.times_times_int B5) K3))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (C tptp.assn) (B tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (let ((_let_1 (@ tptp.dvd_dvd_assn A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_assn B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn A) C))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn A) B))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn) (D2 tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn A) B) (=> (@ (@ tptp.dvd_dvd_assn C) D2) (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) C)) (@ (@ tptp.times_times_assn B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn) (C tptp.assn)) (=> (@ (@ tptp.dvd_dvd_assn (@ (@ tptp.times_times_assn A) B)) C) (@ (@ tptp.dvd_dvd_assn B) C))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.81/7.14 (assert (forall ((A tptp.assn) (B tptp.assn)) (@ (@ tptp.dvd_dvd_assn A) (@ (@ tptp.times_times_assn B) A))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) A)))) (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) A)))) (@ tptp.collect_nat (lambda ((C4 tptp.nat)) (@ (@ tptp.dvd_dvd_nat C4) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) A)))) (@ tptp.collect_int (lambda ((C4 tptp.int)) (@ (@ tptp.dvd_dvd_int C4) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) A)))) (@ tptp.collect_Code_integer (lambda ((C4 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C4) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X7) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X7) S2)))) (=> (@ (@ tptp.ord_less_rat Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X7) S2)))) (=> (@ (@ tptp.ord_less_nat Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X7) S2)))) (=> (@ (@ tptp.ord_less_int Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X7) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X7) S2))))) (=> (@ (@ tptp.ord_less_rat Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X7) S2))))) (=> (@ (@ tptp.ord_less_nat Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X7) S2))))) (=> (@ (@ tptp.ord_less_int Z2) X7) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X7) S2)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X7) S2)))) (=> (@ (@ tptp.ord_less_rat X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X7) S2)))) (=> (@ (@ tptp.ord_less_nat X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X7) S2)))) (=> (@ (@ tptp.ord_less_int X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X7 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D2) (@ (@ tptp.plus_p5714425477246183910nteger X7) S2))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (S2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X7 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D2) (@ (@ tptp.plus_plus_rat X7) S2))))) (=> (@ (@ tptp.ord_less_rat X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.nat) (S2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X7 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D2) (@ (@ tptp.plus_plus_nat X7) S2))))) (=> (@ (@ tptp.ord_less_nat X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (S2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X7 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D2) (@ (@ tptp.plus_plus_int X7) S2))))) (=> (@ (@ tptp.ord_less_int X7) Z2) (= _let_1 _let_1)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (D2 tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D2) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D2)))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (D2 tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D2) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D2)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D2 tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D2)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (D2 tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (=> (@ (@ tptp.dvd_dvd_Code_natural D2) C) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) (@ (@ tptp.divide5121882707175180666atural C) D2)) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) (@ (@ tptp.times_2397367101498566445atural B) D2)))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) C)) B) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.divide5121882707175180666atural B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (let ((_let_2 (@ (@ tptp.times_2397367101498566445atural B) C))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.times_2397367101498566445atural (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 6.81/7.14 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural B) C)) A) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural B) A)) C)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.81/7.14 (assert (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X4 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X4))) (exists ((X4 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X4) tptp.zero_z3403309356797280102nteger)) (@ P X4))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (@ P (@ (@ 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)) (@ P X4))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X4))) (exists ((X4 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X4) tptp.zero_zero_nat)) (@ P X4))))))
% 6.81/7.14 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X4 tptp.int)) (@ P (@ (@ tptp.times_times_int L) X4))) (exists ((X4 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X4) tptp.zero_zero_int)) (@ P X4))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T5 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D3) (forall ((X7 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X7) T5))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T5)))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (D3 tptp.rat) (T5 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D3) (forall ((X7 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X7) T5))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K4) D3))) T5)))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (D3 tptp.int) (T5 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D3) (forall ((X7 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X7) T5))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K4) D3))) T5)))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.code_integer) (D3 tptp.code_integer) (T5 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D2) D3) (forall ((X7 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D2))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X7) T5)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X7) (@ (@ tptp.times_3573771949741848930nteger K4) D3))) T5))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.rat) (D3 tptp.rat) (T5 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D2) D3) (forall ((X7 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X7) T5)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X7) (@ (@ tptp.times_times_rat K4) D3))) T5))))))))
% 6.81/7.14 (assert (forall ((D2 tptp.int) (D3 tptp.int) (T5 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D2) D3) (forall ((X7 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X7) T5)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X7) (@ (@ tptp.times_times_int K4) D3))) T5))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D2) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D2) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D2)))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D2 tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D2) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D2) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D2)))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D2 tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D2) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D2) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D2)))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (C tptp.code_natural) (B tptp.code_natural) (D2 tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (=> (@ (@ tptp.dvd_dvd_Code_natural C) D2) (= (= (@ (@ tptp.divide5121882707175180666atural B) A) (@ (@ tptp.divide5121882707175180666atural D2) C)) (= (@ (@ tptp.times_2397367101498566445atural B) C) (@ (@ tptp.times_2397367101498566445atural A) D2)))))))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (=> (not (= C tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural C) B) (= (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.times_2397367101498566445atural A) C)) B))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (not (= B tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ (@ tptp.dvd_dvd_Code_natural (@ (@ tptp.divide5121882707175180666atural A) B)) C) (@ (@ tptp.dvd_dvd_Code_natural A) (@ (@ tptp.times_2397367101498566445atural C) B)))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural) (C tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) B) (= (= (@ (@ tptp.divide5121882707175180666atural B) A) C) (= B (@ (@ tptp.times_2397367101498566445atural C) A)))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (C tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (A tptp.code_natural) (B tptp.code_natural)) (let ((_let_1 (@ tptp.times_2397367101498566445atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (= (@ _let_1 (@ (@ tptp.divide5121882707175180666atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.divide5121882707175180666atural A) B)) C) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) C)) B)))))
% 6.81/7.14 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((C tptp.code_natural) (B tptp.code_natural) (A tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural A))) (=> (@ (@ tptp.dvd_dvd_Code_natural C) tptp.one_one_Code_natural) (=> (@ (@ tptp.dvd_dvd_Code_natural B) A) (= (@ _let_1 (@ (@ tptp.times_2397367101498566445atural B) C)) (@ (@ tptp.divide5121882707175180666atural (@ _let_1 B)) C)))))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (= A (@ (@ tptp.divide5121882707175180666atural C) B)) (= (@ (@ tptp.times_2397367101498566445atural A) B) C)))))
% 6.81/7.14 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 6.81/7.14 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 6.81/7.14 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 6.81/7.14 (assert (forall ((B tptp.code_natural) (A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (= (@ (@ tptp.divide5121882707175180666atural A) B) C) (= A (@ (@ tptp.times_2397367101498566445atural C) B))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.groups3190895334310489300er_nat F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.groups3188404863801439024er_int F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.groups3455450783089532116nteger F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.groups3674199335183972705nteger F))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups1707563613775114915nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.groups3827104343326376752nteger F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups708209901874060359at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups705719431365010083at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups1705073143266064639nt_int F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.dvd_dvd_int (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.product_prod_nat_nat tptp.nat))) (let ((_let_1 (@ tptp.groups4077766827762148844at_nat F))) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A3)) (@ _let_1 B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.nat)) (G (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3504817904513533571_o_nat F) A3)) (@ (@ tptp.groups3504817904513533571_o_nat G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (G (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups3190895334310489300er_nat F) A3)) (@ (@ tptp.groups3190895334310489300er_nat G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.int)) (G (-> Bool tptp.int))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3502327434004483295_o_int F) A3)) (@ (@ tptp.groups3502327434004483295_o_int G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (G (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.dvd_dvd_int (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.groups3188404863801439024er_int F) A3)) (@ (@ tptp.groups3188404863801439024er_int G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (F (-> Bool tptp.code_integer)) (G (-> Bool tptp.code_integer))) (=> (@ tptp.finite_finite_o B3) (=> (@ (@ tptp.ord_less_eq_set_o A3) B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (@ (@ tptp.dvd_dvd_Code_integer (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups7694694392188491536nteger F) A3)) (@ (@ tptp.groups7694694392188491536nteger G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (G (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (@ (@ tptp.dvd_dvd_Code_integer (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3455450783089532116nteger F) A3)) (@ (@ tptp.groups3455450783089532116nteger G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (G (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (forall ((A4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer A4) A3) (@ (@ tptp.dvd_dvd_Code_integer (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3674199335183972705nteger F) A3)) (@ (@ tptp.groups3674199335183972705nteger G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups1707563613775114915nt_nat F) A3)) (@ (@ tptp.groups1707563613775114915nt_nat G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (G (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (@ (@ tptp.dvd_dvd_Code_integer (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.groups3827104343326376752nteger F) A3)) (@ (@ tptp.groups3827104343326376752nteger G) B3)))))))
% 6.81/7.14 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (@ (@ tptp.dvd_dvd_nat (@ F A4)) (@ G A4)))) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.groups708209901874060359at_nat F) A3)) (@ (@ tptp.groups708209901874060359at_nat G) B3)))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat N2))) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q6) (@ (@ tptp.modulo_modulo_nat N2) Q6)) (@ (@ tptp.dvd_dvd_nat Q6) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.81/7.14 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X)) (@ tptp.archim7778729529865785530nd_rat X))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M)))))))
% 6.81/7.14 (assert (@ (@ (@ tptp.ordering_top_nat tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N) (not (= M3 N))))) tptp.zero_zero_nat))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.divide5121882707175180666atural A) (@ (@ tptp.times_2397367101498566445atural B) A)) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) B))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (B tptp.code_natural)) (=> (not (= A tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B) tptp.one_one_Code_natural) (= (@ (@ tptp.divide5121882707175180666atural A) (@ (@ tptp.times_2397367101498566445atural A) B)) (@ (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural) B))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B4 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B4 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B4) tptp.one_one_nat) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_nat A) B4) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B4)))))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B4 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B4 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B4) tptp.one_one_int) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_times_int A) B4) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B4)))))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B4 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B4 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B4) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B4) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B4)))))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (C tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural A) tptp.one_one_Code_natural) (not (=> (not (= A tptp.zero_z2226904508553997617atural)) (forall ((B4 tptp.code_natural)) (let ((_let_1 (@ tptp.divide5121882707175180666atural tptp.one_one_Code_natural))) (=> (not (= B4 tptp.zero_z2226904508553997617atural)) (=> (@ (@ tptp.dvd_dvd_Code_natural B4) tptp.one_one_Code_natural) (=> (= (@ _let_1 A) B4) (=> (= (@ _let_1 B4) A) (=> (= (@ (@ tptp.times_2397367101498566445atural A) B4) tptp.one_one_Code_natural) (not (= (@ (@ tptp.divide5121882707175180666atural C) A) (@ (@ tptp.times_2397367101498566445atural C) B4)))))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B4 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4))))))))
% 6.81/7.14 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B4 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B4))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B4 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B4))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (=> (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A) (not (forall ((B4 tptp.code_natural)) (not (= A (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) B4))))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat (@ tptp.semiri773545260158071498ct_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.81/7.14 (assert (forall ((Q6 tptp.nat) (N2 tptp.nat) (R3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R3) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q6))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q6)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q6)))))))))))
% 6.81/7.14 (assert (forall ((R3 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R3) N2) (=> (@ (@ tptp.ord_less_eq_nat R3) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R3)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R3))))))
% 6.81/7.14 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_natural _let_1) A) (= (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)) A)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A3)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((A5 tptp.int)) (@ (@ tptp.divide_divide_nat (@ F A5)) B))) (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (@ (@ tptp.dvd_dvd_nat B) (@ F A5))))))) (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (not (@ (@ tptp.dvd_dvd_nat B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (B tptp.nat)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A3))) (let ((_let_2 (@ tptp.groups7237345082560585321er_nat F))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.divide_divide_nat (@ _let_2 A3)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups7237345082560585321er_nat (lambda ((A5 tptp.code_integer)) (@ (@ tptp.divide_divide_nat (@ F A5)) B))) (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ tptp.dvd_dvd_nat B) (@ F A5))))))) (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (not (@ (@ tptp.dvd_dvd_nat B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (B tptp.int)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A3))) (let ((_let_2 (@ tptp.groups7234854612051535045er_int F))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.divide_divide_int (@ _let_2 A3)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups7234854612051535045er_int (lambda ((A5 tptp.code_integer)) (@ (@ tptp.divide_divide_int (@ F A5)) B))) (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ tptp.dvd_dvd_int B) (@ F A5))))))) (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (not (@ (@ tptp.dvd_dvd_int B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int)) (B tptp.int)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.divide_divide_int (@ _let_2 A3)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((A5 tptp.nat)) (@ (@ tptp.divide_divide_int (@ F A5)) B))) (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.dvd_dvd_int B) (@ F A5))))))) (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (not (@ (@ tptp.dvd_dvd_int B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (B tptp.code_integer)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ tptp.groups7873554091576472773nteger F))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 A3)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((A5 tptp.int)) (@ (@ tptp.divide6298287555418463151nteger (@ F A5)) B))) (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5))))))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (not (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (B tptp.code_integer)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A3))) (let ((_let_2 (@ tptp.groups879477027807139574nteger F))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 A3)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.groups879477027807139574nteger (lambda ((A5 tptp.code_integer)) (@ (@ tptp.divide6298287555418463151nteger (@ F A5)) B))) (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5))))))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (not (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (B tptp.code_integer)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.groups7501900531339628137nteger F))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 A3)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((A5 tptp.nat)) (@ (@ tptp.divide6298287555418463151nteger (@ F A5)) B))) (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5))))))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (not (@ (@ tptp.dvd_dvd_Code_integer B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_inf_set_int A3))) (let ((_let_2 (@ tptp.groups6697149243333190288atural F))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A3)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.groups6697149243333190288atural (lambda ((A5 tptp.int)) (@ (@ tptp.divide5121882707175180666atural (@ F A5)) B))) (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5))))))) (@ (@ tptp.divide5121882707175180666atural (@ _let_2 (@ _let_1 (@ tptp.collect_int (lambda ((A5 tptp.int)) (not (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_in1364745209274528805nteger A3))) (let ((_let_2 (@ tptp.groups8926444216418632897atural F))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A3)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.groups8926444216418632897atural (lambda ((A5 tptp.code_integer)) (@ (@ tptp.divide5121882707175180666atural (@ F A5)) B))) (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5))))))) (@ (@ tptp.divide5121882707175180666atural (@ _let_2 (@ _let_1 (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (not (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_natural)) (B tptp.code_natural)) (let ((_let_1 (@ tptp.inf_inf_set_nat A3))) (let ((_let_2 (@ tptp.groups6325495683096345652atural F))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.divide5121882707175180666atural (@ _let_2 A3)) B) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.groups6325495683096345652atural (lambda ((A5 tptp.nat)) (@ (@ tptp.divide5121882707175180666atural (@ F A5)) B))) (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5))))))) (@ (@ tptp.divide5121882707175180666atural (@ _let_2 (@ _let_1 (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (not (@ (@ tptp.dvd_dvd_Code_natural B) (@ F A5)))))))) B))))))))
% 6.81/7.14 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.81/7.14 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_nat))))))))
% 6.81/7.14 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_int))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_Code_integer))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (=> (not (@ (@ tptp.dvd_dvd_Code_natural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A)) (not (forall ((B4 tptp.code_natural)) (not (= A (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) B4)) tptp.one_one_Code_natural))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ _let_1 A))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (@ _let_1 A))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_set_nat) (R (-> tptp.set_nat tptp.set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (forall ((X3 tptp.set_nat)) (not (@ (@ R X3) X3))) (=> (forall ((X3 tptp.set_nat) (Y3 tptp.set_nat) (Z2 tptp.set_nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X3) A3) (exists ((Y6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bot_set_set_nat)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (R (-> tptp.code_integer tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (forall ((X3 tptp.code_integer)) (not (@ (@ R X3) X3))) (=> (forall ((X3 tptp.code_integer) (Y3 tptp.code_integer) (Z2 tptp.code_integer)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) A3) (exists ((Y6 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bo3990330152332043303nteger)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (R (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (forall ((X3 tptp.product_prod_nat_nat)) (not (@ (@ R X3) X3))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (Z2 tptp.product_prod_nat_nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X3) A3) (exists ((Y6 tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bo2099793752762293965at_nat)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_o) (R (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o A3) (=> (forall ((X3 Bool)) (not (@ (@ R X3) X3))) (=> (forall ((X3 Bool) (Y3 Bool) (Z2 Bool)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) A3) (exists ((Y6 Bool)) (and (@ (@ tptp.member_o Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bot_set_o)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (=> (forall ((X3 tptp.nat)) (not (@ (@ R X3) X3))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat) (Z2 tptp.nat)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A3) (exists ((Y6 tptp.nat)) (and (@ (@ tptp.member_nat Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bot_set_nat)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (R (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (=> (forall ((X3 tptp.int)) (not (@ (@ R X3) X3))) (=> (forall ((X3 tptp.int) (Y3 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ R X3))) (=> (@ _let_1 Y3) (=> (@ (@ R Y3) Z2) (@ _let_1 Z2))))) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A3) (exists ((Y6 tptp.int)) (and (@ (@ tptp.member_int Y6) A3) (@ (@ R X3) Y6))))) (= A3 tptp.bot_bot_set_int)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_z3403309356797280102nteger))) (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.81/7.14 (assert (forall ((K tptp.nat) (S tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N9 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N9) (@ (@ tptp.member_nat N9) S))))) (not (@ tptp.finite_finite_nat S)))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M3 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ (@ tptp.member_nat N) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S)) (forall ((M3 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ (@ tptp.member_nat N) S)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.minus_7197305767214868737atural (@ _let_2 M)) tptp.one_one_Code_natural)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (and _let_1 (= A tptp.zero_z3403309356797280102nteger))))))))
% 6.81/7.14 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_Code_natural _let_1) (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.minus_7197305767214868737atural (@ _let_2 M)) tptp.one_one_Code_natural)) _let_3)) (or (= _let_3 tptp.zero_z2226904508553997617atural) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_7079662738309270450atural _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_natural _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide5121882707175180666atural (@ (@ tptp.times_2397367101498566445atural A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z2226904508553997617atural) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide5121882707175180666atural A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.81/7.14 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.81/7.14 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.81/7.14 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M3 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M3) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S)))))))
% 6.81/7.14 (assert (forall ((S tptp.set_int)) (= (not (@ tptp.finite_finite_int S)) (forall ((M3 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_int M3) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat N2)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X) N2))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.member8277197624267554838et_nat (@ (@ tptp.produc4532415448927165861et_nat A3) B3)) tptp.finite_psubset_nat) (and (@ (@ tptp.ord_less_set_nat A3) B3) (@ tptp.finite_finite_nat B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.member2572552093476627150et_int (@ (@ tptp.produc6363374080413544029et_int A3) B3)) tptp.finite_psubset_int) (and (@ (@ tptp.ord_less_set_int A3) B3) (@ tptp.finite_finite_int B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (= (@ (@ tptp.member4307123515891402160nteger (@ (@ tptp.produc7443773368509356479nteger A3) B3)) tptp.finite2416775604798480986nteger) (and (@ (@ tptp.ord_le1307284697595431911nteger A3) B3) (@ tptp.finite6017078050557962740nteger B3)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat A3) B3)) tptp.finite469560695537375940at_nat) (and (@ (@ tptp.ord_le7866589430770878221at_nat A3) B3) (@ tptp.finite6177210948735845034at_nat B3)))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (assert (forall ((A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se168947363167071951atural tptp.zero_zero_nat) A) (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.dvd_dvd_Code_natural _let_1) A))) (@ (@ tptp.times_2397367101498566445atural _let_1) (@ (@ tptp.divide5121882707175180666atural A) _let_1)))))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (assert (= tptp.nat_set_decode (lambda ((X4 tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X4) (@ (@ tptp.power_power_nat _let_1) N))))))))))
% 6.81/7.14 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A5 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A5) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A5) _let_1)))))))
% 6.81/7.14 (assert (= tptp.bit_se569199155075624693atural (lambda ((N tptp.nat) (A5 tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_natural (= N tptp.zero_zero_nat)) tptp.zero_z2226904508553997617atural) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide5121882707175180666atural A5) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A5) _let_1)))))))
% 6.81/7.14 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A5) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A5) _let_1)))))))
% 6.81/7.14 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A5 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A5) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A5) _let_1)))))))
% 6.81/7.14 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q7 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q7 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q7 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo8411746178871703098atural tptp.one_one_Code_natural) (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.81/7.14 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) A3) (@ (@ tptp.member_o (@ (@ F A) B)) (@ (@ tptp.image_3693632289388996572_nat_o (@ tptp.produc6081775807080527818_nat_o F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat tptp.nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) A3) (@ (@ tptp.member_nat (@ (@ F A) B)) (@ (@ tptp.image_2486076414777270412at_nat (@ tptp.produc6842872674320459806at_nat F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat tptp.int))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) A3) (@ (@ tptp.member_int (@ (@ F A) B)) (@ (@ tptp.image_2483585944268220136at_int (@ tptp.produc6840382203811409530at_int F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) A3) (@ (@ tptp.member_o (@ (@ F A) B)) (@ (@ tptp.image_2135063354759101220_int_o (@ tptp.produc4947309494688390418_int_o F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int tptp.int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) A3) (@ (@ tptp.member_int (@ (@ F A) B)) (@ (@ tptp.image_5042161079198086560nt_int (@ tptp.produc8211389475949308722nt_int F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat tptp.set_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) A3) (@ (@ tptp.member_set_nat (@ (@ F A) B)) (@ (@ tptp.image_15824709712370754et_nat (@ tptp.produc6189476227299908564et_nat F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.nat) (B tptp.nat) (A3 tptp.set_Pr1261947904930325089at_nat) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat))) (=> (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat A) B)) A3) (@ (@ tptp.member8440522571783428010at_nat (@ (@ F A) B)) (@ (@ tptp.image_5168914502847457605at_nat (@ tptp.produc2626176000494625587at_nat F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.int) (B tptp.int) (A3 tptp.set_Pr958786334691620121nt_int) (F (-> tptp.int tptp.int tptp.product_prod_int_int))) (=> (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int A) B)) A3) (@ (@ tptp.member5262025264175285858nt_int (@ (@ F A) B)) (@ (@ tptp.image_2653370878348428101nt_int (@ tptp.produc4245557441103728435nt_int F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A3 tptp.set_Pr7098220151150636591it_nat) (F (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (=> (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A) B)) A3) (@ (@ tptp.member_o (@ (@ F A) B)) (@ (@ tptp.image_1991556864075471768_nat_o (@ tptp.produc8860486935419594360_nat_o F)) A3)))))
% 6.81/7.14 (assert (forall ((A tptp.a) (B tptp.produc6653097349344004940it_nat) (A3 tptp.set_Pr7098220151150636591it_nat) (F (-> tptp.a tptp.produc6653097349344004940it_nat tptp.nat))) (=> (@ (@ tptp.member4554412811331277712it_nat (@ (@ tptp.produc9178034014595674355it_nat A) B)) A3) (@ (@ tptp.member_nat (@ (@ F A) B)) (@ (@ tptp.image_1030127162643715024at_nat (@ tptp.produc7727125748877983984at_nat F)) A3)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc3610074571335452306at_nat (@ tptp.produc27273713700761075at_nat F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc3704529784387675049_nat_o (@ tptp.produc8739625826339149834_nat_o F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int))) (= (@ tptp.produc8249235968001453780nt_int (@ tptp.produc4245557441103728435nt_int F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool))) (= (@ tptp.produc175634133007206835_int_o (@ tptp.produc4947309494688390418_int_o F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.int))) (= (@ tptp.produc1016772743285680337nt_int (@ tptp.produc8211389475949308722nt_int F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (@ tptp.produc3610074571335452306at_nat F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (@ tptp.produc3704529784387675049_nat_o F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (@ tptp.produc8249235968001453780nt_int F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (@ tptp.produc175634133007206835_int_o F)) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (@ tptp.produc1016772743285680337nt_int F)) F)))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.81/7.14 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.81/7.14 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 6.81/7.14 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 6.81/7.14 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P X4))))) A3) (@ (@ tptp.groups7873554091576472773nteger F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P X4))))) A3) (@ (@ tptp.groups879477027807139574nteger F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ F X4)) (@ tptp.zero_n356916108424825756nteger (@ P X4))))) A3) (@ (@ tptp.groups7501900531339628137nteger F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))))) A3) (@ (@ tptp.groups3906332499630173760nt_rat F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.rat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))))) A3) (@ (@ tptp.groups6602215022474089585er_rat F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ F X4)) (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))))) A3) (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ F X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P X4))))) A3) (@ (@ tptp.groups4541462559716669496nt_nat F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_nat (@ F X4)) (@ tptp.zero_n2687167440665602831ol_nat (@ P X4))))) A3) (@ (@ tptp.groups7237345082560585321er_nat F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int)) (P (-> tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_int (@ F X4)) (@ tptp.zero_n2684676970156552555ol_int (@ P X4))))) A3) (@ (@ tptp.groups7234854612051535045er_int F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ F X4)) (@ tptp.zero_n2684676970156552555ol_int (@ P X4))))) A3) (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (F (-> tptp.int tptp.code_integer))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups7873554091576472773nteger F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.code_integer))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups879477027807139574nteger F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.code_integer))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups7501900531339628137nteger F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups3906332499630173760nt_rat F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.rat))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups6602215022474089585er_rat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups6602215022474089585er_rat F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool)) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups4541462559716669496nt_nat F) (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups7237345082560585321er_nat F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool)) (F (-> tptp.code_integer tptp.int))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups7234854612051535045er_int F) (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P)))))))
% 6.81/7.14 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool)) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ P X4))) (@ F X4)))) A3) (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se569199155075624693atural M) _let_1) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera5444537566228673987atural _let_1))) (= (@ (@ tptp.bit_se569199155075624693atural N2) _let_2) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.81/7.14 (assert (= tptp.produc27273713700761075at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ (@ F3 A5) B5) Y4))) X4))))
% 6.81/7.14 (assert (= tptp.produc8739625826339149834_nat_o (lambda ((F3 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((A5 tptp.nat) (B5 tptp.nat)) (@ (@ (@ F3 A5) B5) Y4))) X4))))
% 6.81/7.14 (assert (= tptp.produc27273713700761075at_nat (lambda ((F3 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((L2 tptp.nat) (R4 tptp.nat)) (@ (@ (@ F3 L2) R4) Y4))) X4))))
% 6.81/7.14 (assert (= tptp.produc8739625826339149834_nat_o (lambda ((F3 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((L2 tptp.nat) (R4 tptp.nat)) (@ (@ (@ F3 L2) R4) Y4))) X4))))
% 6.81/7.14 (assert (forall ((H (-> Bool Bool)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> Bool tptp.int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.int Bool)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.int tptp.int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.product_prod_int_int Bool)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.product_prod_int_int tptp.int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc8211389475949308722nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> Bool tptp.product_prod_int_int)) (F (-> tptp.int tptp.int Bool)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4947309494688390418_int_o F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc8211389475949308722nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> tptp.product_prod_int_int tptp.product_prod_int_int)) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (Prod tptp.product_prod_int_int)) (= (@ H (@ (@ tptp.produc4245557441103728435nt_int F) Prod)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((X13 tptp.int) (X23 tptp.int)) (@ H (@ (@ F X13) X23)))) Prod))))
% 6.81/7.14 (assert (forall ((H (-> (-> tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat Bool)) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Prod tptp.product_prod_nat_nat)) (= (@ H (@ (@ tptp.produc8739625826339149834_nat_o F) Prod)) (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X13 tptp.nat) (X23 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ H (@ (@ F X13) X23)) __flatten_var_0))) Prod))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q6)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q6)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.81/7.14 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.81/7.14 (assert (forall ((Q6 tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X3) Y3) Q6) (= (@ (@ F X3) Y3) (@ (@ G X3) Y3)))) (=> (= P3 Q6) (= (@ (@ tptp.produc27273713700761075at_nat F) P3) (@ (@ tptp.produc27273713700761075at_nat G) Q6))))))
% 6.81/7.14 (assert (forall ((Q6 tptp.product_prod_nat_nat) (F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat)) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat X3) Y3) Q6) (= (@ (@ F X3) Y3) (@ (@ G X3) Y3)))) (=> (= P3 Q6) (= (@ (@ tptp.produc8739625826339149834_nat_o F) P3) (@ (@ tptp.produc8739625826339149834_nat_o G) Q6))))))
% 6.81/7.14 (assert (forall ((Q6 tptp.product_prod_int_int) (F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.int tptp.int tptp.product_prod_int_int)) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int X3) Y3) Q6) (= (@ (@ F X3) Y3) (@ (@ G X3) Y3)))) (=> (= P3 Q6) (= (@ (@ tptp.produc4245557441103728435nt_int F) P3) (@ (@ tptp.produc4245557441103728435nt_int G) Q6))))))
% 6.81/7.14 (assert (forall ((Q6 tptp.product_prod_int_int) (F (-> tptp.int tptp.int Bool)) (G (-> tptp.int tptp.int Bool)) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int X3) Y3) Q6) (= (@ (@ F X3) Y3) (@ (@ G X3) Y3)))) (=> (= P3 Q6) (= (@ (@ tptp.produc4947309494688390418_int_o F) P3) (@ (@ tptp.produc4947309494688390418_int_o G) Q6))))))
% 6.81/7.14 (assert (forall ((Q6 tptp.product_prod_int_int) (F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.int tptp.int tptp.int)) (P3 tptp.product_prod_int_int)) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int X3) Y3) Q6) (= (@ (@ F X3) Y3) (@ (@ G X3) Y3)))) (=> (= P3 Q6) (= (@ (@ tptp.produc8211389475949308722nt_int F) P3) (@ (@ tptp.produc8211389475949308722nt_int G) Q6))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X2)) (@ (@ F X1) X2))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X2 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X2)) (@ (@ F X1) X2))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X2)) (@ (@ F X1) X2))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X2)) (@ (@ F X1) X2))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X2 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X2)) (@ (@ F X1) X2))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3925858234332021118et_nat)) (= (@ (@ tptp.produc4058941399401191971et_nat tptp.produc5001842942810119800et_nat) P3) P3)))
% 6.81/7.14 (assert (forall ((P3 tptp.produc2732055786443039994et_nat)) (= (@ (@ tptp.produc2377985495875741467et_nat tptp.produc2245416461498447860et_nat) P3) P3)))
% 6.81/7.14 (assert (forall ((P3 tptp.produc2285326912895808259nt_int)) (= (@ (@ tptp.produc8492565224438309093nt_int tptp.produc5700946648718959541nt_int) P3) P3)))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int)) (= (@ (@ tptp.produc5122537100556696953nt_int tptp.produc4305682042979456191nt_int) P3) P3)))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat)) (= (@ (@ tptp.produc2183267410226956569it_nat tptp.produc9178034014595674355it_nat) P3) P3)))
% 6.81/7.14 (assert (forall ((P3 tptp.product_prod_int_int)) (= (@ (@ tptp.produc4245557441103728435nt_int tptp.product_Pair_int_int) P3) P3)))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X3 tptp.nat) (Y3 tptp.nat)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_nat_nat X3) Y3)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X3 tptp.int) (Y3 tptp.int)) (= (@ (@ F X3) Y3) (@ G (@ (@ tptp.product_Pair_int_int X3) Y3)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X4) Y4)) __flatten_var_0))) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X4) Y4)) __flatten_var_0))) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X4) Y4)))) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X4) Y4)))) F)))
% 6.81/7.14 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X4 tptp.int) (Y4 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X4) Y4)))) F)))
% 6.81/7.14 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ Q (@ (@ P X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.81/7.14 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.81/7.14 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M) (= M N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N2) (not (@ (@ tptp.dvd_dvd_int N2) M))))))
% 6.81/7.14 (assert (= tptp.uncurr8011562610307062878at_nat tptp.produc27273713700761075at_nat))
% 6.81/7.14 (assert (= tptp.uncurr7511940902602773877_nat_o tptp.produc8739625826339149834_nat_o))
% 6.81/7.14 (assert (= tptp.uncurr7650761721940715016nt_int tptp.produc4245557441103728435nt_int))
% 6.81/7.14 (assert (= tptp.uncurry_int_int_o tptp.produc4947309494688390418_int_o))
% 6.81/7.14 (assert (= tptp.uncurry_int_int_int tptp.produc8211389475949308722nt_int))
% 6.81/7.14 (assert (= tptp.produc1854806715440696265at_nat tptp.produc27273713700761075at_nat))
% 6.81/7.14 (assert (= tptp.produc4780622933104268256_nat_o tptp.produc8739625826339149834_nat_o))
% 6.81/7.14 (assert (= tptp.produc297006045350968285nt_int tptp.produc4245557441103728435nt_int))
% 6.81/7.14 (assert (= tptp.produc8005341501107743676_int_o tptp.produc4947309494688390418_int_o))
% 6.81/7.14 (assert (= tptp.produc7926200574084438792nt_int tptp.produc8211389475949308722nt_int))
% 6.81/7.14 (assert (forall ((I2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D5 tptp.int)) (@ (@ tptp.dvd_dvd_int D5) I2)))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z) N2)))))
% 6.81/7.14 (assert (forall ((I2 tptp.int) (D2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D2) I2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D2)) (@ tptp.abs_abs_int I2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.14 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N2)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 K))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N2) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A4 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A4) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.code_integer) (B4 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B4)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.code_natural Bool)) (A tptp.code_natural)) (=> (forall ((A4 tptp.code_natural)) (=> (= (@ (@ tptp.divide5121882707175180666atural A4) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.code_natural) (B4 Bool)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p4538020629002901425atural (@ tptp.zero_n8403883297036319079atural B4)) (@ (@ tptp.times_2397367101498566445atural _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide5121882707175180666atural _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A4 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.nat) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B4)) (@ (@ tptp.times_times_nat _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.81/7.14 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A4 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A4) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A4) (@ P A4))) (=> (forall ((A4 tptp.int) (B4 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B4)) (@ (@ tptp.times_times_int _let_1) A4)))) (=> (@ P A4) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A4) (@ P _let_2)))))) (@ P A)))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.81/7.14 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q7 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q7)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M3) N)) N))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo8411746178871703098atural _let_2) (@ _let_1 N2)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.code_natural)) (let ((_let_1 (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N2)) A) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N2) (@ (@ tptp.divide5121882707175180666atural A) _let_1))) _let_1)) (@ (@ tptp.modulo8411746178871703098atural A) _let_1))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.81/7.14 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.81/7.14 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q7 tptp.nat) (R4 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R4)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R4) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_7079662738309270450atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide5121882707175180666atural _let_2) (@ _let_1 N2)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.zero_n8403883297036319079atural (and (not (= _let_2 tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.81/7.14 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q7 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R4)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R4) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q7 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q7)))))) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q7 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q7) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q7 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q7) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q7 tptp.code_integer) (R4 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q7) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R4)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.81/7.14 (assert (forall ((Q6 tptp.int) (R3 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q6) R3)) (@ (@ tptp.plus_plus_int Q6) (@ tptp.zero_n2684676970156552555ol_int (not (= R3 tptp.zero_zero_int)))))))
% 6.81/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M3) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M3) (@ tptp.bit0 N)))))))
% 6.81/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M3) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M3) (@ tptp.bit0 N)))))))
% 6.81/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M3) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M3) (@ tptp.bit0 N)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc1437786849005270451_nat_o F) (@ (@ tptp.produc5001842942810119800et_nat A) B)))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc838355143741117751_nat_o F) (@ (@ tptp.produc2245416461498447860et_nat A) B)))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ F A) B) (@ (@ tptp.produc8860486935419594360_nat_o F) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3925858234332021118et_nat) (C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc1437786849005270451_nat_o C) P3))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc2732055786443039994et_nat) (C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3925858234332021118et_nat)) (=> (= P3 (@ (@ tptp.produc2245416461498447860et_nat A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc838355143741117751_nat_o C) P3))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc2285326912895808259nt_int) (C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc1573362020775583542_int_o C) P3))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc2558449545302689196_int_o C) P3))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat Bool))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc8860486935419594360_nat_o C) P3))))
% 6.81/7.14 (assert (forall ((P3 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int A4) B4)) (@ (@ C A4) B4))) (@ (@ tptp.produc4947309494688390418_int_o C) P3))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_o Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc5350075035600711000_set_o C) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc7315013382793309350et_nat C) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_int)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3137162363284112642et_int C) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.set_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_set_nat)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member_set_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8632796428668088668et_nat C) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.product_prod_nat_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_Pr1261947904930325089at_nat)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8253449849199807809at_nat C) (@ (@ tptp.produc9178034014595674355it_nat A) B)))))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_o)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_o Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8646739037753556108_set_o C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8289552606927098482et_nat C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_int)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4111701587417901774et_int C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.81/7.14 (assert (forall ((Z tptp.set_nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_set_nat)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_set_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3577156405726439208et_nat C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.set_o)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (let ((_let_1 (@ tptp.member_o Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc7715693535893868691_set_o C) (@ (@ tptp.produc5001842942810119800et_nat A) B)))))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z Bool) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ tptp.member_o Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_o Z) (@ (@ tptp.produc5350075035600711000_set_o C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ tptp.member_nat Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc7315013382793309350et_nat C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.int) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_int))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ tptp.member_int Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc3137162363284112642et_int C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.set_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_set_nat))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ tptp.member_set_nat Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc8632796428668088668et_nat C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3260487557148687353it_nat) (Z tptp.product_prod_nat_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_Pr1261947904930325089at_nat))) (=> (forall ((A4 tptp.a) (B4 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat A4) B4)) (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ C A4) B4)))) (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ tptp.produc8253449849199807809at_nat C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int) (Z Bool) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_o))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (@ (@ tptp.member_o Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_o Z) (@ (@ tptp.produc8646739037753556108_set_o C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int) (Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (@ (@ tptp.member_nat Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc8289552606927098482et_nat C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int) (Z tptp.int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_int))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (@ (@ tptp.member_int Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc4111701587417901774et_int C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc7773217078559923341nt_int) (Z tptp.set_nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_set_nat))) (=> (forall ((A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (@ (@ tptp.member_set_nat Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc3577156405726439208et_nat C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.produc3925858234332021118et_nat) (Z Bool) (C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.set_o))) (=> (forall ((A4 (-> tptp.produc3658429121746597890et_nat Bool)) (B4 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat A4) B4)) (@ (@ tptp.member_o Z) (@ (@ C A4) B4)))) (@ (@ tptp.member_o Z) (@ (@ tptp.produc7715693535893868691_set_o C) P3)))))
% 6.81/7.14 (assert (forall ((P3 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A4) B4) P3) (@ (@ (@ C A4) B4) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P3) X))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.81/7.14 (assert (forall ((R3 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q7 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q7)))) (@ (@ tptp.bit_take_bit_num N2) M)))))
% 6.81/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.81/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.81/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.numera6620942414471956472nteger N2)) (@ (@ (@ tptp.case_o356765784539232260er_num tptp.zero_z3403309356797280102nteger) tptp.numera6620942414471956472nteger) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se569199155075624693atural _let_1) (@ tptp.numera5444537566228673987atural N2)) (@ (@ (@ tptp.case_o5621594795226839503al_num tptp.zero_z2226904508553997617atural) tptp.numera5444537566228673987atural) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2925701944663578781it_nat _let_1) (@ tptp.numeral_numeral_nat N2)) (@ (@ (@ tptp.case_option_nat_num tptp.zero_zero_nat) tptp.numeral_numeral_nat) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_o)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_o Z) (@ (@ tptp.produc5350075035600711000_set_o C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_o Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_nat)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc7315013382793309350et_nat C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_int)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc3137162363284112642et_int C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.set_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_set_nat)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc8632796428668088668et_nat C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member_set_nat Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.product_prod_nat_nat) (C (-> tptp.a tptp.produc6653097349344004940it_nat tptp.set_Pr1261947904930325089at_nat)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ tptp.produc8253449849199807809at_nat C) P3)) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ tptp.member8440522571783428010at_nat Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_o)) (P3 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_o Z) (@ (@ tptp.produc8646739037753556108_set_o C) P3)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_o Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_nat)) (P3 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc8289552606927098482et_nat C) P3)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_nat Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_int)) (P3 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc4111701587417901774et_int C) P3)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_int Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z tptp.set_nat) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_set_nat)) (P3 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc3577156405726439208et_nat C) P3)) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ tptp.member_set_nat Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((Z Bool) (C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat tptp.set_o)) (P3 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.member_o Z) (@ (@ tptp.produc7715693535893868691_set_o C) P3)) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)) (not (@ (@ tptp.member_o Z) (@ (@ C X3) Y3)))))))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.produc1437786849005270451_nat_o F) (@ (@ tptp.produc5001842942810119800et_nat A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) (A (-> tptp.produc3658429121746597890et_nat Bool)) (B tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.produc838355143741117751_nat_o F) (@ (@ tptp.produc2245416461498447860et_nat A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) (A tptp.a) (B tptp.produc6653097349344004940it_nat)) (=> (@ (@ tptp.produc8860486935419594360_nat_o F) (@ (@ tptp.produc9178034014595674355it_nat A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.81/7.14 (assert (forall ((C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3658429121746597890et_nat Bool)) (P3 tptp.produc3925858234332021118et_nat)) (=> (@ (@ tptp.produc1437786849005270451_nat_o C) P3) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3658429121746597890et_nat)) (=> (= P3 (@ (@ tptp.produc5001842942810119800et_nat X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((C (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.produc3925858234332021118et_nat Bool)) (P3 tptp.produc2732055786443039994et_nat)) (=> (@ (@ tptp.produc838355143741117751_nat_o C) P3) (not (forall ((X3 (-> tptp.produc3658429121746597890et_nat Bool)) (Y3 tptp.produc3925858234332021118et_nat)) (=> (= P3 (@ (@ tptp.produc2245416461498447860et_nat X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P3 tptp.produc2285326912895808259nt_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o C) P3) (not (forall ((X3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc5700946648718959541nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P3 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o C) P3) (not (forall ((X3 (-> tptp.int tptp.option6357759511663192854e_term)) (Y3 tptp.product_prod_int_int)) (=> (= P3 (@ (@ tptp.produc4305682042979456191nt_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((C (-> tptp.a tptp.produc6653097349344004940it_nat Bool)) (P3 tptp.produc3260487557148687353it_nat)) (=> (@ (@ tptp.produc8860486935419594360_nat_o C) P3) (not (forall ((X3 tptp.a) (Y3 tptp.produc6653097349344004940it_nat)) (=> (= P3 (@ (@ tptp.produc9178034014595674355it_nat X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P3 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P3) (not (forall ((X3 tptp.int) (Y3 tptp.int)) (=> (= P3 (@ (@ tptp.product_Pair_int_int X3) Y3)) (not (@ (@ C X3) Y3))))))))
% 6.81/7.14 (assert (forall ((R (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R A) B) C))))
% 6.81/7.14 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P3 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P3) Z) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (=> (= P3 (@ (@ tptp.product_Pair_nat_nat X3) Y3)) (not (@ (@ (@ C X3) Y3) Z))))))))
% 6.81/7.14 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q7 tptp.int) (R4 tptp.int)) (@ (@ tptp.plus_plus_int Q7) (@ tptp.zero_n2684676970156552555ol_int (not (= R4 tptp.zero_zero_int))))))))
% 6.81/7.14 (assert (forall ((A3 (-> tptp.int tptp.int Bool)) (B3 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A3) B3) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A3))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B3))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.81/7.14 (assert (forall ((F tptp.heap_Time_Heap_a) (G (-> tptp.a tptp.heap_Time_Heap_a)) (H tptp.heap_e7401611519738050253t_unit)) (= (@ (@ tptp.heap_Time_execute_a (@ (@ tptp.heap_Time_bind_a_a F) G)) H) (@ (@ (@ tptp.case_o6061097939050036047it_nat tptp.none_P2651198173097904984it_nat) (@ tptp.produc7850007024774191849it_nat (lambda ((X4 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc5645566021302314940it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711335rame_a N) (@ (@ tptp.heap_Time_execute_a (@ G X4)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F) H)))))
% 6.81/7.14 (assert (= tptp.map_to_set_int_int (lambda ((M3 (-> tptp.int tptp.option_int))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((K3 tptp.int) (V2 tptp.int)) (= (@ M3 K3) (@ tptp.some_int V2))))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.num) (Q6 tptp.num)) (=> (= (@ (@ tptp.bit_take_bit_num M) N2) (@ tptp.some_num Q6)) (= (@ (@ tptp.bit_se1745604003318907178nteger M) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q6)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.num) (Q6 tptp.num)) (=> (= (@ (@ tptp.bit_take_bit_num M) N2) (@ tptp.some_num Q6)) (= (@ (@ tptp.bit_se569199155075624693atural M) (@ tptp.numera5444537566228673987atural N2)) (@ tptp.numera5444537566228673987atural Q6)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.num) (Q6 tptp.num)) (=> (= (@ (@ tptp.bit_take_bit_num M) N2) (@ tptp.some_num Q6)) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q6)))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.num) (Q6 tptp.num)) (=> (= (@ (@ tptp.bit_take_bit_num M) N2) (@ tptp.some_num Q6)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q6)))))
% 6.81/7.14 (assert (= tptp.heap_Time_bind_a_a (lambda ((F3 tptp.heap_Time_Heap_a) (G3 (-> tptp.a tptp.heap_Time_Heap_a))) (@ tptp.heap_Time_Heap_a2 (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o6061097939050036047it_nat tptp.none_P2651198173097904984it_nat) (@ tptp.produc7850007024774191849it_nat (lambda ((R4 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc5645566021302314940it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T7616092557645711335rame_a N) (@ (@ tptp.heap_Time_execute_a (@ G3 R4)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))
% 6.81/7.14 (assert (= tptp.heap_T8685611227969916822t_unit (lambda ((F3 tptp.heap_Time_Heap_a) (G3 (-> tptp.a tptp.heap_T5738788834812785303t_unit))) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ (@ (@ tptp.case_o7727800614283616222it_nat tptp.none_P9117596204409417319it_nat) (@ tptp.produc5648861294512138360it_nat (lambda ((R4 tptp.a) (__flatten_var_0 tptp.produc6653097349344004940it_nat)) (@ (@ tptp.produc7488178964372371019it_nat (lambda ((H7 tptp.heap_e7401611519738050253t_unit) (N tptp.nat)) (@ (@ tptp.heap_T3616969660504097270t_unit N) (@ (@ tptp.heap_T875086893843062177t_unit (@ G3 R4)) H7)))) __flatten_var_0)))) (@ (@ tptp.heap_Time_execute_a F3) H6)))))))
% 6.81/7.14 (assert (= tptp.finite_psubset_nat (@ tptp.collec6662362479098859352et_nat (@ tptp.produc6247414631856714078_nat_o (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_set_nat A6) B6) (@ tptp.finite_finite_nat B6)))))))
% 6.81/7.14 (assert (= tptp.finite_psubset_int (@ tptp.collec957716948307931664et_int (@ tptp.produc4109468873575309990_int_o (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_set_int A6) B6) (@ tptp.finite_finite_int B6)))))))
% 6.81/7.14 (assert (= tptp.finite2416775604798480986nteger (@ tptp.collec2770208431294612722nteger (@ tptp.produc1658495936642081476eger_o (lambda ((A6 tptp.set_Code_integer) (B6 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le1307284697595431911nteger A6) B6) (@ tptp.finite6017078050557962740nteger B6)))))))
% 6.81/7.14 (assert (= tptp.finite469560695537375940at_nat (@ tptp.collec6321179662152712658at_nat (@ tptp.produc410239310623530412_nat_o (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.ord_le7866589430770878221at_nat A6) B6) (@ tptp.finite6177210948735845034at_nat B6)))))))
% 6.81/7.14 (assert (= tptp.rel_of4838799251197538391et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option936205604648967762et_nat)) (P4 (-> tptp.produc3925858234332021118et_nat Bool))) (@ tptp.collec1402215087704437587et_nat (@ tptp.produc1437786849005270451_nat_o (lambda ((K3 (-> tptp.produc3658429121746597890et_nat Bool)) (V2 tptp.produc3658429121746597890et_nat)) (and (= (@ M3 K3) (@ tptp.some_P624177172695371229et_nat V2)) (@ P4 (@ (@ tptp.produc5001842942810119800et_nat K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.rel_of7774016450764239315et_nat (lambda ((M3 (-> (-> tptp.produc3658429121746597890et_nat Bool) tptp.option5190343406534369742et_nat)) (P4 (-> tptp.produc2732055786443039994et_nat Bool))) (@ tptp.collec5543584681430388431et_nat (@ tptp.produc838355143741117751_nat_o (lambda ((K3 (-> tptp.produc3658429121746597890et_nat Bool)) (V2 tptp.produc3925858234332021118et_nat)) (and (= (@ M3 K3) (@ tptp.some_P750831030444334937et_nat V2)) (@ P4 (@ (@ tptp.produc2245416461498447860et_nat K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.rel_of8306664904814525588nt_int (lambda ((M3 (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.option4624381673175914239nt_int)) (P4 (-> tptp.produc2285326912895808259nt_int Bool))) (@ tptp.collec1790188477890212312nt_int (@ tptp.produc1573362020775583542_int_o (lambda ((K3 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (V2 tptp.product_prod_int_int)) (and (= (@ M3 K3) (@ tptp.some_P4184893108420464158nt_int V2)) (@ P4 (@ (@ tptp.produc5700946648718959541nt_int K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.rel_of5543720577181062686nt_int (lambda ((M3 (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.option4624381673175914239nt_int)) (P4 (-> tptp.produc7773217078559923341nt_int Bool))) (@ tptp.collec506566255779805410nt_int (@ tptp.produc2558449545302689196_int_o (lambda ((K3 (-> tptp.int tptp.option6357759511663192854e_term)) (V2 tptp.product_prod_int_int)) (and (= (@ M3 K3) (@ tptp.some_P4184893108420464158nt_int V2)) (@ P4 (@ (@ tptp.produc4305682042979456191nt_int K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.rel_of2761222537318653906it_nat (lambda ((M3 (-> tptp.a tptp.option233860712434008220it_nat)) (P4 (-> tptp.produc3260487557148687353it_nat Bool))) (@ tptp.collec4148678073425210574it_nat (@ tptp.produc8860486935419594360_nat_o (lambda ((K3 tptp.a) (V2 tptp.produc6653097349344004940it_nat)) (and (= (@ M3 K3) (@ tptp.some_P1054239925786823975it_nat V2)) (@ P4 (@ (@ tptp.produc9178034014595674355it_nat K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.rel_of_int_int (lambda ((M3 (-> tptp.int tptp.option_int)) (P4 (-> tptp.product_prod_int_int Bool))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((K3 tptp.int) (V2 tptp.int)) (and (= (@ M3 K3) (@ tptp.some_int V2)) (@ P4 (@ (@ tptp.product_Pair_int_int K3) V2)))))))))
% 6.81/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.81/7.14 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.81/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.81/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.81/7.14 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.81/7.14 (assert (= tptp.mlex_prod_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (R6 tptp.set_Pr1261947904930325089at_nat)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (@ F3 Y4))) (let ((_let_2 (@ F3 X4))) (or (@ (@ tptp.ord_less_nat _let_2) _let_1) (and (@ (@ tptp.ord_less_eq_nat _let_2) _let_1) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat X4) Y4)) R6)))))))))))
% 6.81/7.14 (assert (= tptp.mlex_prod_int (lambda ((F3 (-> tptp.int tptp.nat)) (R6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((X4 tptp.int) (Y4 tptp.int)) (let ((_let_1 (@ F3 Y4))) (let ((_let_2 (@ F3 X4))) (or (@ (@ tptp.ord_less_nat _let_2) _let_1) (and (@ (@ tptp.ord_less_eq_nat _let_2) _let_1) (@ (@ tptp.member5262025264175285858nt_int (@ (@ tptp.product_Pair_int_int X4) Y4)) R6)))))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q7 tptp.int) (R4 tptp.int)) (@ (@ tptp.product_Pair_int_int Q7) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q7 tptp.nat) (R4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q7 tptp.code_integer) (R4 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q7) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R4)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.81/7.14 (assert (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z6) (@ (@ tptp.ord_less_int Z8) Z6))))))))
% 6.81/7.14 (assert (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z8 tptp.int) (Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z8) (@ (@ tptp.ord_less_int Z8) Z6))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((P Bool) (Q (-> tptp.int tptp.int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (B5 tptp.int)) (and P (@ (@ Q A5) B5)))) (lambda ((Ab tptp.product_prod_int_int)) (and P (@ (@ tptp.produc4947309494688390418_int_o Q) Ab))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.81/7.14 (assert (forall ((Prod tptp.product_prod_int_int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((Uu2 tptp.int) (Uv tptp.int)) true)) Prod)))
% 6.81/7.14 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N5))))) (=> (forall ((N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N5))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N5))))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N5))))) (=> (forall ((M5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N5))))) (not (forall ((M5 tptp.num) (N5 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N5))))))))))))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera5444537566228673987atural N2))) (= (@ tptp.numera5444537566228673987atural (@ tptp.bit1 N2)) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.plus_p4538020629002901425atural _let_1) _let_1)) tptp.one_one_Code_natural)))))
% 6.81/7.14 (assert (forall ((Z tptp.code_integer) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger Z) _let_2)) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.assn) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_assn Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W2)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W2))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn Z) _let_2)) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.rat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (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 Z) _let_2)) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.nat) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (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 Z) _let_2)) _let_2))))))
% 6.81/7.14 (assert (forall ((Z tptp.int) (W2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (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 Z) _let_2)) _let_2))))))
% 6.81/7.14 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.times_3573771949741848930nteger A) A)) A))))
% 6.81/7.14 (assert (forall ((A tptp.assn)) (= (@ (@ tptp.power_power_assn A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_assn (@ (@ tptp.times_times_assn A) A)) A))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.suc N2)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural N2) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.81/7.14 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.81/7.14 (assert (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q7 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q7)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M)))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 K))) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.numeral_numeral_nat L)) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 K))) (@ (@ tptp.plus_p4538020629002901425atural (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ tptp.pred_numeral L)) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_natural))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups4077766827762148844at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups4075276357253098568at_int (@ tptp.produc6840382203811409530at_int G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.81/7.14 (assert (forall ((I2 Bool) (K Bool)) (= (@ (@ tptp.member_o I2) (@ tptp.set_ord_lessThan_o K)) (@ (@ tptp.ord_less_o I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (@ (@ tptp.member_set_nat I2) (@ tptp.set_or890127255671739683et_nat K)) (@ (@ tptp.ord_less_set_nat I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.assn) (K tptp.assn)) (= (@ (@ tptp.member_assn I2) (@ tptp.set_or7637083652282234053n_assn K)) (@ (@ tptp.ord_less_assn I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.81/7.14 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))))
% 6.81/7.14 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3455450783089532116nteger G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6906906614972039071t_assn G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_assn (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups73079841787564623at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))))
% 6.81/7.14 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))))
% 6.81/7.14 (assert (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M))))))
% 6.81/7.14 (assert (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (= tptp.set_or7637083652282234053n_assn (lambda ((U2 tptp.assn)) (@ tptp.collect_assn (lambda ((X4 tptp.assn)) (@ (@ tptp.ord_less_assn X4) U2))))))
% 6.81/7.14 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat X4) U2))))))
% 6.81/7.14 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X4 tptp.num)) (@ (@ tptp.ord_less_num X4) U2))))))
% 6.81/7.14 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) U2))))))
% 6.81/7.14 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X4 tptp.int)) (@ (@ tptp.ord_less_int X4) U2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))))
% 6.81/7.14 (assert (forall ((N2 Bool)) (= (= (@ tptp.set_ord_lessThan_o N2) tptp.bot_bot_set_o) (= N2 tptp.bot_bot_o))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.bot_bot_nat))))
% 6.81/7.14 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.81/7.14 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.81/7.14 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N2)) (@ (@ tptp.ord_less_rat M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.14 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups708209901874060359at_nat G) _let_1)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) _let_1) (@ (@ tptp.groups705719431365010083at_int G) _let_1)))))
% 6.81/7.14 (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_or4029947393144176647an_rat L) U)) (@ tptp.set_ord_lessThan_rat U)))))
% 6.81/7.14 (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_or1222409239386451017an_num L) U)) (@ tptp.set_ord_lessThan_num U)))))
% 6.81/7.14 (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_or4665077453230672383an_nat L) U)) (@ tptp.set_ord_lessThan_nat U)))))
% 6.81/7.14 (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_or4662586982721622107an_int L) U)) (@ tptp.set_ord_lessThan_int U)))))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ tptp.set_or5754767410780653050nteger L)) (@ (@ tptp.set_or8404916559141939852nteger L) U)) (@ tptp.set_or5754767410780653050nteger U)))))
% 6.81/7.14 (assert (forall ((L Bool) (U Bool)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.set_ord_lessThan_o L)) (@ (@ tptp.set_or8904488021354931149Most_o L) U)) tptp.bot_bot_set_o)))
% 6.81/7.14 (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)))
% 6.81/7.14 (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)))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ tptp.set_or5754767410780653050nteger L)) (@ (@ tptp.set_or189985376899183464nteger L) U)) tptp.bot_bo3990330152332043303nteger)))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (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))))
% 6.81/7.14 (assert (forall ((L Bool) (U Bool)) (= (@ (@ tptp.inf_inf_set_o (@ tptp.set_ord_lessThan_o L)) (@ (@ tptp.set_or7139685690850216873Than_o L) U)) tptp.bot_bot_set_o)))
% 6.81/7.14 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.inf_inf_set_nat (@ tptp.set_ord_lessThan_nat L)) (@ (@ tptp.set_or4665077453230672383an_nat L) U)) tptp.bot_bot_set_nat)))
% 6.81/7.14 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.inf_inf_set_int (@ tptp.set_ord_lessThan_int L)) (@ (@ tptp.set_or4662586982721622107an_int L) U)) tptp.bot_bot_set_int)))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.inf_in1364745209274528805nteger (@ tptp.set_or5754767410780653050nteger L)) (@ (@ tptp.set_or8404916559141939852nteger L) U)) tptp.bot_bo3990330152332043303nteger)))
% 6.81/7.14 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N2))) (=> (forall ((X3 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _let_1))))))
% 6.81/7.14 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X3)) (@ P X3))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X4)) (@ Q X4)))) _let_1))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_3573771949741848930nteger (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_assn (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((F (-> tptp.nat tptp.nat)) (Mm tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ F (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat Mm)) (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) Mm)))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K))) (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K))) (@ (@ tptp.groups708209901874060359at_nat G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((M3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M3) K))) (@ (@ tptp.groups705719431365010083at_int G) (@ (@ tptp.set_or4665077453230672383an_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) K)))))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat N2) K))))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((A (-> tptp.nat tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (@ A I4)) (@ tptp.set_ord_lessThan_nat I4)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.groups705719431365010083at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ (@ A I4) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))))
% 6.81/7.14 (assert (forall ((K tptp.num)) (= (@ tptp.semiri3624122377584611663nteger (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger K)) (@ tptp.semiri3624122377584611663nteger (@ tptp.pred_numeral K))))))
% 6.81/7.14 (assert (forall ((K tptp.num)) (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.semiri773545260158071498ct_rat (@ tptp.pred_numeral K))))))
% 6.81/7.14 (assert (forall ((K tptp.num)) (= (@ tptp.semiri2447717529341329178atural (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural K)) (@ tptp.semiri2447717529341329178atural (@ tptp.pred_numeral K))))))
% 6.81/7.14 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat _let_1) (@ tptp.semiri1408675320244567234ct_nat (@ tptp.pred_numeral K)))))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (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)))))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger L) U) (= (@ (@ tptp.sup_su848401254843788991nteger (@ tptp.set_or5754767410780653050nteger L)) (@ (@ tptp.set_or189985376899183464nteger L) U)) (@ tptp.set_or9101266186257409494nteger U)))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (let ((_let_2 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_2 X)) (@ (@ tptp.groups7501900531339628137nteger _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 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 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ _let_1 N2)) 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 N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) 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 N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 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 N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))))
% 6.81/7.14 (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)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.multis2468970476368604999at_nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups6857163185585827899at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6857163185585827899at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.code_integer)) (N2 tptp.nat)) (= (@ (@ tptp.groups3455450783089532116nteger G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_3573771949741848930nteger (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3455450783089532116nteger (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.assn)) (N2 tptp.nat)) (= (@ (@ tptp.groups6906906614972039071t_assn G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_assn (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6906906614972039071t_assn (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups73079841787564623at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups73079841787564623at_rat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups705719431365010083at_int (lambda ((I4 tptp.nat)) (@ G (@ tptp.suc I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))))
% 6.81/7.14 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 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 N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X)))))))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (N2 tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((P7 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger X) P7)) (@ (@ tptp.power_8256067586552552935nteger Y) (@ (@ tptp.minus_minus_nat N2) P7))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ 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 ((P7 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P7)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P7))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P7 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P7)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P7))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (N2 tptp.nat) (Y tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger X) Y)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4)))) (@ (@ tptp.power_8256067586552552935nteger X) I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4)))) (@ (@ tptp.power_power_rat X) I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4)))) (@ (@ tptp.power_power_int X) I4)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K))) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.pred_numeral L)) (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se569199155075624693atural (@ tptp.numeral_numeral_nat L)) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 K))) (@ (@ tptp.times_2397367101498566445atural (@ (@ tptp.bit_se569199155075624693atural (@ tptp.pred_numeral L)) (@ tptp.numera5444537566228673987atural K))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.81/7.14 (assert (forall ((X tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger X) N2)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 X)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((I4 tptp.nat)) (@ (@ tptp.power_8256067586552552935nteger X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.81/7.14 (assert (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N2)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I4 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I4))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.81/7.14 (assert (forall ((G (-> tptp.nat tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups977919841031483927at_nat (@ tptp.produc6842872674320459806at_nat G)) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I4) J3)) N2))))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I4 tptp.nat)) (@ (@ G I4) (@ (@ tptp.minus_minus_nat K3) I4)))) (@ tptp.set_ord_atMost_nat K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2119862282449309892nteger (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger (@ tptp.pred_numeral N2)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se943457434206027407atural (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ tptp.bit_se943457434206027407atural (@ tptp.pred_numeral N2)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N2)))))))
% 6.81/7.14 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N2)))))))
% 6.81/7.14 (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))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 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_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 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_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 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_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y)))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.81/7.14 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q7 tptp.code_integer) (R4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q7))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R4)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R4) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R4)))))) __flatten_var_0))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))))
% 6.81/7.14 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (= (@ _let_1 K) (@ _let_1 L))))))
% 6.81/7.14 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_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_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit0 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_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_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 X))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 Y))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.numera6620942414471956472nteger X)) (@ tptp.numera6620942414471956472nteger Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural (@ tptp.bit1 X))) (@ tptp.numera5444537566228673987atural (@ tptp.bit1 Y))) (@ (@ tptp.times_2397367101498566445atural (@ tptp.numera5444537566228673987atural (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se2046307713759805098atural (@ tptp.numera5444537566228673987atural X)) (@ tptp.numera5444537566228673987atural Y))))))
% 6.81/7.14 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.81/7.14 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.81/7.14 (assert (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D tptp.code_integer) (I3 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F2) (@ (@ tptp.produc1086072967326762835nteger D) I3))))))))
% 6.81/7.14 (assert (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D tptp.code_integer) (I3 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F2) (@ (@ tptp.produc1086072967326762835nteger D) I3))))))))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.image_4470545334726330049nteger (lambda ((X4 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger X4) L))) (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.minus_8373710615458151222nteger U) L))) (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 6.81/7.14 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.81/7.14 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.81/7.14 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger L) (@ (@ tptp.plus_p5714425477246183910nteger U) tptp.one_one_Code_integer)) (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 6.81/7.14 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.81/7.15 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.81/7.15 (assert (= tptp.groups8594936613892548326nteger (lambda ((F3 (-> tptp.int tptp.code_integer)) (A5 tptp.code_integer) (Xs3 tptp.list_int)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((N tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ F3 (@ (@ tptp.nth_int Xs3) N))) (@ (@ tptp.power_8256067586552552935nteger A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs3))))))
% 6.81/7.15 (assert (= tptp.groups8223283053655703690nteger (lambda ((F3 (-> tptp.nat tptp.code_integer)) (A5 tptp.code_integer) (Xs3 tptp.list_nat)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((N tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ F3 (@ (@ tptp.nth_nat Xs3) N))) (@ (@ tptp.power_8256067586552552935nteger A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs3))))))
% 6.81/7.15 (assert (= tptp.groups3417619833198082522nteger (lambda ((F3 (-> Bool tptp.code_integer)) (A5 tptp.code_integer) (Xs3 tptp.list_o)) (@ (@ tptp.groups7501900531339628137nteger (lambda ((N tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_8256067586552552935nteger A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))
% 6.81/7.15 (assert (= tptp.groups7852591826665563233nt_rat (lambda ((F3 (-> tptp.int tptp.rat)) (A5 tptp.rat) (Xs3 tptp.list_int)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_rat (@ F3 (@ (@ tptp.nth_int Xs3) N))) (@ (@ tptp.power_power_rat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs3))))))
% 6.81/7.15 (assert (= tptp.groups6853238114764508677at_rat (lambda ((F3 (-> tptp.nat tptp.rat)) (A5 tptp.rat) (Xs3 tptp.list_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_rat (@ F3 (@ (@ tptp.nth_nat Xs3) N))) (@ (@ tptp.power_power_rat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs3))))))
% 6.81/7.15 (assert (= tptp.groups8483887719401441109_o_rat (lambda ((F3 (-> Bool tptp.rat)) (A5 tptp.rat) (Xs3 tptp.list_o)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_rat (@ F3 (@ (@ tptp.nth_o Xs3) N))) (@ (@ tptp.power_power_rat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs3))))))
% 6.81/7.15 (assert (= tptp.groups8485231416243008693nt_int (lambda ((F3 (-> tptp.int tptp.int)) (A5 tptp.int) (Xs3 tptp.list_int)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F3 (@ (@ tptp.nth_int Xs3) N))) (@ (@ tptp.power_power_int A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs3))))))
% 6.81/7.15 (assert (= tptp.groups7485877704341954137at_int (lambda ((F3 (-> tptp.nat tptp.int)) (A5 tptp.int) (Xs3 tptp.list_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F3 (@ (@ tptp.nth_nat Xs3) N))) (@ (@ tptp.power_power_int A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs3))))))
% 6.81/7.15 (assert (= tptp.groups8487721886752058969nt_nat (lambda ((F3 (-> tptp.int tptp.nat)) (A5 tptp.nat) (Xs3 tptp.list_int)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F3 (@ (@ tptp.nth_int Xs3) N))) (@ (@ tptp.power_power_nat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs3))))))
% 6.81/7.15 (assert (= tptp.groups7488368174851004413at_nat (lambda ((F3 (-> tptp.nat tptp.nat)) (A5 tptp.nat) (Xs3 tptp.list_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N tptp.nat)) (@ (@ tptp.times_times_nat (@ F3 (@ (@ tptp.nth_nat Xs3) N))) (@ (@ tptp.power_power_nat A5) N)))) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs3))))))
% 6.81/7.15 (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))))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N2)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.81/7.15 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M3 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A5 tptp.nat) (X4 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P7 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q7 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q7)))) (@ (@ tptp.bit_take_bit_num O) P7)))) (lambda ((P7 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P7))))) X4))) A5))) (@ (@ tptp.product_Pair_nat_num N) M3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.nat))) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ tptp.finite_finite_o A3) (= (@ _let_1 (@ (@ tptp.groups8507830703676809646_o_nat F) A3)) (@ _let_1 (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ tptp.finite_finite_int A3) (= (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) A3)) (@ _let_1 (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ _let_1 (@ (@ tptp.groups7237345082560585321er_nat F) A3)) (@ _let_1 (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A3) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups8505340233167759370_o_int F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups3539618377306564664at_int F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.int))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ (@ tptp.groups7234854612051535045er_int F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A3) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (F (-> Bool tptp.code_integer))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_o A3) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ (@ tptp.groups4406642042086082107nteger F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((A5 Bool)) (and (@ (@ tptp.member_o A5) A3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.code_integer))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_nat A3) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ (@ tptp.groups7501900531339628137nteger F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((A5 tptp.nat)) (and (@ (@ tptp.member_nat A5) A3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.code_integer))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite_finite_int A3) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ (@ tptp.groups7873554091576472773nteger F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((A5 tptp.int)) (and (@ (@ tptp.member_int A5) A3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.code_integer))) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ (@ tptp.groups879477027807139574nteger F) A3)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((A5 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer A5) A3) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ F A5)))))))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_nat I4) N2)))) N2)))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger L) U))))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or189985376899183464nteger L) U))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I4) N2)))) (@ tptp.suc N2))))
% 6.81/7.15 (assert (= (@ tptp.finite_card_set_nat tptp.bot_bot_set_set_nat) tptp.zero_zero_nat))
% 6.81/7.15 (assert (= (@ tptp.finite_card_list_nat tptp.bot_bot_set_list_nat) tptp.zero_zero_nat))
% 6.81/7.15 (assert (= (@ tptp.finite711546835091564841at_nat tptp.bot_bo2099793752762293965at_nat) tptp.zero_zero_nat))
% 6.81/7.15 (assert (= (@ tptp.finite_card_o tptp.bot_bot_set_o) tptp.zero_zero_nat))
% 6.81/7.15 (assert (= (@ tptp.finite_card_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.81/7.15 (assert (= (@ tptp.finite_card_int tptp.bot_bot_set_int) tptp.zero_zero_nat))
% 6.81/7.15 (assert (forall ((Y tptp.nat) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups4248547760180025341at_nat (lambda ((X4 tptp.set_nat)) Y)) A3) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_set_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.nat) (A3 tptp.set_list_nat)) (= (@ (@ tptp.groups2907647131375434839at_nat (lambda ((X4 tptp.list_nat)) Y)) A3) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_list_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups4246057289670975065at_int (lambda ((X4 tptp.set_nat)) Y)) A3) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_set_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_list_nat)) (= (@ (@ tptp.groups2905156660866384563at_int (lambda ((X4 tptp.list_nat)) Y)) A3) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_list_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.power_power_nat Y) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X4 tptp.int)) Y)) A3) (@ (@ tptp.power_power_int Y) (@ tptp.finite_card_int A3)))))
% 6.81/7.15 (assert (forall ((A tptp.option_num) (F (-> tptp.nat tptp.option_num)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_option_num A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.81/7.15 (assert (forall ((A Bool) (F (-> tptp.nat Bool)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_o A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (V tptp.num)) (= (@ (@ (@ tptp.case_nat_nat A) F) (@ tptp.numeral_numeral_nat V)) (@ F (@ tptp.pred_numeral V)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (= (@ tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_set_nat)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (= (@ tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_list_nat)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (= (@ tptp.finite4902975817058060853nteger A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo3990330152332043303nteger)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (= (@ tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bo2099793752762293965at_nat)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o)) (=> (@ tptp.finite_finite_o A3) (= (= (@ tptp.finite_card_o A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_o)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (= (= (@ tptp.finite_card_nat A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_nat)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (= (= (@ tptp.finite_card_int A3) tptp.zero_zero_nat) (= A3 tptp.bot_bot_set_int)))))
% 6.81/7.15 (assert (forall ((Y tptp.rat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.code_integer) (A3 tptp.set_nat)) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.nat) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) Y)) A3) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) Y)) A3) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_int A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.rat) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups7659867448343625626at_rat (lambda ((X4 tptp.set_nat)) Y)) A3) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_set_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.rat) (A3 tptp.set_list_nat)) (= (@ (@ tptp.groups3760926236672600436at_rat (lambda ((X4 tptp.list_nat)) Y)) A3) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_list_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups8292507037921071086at_int (lambda ((X4 tptp.set_nat)) Y)) A3) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_set_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (A3 tptp.set_list_nat)) (= (@ (@ tptp.groups4393565826250045896at_int (lambda ((X4 tptp.list_nat)) Y)) A3) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_list_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.nat) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) Y)) A3) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_set_nat A3))) Y))))
% 6.81/7.15 (assert (forall ((A tptp.option_num) (F (-> tptp.nat tptp.option_num)) (V tptp.num) (N2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_option_num A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N2)))))
% 6.81/7.15 (assert (forall ((A Bool) (F (-> tptp.nat Bool)) (V tptp.num) (N2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_o A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N2)))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (F (-> tptp.nat tptp.nat)) (V tptp.num) (N2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_nat A) F) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ F (@ (@ tptp.plus_plus_nat (@ tptp.pred_numeral V)) N2)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7873554091576472773nteger (lambda ((X4 tptp.int)) (@ tptp.zero_n356916108424825756nteger (@ P X4)))) A3) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups879477027807139574nteger (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n356916108424825756nteger (@ P X4)))) A3) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((X4 tptp.nat)) (@ tptp.zero_n356916108424825756nteger (@ P X4)))) A3) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X4 tptp.int)) (@ tptp.zero_n2687167440665602831ol_nat (@ P X4)))) A3) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n2687167440665602831ol_nat (@ P X4)))) A3) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (P (-> tptp.code_integer Bool))) (let ((_let_1 (@ tptp.finite6017078050557962740nteger A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups7234854612051535045er_int (lambda ((X4 tptp.code_integer)) (@ tptp.zero_n2684676970156552555ol_int (@ P X4)))) A3) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite4902975817058060853nteger (@ (@ tptp.inf_in1364745209274528805nteger A3) (@ tptp.collect_Code_integer P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((X4 tptp.nat)) (@ tptp.zero_n2684676970156552555ol_int (@ P X4)))) A3) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.finite_finite_nat A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ P X4)))) A3) (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat (@ (@ tptp.inf_inf_set_nat A3) (@ tptp.collect_nat P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.finite_finite_int A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X4 tptp.int)) (@ tptp.zero_n2684676970156552555ol_int (@ P X4)))) A3) (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_int (@ (@ tptp.inf_inf_set_int A3) (@ tptp.collect_int P))))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (let ((_let_1 (@ tptp.finite1152437895449049373et_nat A3))) (=> _let_1 (=> _let_1 (= (@ (@ tptp.groups9190459664516455967nteger (lambda ((X4 tptp.set_nat)) (@ tptp.zero_n356916108424825756nteger (@ P X4)))) A3) (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_set_nat (@ (@ tptp.inf_inf_set_set_nat A3) (@ tptp.collect_set_nat P))))))))))
% 6.81/7.15 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 6.81/7.15 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.81/7.15 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_int Xa) X))))
% 6.81/7.15 (assert (forall ((U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U))))
% 6.81/7.15 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.option_num Bool)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.option_num tptp.nat)) (F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_option_num F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> Bool tptp.option_num)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> Bool Bool)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> Bool tptp.nat)) (F1 Bool) (F22 (-> tptp.nat Bool)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_o F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.nat tptp.option_num)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_option_num (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.nat Bool)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_o (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.nat tptp.nat)) (F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (Nat tptp.nat)) (= (@ H (@ (@ (@ tptp.case_nat_nat F1) F22) Nat)) (@ (@ (@ tptp.case_nat_nat (@ H F1)) (lambda ((X4 tptp.nat)) (@ H (@ F22 X4)))) Nat))))
% 6.81/7.15 (assert (forall ((H (-> tptp.option_num tptp.option_num)) (F1 tptp.option_num) (F22 (-> tptp.num tptp.option_num)) (F32 (-> tptp.num tptp.option_num)) (Num tptp.num)) (= (@ H (@ (@ (@ (@ tptp.case_num_option_num F1) F22) F32) Num)) (@ (@ (@ (@ tptp.case_num_option_num (@ H F1)) (lambda ((X4 tptp.num)) (@ H (@ F22 X4)))) (lambda ((X4 tptp.num)) (@ H (@ F32 X4)))) Num))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (K tptp.nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (= (@ tptp.finite1149291290879098388et_nat (@ tptp.collect_set_set_nat (lambda ((B6 tptp.set_set_nat)) (and (@ (@ tptp.ord_le6893508408891458716et_nat B6) A3) (= (@ tptp.finite_card_set_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_set_nat A3)) K)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (K tptp.nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (= (@ tptp.finite2364142230527598318st_nat (@ tptp.collect_set_list_nat (lambda ((B6 tptp.set_list_nat)) (and (@ (@ tptp.ord_le6045566169113846134st_nat B6) A3) (= (@ tptp.finite_card_list_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_list_nat A3)) K)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (=> (@ tptp.finite_finite_nat A3) (= (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (and (@ (@ tptp.ord_less_eq_set_nat B6) A3) (= (@ tptp.finite_card_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_nat A3)) K)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (K tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger A3) (= (@ tptp.finite1340570857867686763nteger (@ tptp.collec574505750873337192nteger (lambda ((B6 tptp.set_Code_integer)) (and (@ (@ tptp.ord_le7084787975880047091nteger B6) A3) (= (@ tptp.finite4902975817058060853nteger B6) K))))) (@ (@ tptp.binomial (@ tptp.finite4902975817058060853nteger A3)) K)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (K tptp.nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (= (@ tptp.finite4356350796350151305at_nat (@ tptp.collec5514110066124741708at_nat (lambda ((B6 tptp.set_Pr1261947904930325089at_nat)) (and (@ (@ tptp.ord_le3146513528884898305at_nat B6) A3) (= (@ tptp.finite711546835091564841at_nat B6) K))))) (@ (@ tptp.binomial (@ tptp.finite711546835091564841at_nat A3)) K)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (K tptp.nat)) (=> (@ tptp.finite_finite_int A3) (= (@ tptp.finite_card_set_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B6) A3) (= (@ tptp.finite_card_int B6) K))))) (@ (@ tptp.binomial (@ tptp.finite_card_int A3)) K)))))
% 6.81/7.15 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num))) (= (@ (@ (@ tptp.case_nat_option_num F1) F22) tptp.zero_zero_nat) F1)))
% 6.81/7.15 (assert (forall ((F1 Bool) (F22 (-> tptp.nat Bool))) (= (@ (@ (@ tptp.case_nat_o F1) F22) tptp.zero_zero_nat) F1)))
% 6.81/7.15 (assert (forall ((F1 tptp.nat) (F22 (-> tptp.nat tptp.nat))) (= (@ (@ (@ tptp.case_nat_nat F1) F22) tptp.zero_zero_nat) F1)))
% 6.81/7.15 (assert (forall ((F1 tptp.option_num) (F22 (-> tptp.nat tptp.option_num)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_option_num F1) F22) (@ tptp.suc X2)) (@ F22 X2))))
% 6.81/7.15 (assert (forall ((F1 Bool) (F22 (-> tptp.nat Bool)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_o F1) F22) (@ tptp.suc X2)) (@ F22 X2))))
% 6.81/7.15 (assert (forall ((F1 tptp.nat) (F22 (-> tptp.nat tptp.nat)) (X2 tptp.nat)) (= (@ (@ (@ tptp.case_nat_nat F1) F22) (@ tptp.suc X2)) (@ F22 X2))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite1152437895449049373et_nat A3)) (exists ((B10 tptp.set_set_nat)) (and (@ tptp.finite1152437895449049373et_nat B10) (= (@ tptp.finite_card_set_nat B10) N2) (@ (@ tptp.ord_le6893508408891458716et_nat B10) A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite8100373058378681591st_nat A3)) (exists ((B10 tptp.set_list_nat)) (and (@ tptp.finite8100373058378681591st_nat B10) (= (@ tptp.finite_card_list_nat B10) N2) (@ (@ tptp.ord_le6045566169113846134st_nat B10) A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat A3)) (exists ((B10 tptp.set_nat)) (and (@ tptp.finite_finite_nat B10) (= (@ tptp.finite_card_nat B10) N2) (@ (@ tptp.ord_less_eq_set_nat B10) A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (N2 tptp.nat)) (=> (not (@ tptp.finite6017078050557962740nteger A3)) (exists ((B10 tptp.set_Code_integer)) (and (@ tptp.finite6017078050557962740nteger B10) (= (@ tptp.finite4902975817058060853nteger B10) N2) (@ (@ tptp.ord_le7084787975880047091nteger B10) A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite6177210948735845034at_nat A3)) (exists ((B10 tptp.set_Pr1261947904930325089at_nat)) (and (@ tptp.finite6177210948735845034at_nat B10) (= (@ tptp.finite711546835091564841at_nat B10) N2) (@ (@ tptp.ord_le3146513528884898305at_nat B10) A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_int A3)) (exists ((B10 tptp.set_int)) (and (@ tptp.finite_finite_int B10) (= (@ tptp.finite_card_int B10) N2) (@ (@ tptp.ord_less_eq_set_int B10) A3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (=> (= (@ tptp.finite_card_set_nat A3) (@ tptp.finite_card_set_nat B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B3) (=> (= (@ tptp.finite_card_list_nat A3) (@ tptp.finite_card_list_nat B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (= (@ tptp.finite_card_nat A3) (@ tptp.finite_card_nat B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (= (@ tptp.finite4902975817058060853nteger A3) (@ tptp.finite4902975817058060853nteger B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (= (@ tptp.finite711546835091564841at_nat A3) (@ tptp.finite711546835091564841at_nat B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (= (@ tptp.finite_card_int A3) (@ tptp.finite_card_int B3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_o) (R3 (-> Bool Bool Bool))) (=> (@ tptp.finite_finite_o B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B4 Bool)) (=> (@ (@ tptp.member_o A13) A3) (=> (@ (@ tptp.member_o A24) A3) (=> (@ (@ tptp.member_o B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_o B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_int) (R3 (-> tptp.int Bool Bool))) (=> (@ tptp.finite_finite_o B3) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B4 Bool)) (=> (@ (@ tptp.member_int A13) A3) (=> (@ (@ tptp.member_int A24) A3) (=> (@ (@ tptp.member_o B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_o B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_o) (A3 tptp.set_nat) (R3 (-> tptp.nat Bool Bool))) (=> (@ tptp.finite_finite_o B3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (exists ((B11 Bool)) (and (@ (@ tptp.member_o B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B4 Bool)) (=> (@ (@ tptp.member_nat A13) A3) (=> (@ (@ tptp.member_nat A24) A3) (=> (@ (@ tptp.member_o B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_o B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_o) (R3 (-> Bool tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B4 tptp.nat)) (=> (@ (@ tptp.member_o A13) A3) (=> (@ (@ tptp.member_o A24) A3) (=> (@ (@ tptp.member_nat B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_nat B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_int) (R3 (-> tptp.int tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B4 tptp.nat)) (=> (@ (@ tptp.member_int A13) A3) (=> (@ (@ tptp.member_int A24) A3) (=> (@ (@ tptp.member_nat B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_nat B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat) (R3 (-> tptp.nat tptp.nat Bool))) (=> (@ tptp.finite_finite_nat B3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (exists ((B11 tptp.nat)) (and (@ (@ tptp.member_nat B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.member_nat A13) A3) (=> (@ (@ tptp.member_nat A24) A3) (=> (@ (@ tptp.member_nat B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_o) (R3 (-> Bool tptp.int Bool))) (=> (@ tptp.finite_finite_int B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B4 tptp.int)) (=> (@ (@ tptp.member_o A13) A3) (=> (@ (@ tptp.member_o A24) A3) (=> (@ (@ tptp.member_int B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite_card_int B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int) (R3 (-> tptp.int tptp.int Bool))) (=> (@ tptp.finite_finite_int B3) (=> (forall ((A4 tptp.int)) (=> (@ (@ tptp.member_int A4) A3) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.int) (A24 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.member_int A13) A3) (=> (@ (@ tptp.member_int A24) A3) (=> (@ (@ tptp.member_int B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_nat) (R3 (-> tptp.nat tptp.int Bool))) (=> (@ tptp.finite_finite_int B3) (=> (forall ((A4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (exists ((B11 tptp.int)) (and (@ (@ tptp.member_int B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 tptp.nat) (A24 tptp.nat) (B4 tptp.int)) (=> (@ (@ tptp.member_nat A13) A3) (=> (@ (@ tptp.member_nat A24) A3) (=> (@ (@ tptp.member_int B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_int B3)))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_o) (R3 (-> Bool tptp.code_integer Bool))) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (forall ((A4 Bool)) (=> (@ (@ tptp.member_o A4) A3) (exists ((B11 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer B11) B3) (@ (@ R3 A4) B11))))) (=> (forall ((A13 Bool) (A24 Bool) (B4 tptp.code_integer)) (=> (@ (@ tptp.member_o A13) A3) (=> (@ (@ tptp.member_o A24) A3) (=> (@ (@ tptp.member_Code_integer B4) B3) (=> (@ (@ R3 A13) B4) (=> (@ (@ R3 A24) B4) (= A13 A24))))))) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_o A3)) (@ tptp.finite4902975817058060853nteger B3)))))))
% 6.81/7.15 (assert (forall ((Xa tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_eq_int Xa) X))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_o) (T5 tptp.set_o) (R (-> Bool Bool Bool)) (K (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_o T5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T5) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_o) (T5 tptp.set_int) (R (-> Bool tptp.int Bool)) (K (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_o) (T5 tptp.set_Code_integer) (R (-> Bool tptp.code_integer Bool)) (K (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_o) (R (-> tptp.int Bool Bool)) (K (-> Bool tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_o T5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_int) (R (-> tptp.int tptp.int Bool)) (K (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_int) (T5 tptp.set_Code_integer) (R (-> tptp.int tptp.code_integer Bool)) (K (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite_finite_int S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_o) (R (-> tptp.code_integer Bool Bool)) (K (-> Bool tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_o T5) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T5) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I4 tptp.code_integer)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups8507830703676809646_o_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_int) (R (-> tptp.code_integer tptp.int Bool)) (K (-> tptp.int tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite_finite_int T5) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T5) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I4 tptp.code_integer)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups4541462559716669496nt_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_Code_integer) (T5 tptp.set_Code_integer) (R (-> tptp.code_integer tptp.code_integer Bool)) (K (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger S2) (=> (@ tptp.finite6017078050557962740nteger T5) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T5) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I4 tptp.code_integer)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups7237345082560585321er_nat K) T5)))))))
% 6.81/7.15 (assert (forall ((S2 tptp.set_o) (T5 tptp.set_nat) (R (-> Bool tptp.nat Bool)) (K (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_o S2) (=> (@ tptp.finite_finite_nat T5) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T5) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S2) (@ (@ R I4) X3))))) (@ K X3)))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T5) (@ (@ R I4) J3))))))) S2) (@ (@ tptp.groups3542108847815614940at_nat K) T5)))))))
% 6.81/7.15 (assert (= tptp.finite_card_set_nat (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) tptp.one_one_nat))))
% 6.81/7.15 (assert (= tptp.finite_card_list_nat (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) tptp.one_one_nat))))
% 6.81/7.15 (assert (= tptp.finite_card_nat (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) tptp.one_one_nat))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat)) (= (= (@ tptp.finite_card_set_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_set_nat) (not (@ tptp.finite1152437895449049373et_nat A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat)) (= (= (@ tptp.finite_card_list_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_list_nat) (not (@ tptp.finite8100373058378681591st_nat A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer)) (= (= (@ tptp.finite4902975817058060853nteger A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo3990330152332043303nteger) (not (@ tptp.finite6017078050557962740nteger A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (= (@ tptp.finite711546835091564841at_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bo2099793752762293965at_nat) (not (@ tptp.finite6177210948735845034at_nat A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o)) (= (= (@ tptp.finite_card_o A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_o) (not (@ tptp.finite_finite_o A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat)) (= (= (@ tptp.finite_card_nat A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_nat) (not (@ tptp.finite_finite_nat A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int)) (= (= (@ tptp.finite_card_int A3) tptp.zero_zero_nat) (or (= A3 tptp.bot_bot_set_int) (not (@ tptp.finite_finite_int A3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A3)) (@ tptp.finite1152437895449049373et_nat A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A3)) (@ tptp.finite8100373058378681591st_nat A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A3)) (@ tptp.finite_finite_nat A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A3)) (@ tptp.finite_finite_int A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite4902975817058060853nteger A3)) (@ tptp.finite6017078050557962740nteger A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite6177210948735845034at_nat A3))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_nat_int F) A3))) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_nat_nat F) A3))) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.image_int_int F) A3))) (@ tptp.finite_card_int A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_int_nat F) A3))) (@ tptp.finite_card_int A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (F (-> tptp.code_integer tptp.nat))) (=> (@ tptp.finite6017078050557962740nteger A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_951025933927791156er_nat F) A3))) (@ tptp.finite4902975817058060853nteger A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (F (-> tptp.set_nat tptp.nat))) (=> (@ tptp.finite1152437895449049373et_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_set_nat_nat F) A3))) (@ tptp.finite_card_set_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (F (-> tptp.list_nat tptp.nat))) (=> (@ tptp.finite8100373058378681591st_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.image_list_nat_nat F) A3))) (@ tptp.finite_card_list_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.set_nat))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.image_nat_set_nat F) A3))) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (F (-> tptp.nat tptp.list_nat))) (=> (@ tptp.finite_finite_nat A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.image_nat_list_nat F) A3))) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (F (-> tptp.int tptp.set_nat))) (=> (@ tptp.finite_finite_int A3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.image_int_set_nat F) A3))) (@ tptp.finite_card_int A3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_set_nat) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat G4) F4) (=> (@ tptp.finite1152437895449049373et_nat G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat G4)) C3)))) (and (@ tptp.finite1152437895449049373et_nat F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat F4)) C3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_list_nat) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat G4) F4) (=> (@ tptp.finite8100373058378681591st_nat G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat G4)) C3)))) (and (@ tptp.finite8100373058378681591st_nat F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat F4)) C3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_nat) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat G4) F4) (=> (@ tptp.finite_finite_nat G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat G4)) C3)))) (and (@ tptp.finite_finite_nat F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat F4)) C3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_Code_integer) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger G4) F4) (=> (@ tptp.finite6017078050557962740nteger G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger G4)) C3)))) (and (@ tptp.finite6017078050557962740nteger F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger F4)) C3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_Pr1261947904930325089at_nat) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat G4) F4) (=> (@ tptp.finite6177210948735845034at_nat G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat G4)) C3)))) (and (@ tptp.finite6177210948735845034at_nat F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat F4)) C3)))))
% 6.81/7.15 (assert (forall ((F4 tptp.set_int) (C3 tptp.nat)) (=> (forall ((G4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int G4) F4) (=> (@ tptp.finite_finite_int G4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int G4)) C3)))) (and (@ tptp.finite_finite_int F4) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int F4)) C3)))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat B3)) (@ tptp.finite_card_set_nat A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat B3)) (@ tptp.finite_card_list_nat A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat B3)) (@ tptp.finite_card_nat A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger B3)) (@ tptp.finite4902975817058060853nteger A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat B3)) (@ tptp.finite711546835091564841at_nat A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int B3)) (@ tptp.finite_card_int A3)) (= A3 B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_le6045566169113846134st_nat A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le7084787975880047091nteger A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger A3)) (@ tptp.finite4902975817058060853nteger B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A3) B3) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B3))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_set_nat S)) (not (forall ((T6 tptp.set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat T6) S) (=> (= (@ tptp.finite_card_set_nat T6) N2) (not (@ tptp.finite1152437895449049373et_nat T6)))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_list_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_list_nat S)) (not (forall ((T6 tptp.set_list_nat)) (=> (@ (@ tptp.ord_le6045566169113846134st_nat T6) S) (=> (= (@ tptp.finite_card_list_nat T6) N2) (not (@ tptp.finite8100373058378681591st_nat T6)))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_nat S)) (not (forall ((T6 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat T6) S) (=> (= (@ tptp.finite_card_nat T6) N2) (not (@ tptp.finite_finite_nat T6)))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_Code_integer)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite4902975817058060853nteger S)) (not (forall ((T6 tptp.set_Code_integer)) (=> (@ (@ tptp.ord_le7084787975880047091nteger T6) S) (=> (= (@ tptp.finite4902975817058060853nteger T6) N2) (not (@ tptp.finite6017078050557962740nteger T6)))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite711546835091564841at_nat S)) (not (forall ((T6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le3146513528884898305at_nat T6) S) (=> (= (@ tptp.finite711546835091564841at_nat T6) N2) (not (@ tptp.finite6177210948735845034at_nat T6)))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (S tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.finite_card_int S)) (not (forall ((T6 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int T6) S) (=> (= (@ tptp.finite_card_int T6) N2) (not (@ tptp.finite_finite_int T6)))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B3))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B3))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B3))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger A3)) (@ tptp.finite4902975817058060853nteger B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3)) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A3) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat A3) B3))) (@ tptp.finite_card_set_nat (@ (@ tptp.minus_2163939370556025621et_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat A3) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat A3) B3))) (@ tptp.finite_card_list_nat (@ (@ tptp.minus_7954133019191499631st_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A3) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int A3) B3))) (@ tptp.finite_card_int (@ (@ tptp.minus_minus_set_int B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer) (B3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger A3) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger A3)) (@ tptp.finite4902975817058060853nteger B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger A3) B3))) (@ tptp.finite4902975817058060853nteger (@ (@ tptp.minus_2355218937544613996nteger B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat A3) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat A3) B3))) (@ tptp.finite711546835091564841at_nat (@ (@ tptp.minus_1356011639430497352at_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A3) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat A3) B3))) (@ tptp.finite_card_nat (@ (@ tptp.minus_minus_set_nat B3) A3))))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_set_nat) (A3 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ (@ tptp.ord_less_set_set_nat A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_list_nat) (A3 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat B3) (=> (@ (@ tptp.ord_le1190675801316882794st_nat A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_nat) (A3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_set_nat A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_int) (A3 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_set_int A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite_card_int A3)) (@ tptp.finite_card_int B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Code_integer) (A3 tptp.set_Code_integer)) (=> (@ tptp.finite6017078050557962740nteger B3) (=> (@ (@ tptp.ord_le1307284697595431911nteger A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite4902975817058060853nteger A3)) (@ tptp.finite4902975817058060853nteger B3))))))
% 6.81/7.15 (assert (forall ((B3 tptp.set_Pr1261947904930325089at_nat) (A3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat B3) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A3) B3) (@ (@ tptp.ord_less_nat (@ tptp.finite711546835091564841at_nat A3)) (@ tptp.finite711546835091564841at_nat B3))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat) (B3 tptp.set_set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_set_nat (@ (@ tptp.sup_sup_set_set_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_set_nat A3)) (@ tptp.finite_card_set_nat B3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat) (B3 tptp.set_list_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_list_nat (@ (@ tptp.sup_sup_set_list_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat A3)) (@ tptp.finite_card_list_nat B3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr8693737435421807431at_nat) (B3 tptp.set_Pr8693737435421807431at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite1207074278014112911at_nat (@ (@ tptp.sup_su718114333110466843at_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite1207074278014112911at_nat A3)) (@ tptp.finite1207074278014112911at_nat B3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr8551490117392284871at_nat) (B3 tptp.set_Pr8551490117392284871at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite7007076676225009423at_nat (@ (@ tptp.sup_su3035147773818789531at_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite7007076676225009423at_nat A3)) (@ tptp.finite7007076676225009423at_nat B3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr4329608150637261639at_nat) (B3 tptp.set_Pr4329608150637261639at_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite3771342082235030671at_nat (@ (@ tptp.sup_su5525570899277871387at_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite3771342082235030671at_nat A3)) (@ tptp.finite3771342082235030671at_nat B3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat (@ (@ tptp.sup_sup_set_nat A3) B3))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_nat A3)) (@ tptp.finite_card_nat B3)))))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M6)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M6) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M6) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M6) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M6) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M6) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M6) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M6) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A3))))) (=> (@ (@ tptp.ord_less_eq_set_nat A3) _let_1) (= A3 _let_1)))))
% 6.81/7.15 (assert (forall ((F (-> tptp.set_nat tptp.nat)) (A3 tptp.set_set_nat)) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X4 tptp.set_nat)) (@ tptp.suc (@ F X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A3)) (@ tptp.finite_card_set_nat A3)))))
% 6.81/7.15 (assert (forall ((F (-> tptp.list_nat tptp.nat)) (A3 tptp.set_list_nat)) (= (@ (@ tptp.groups4396056296759096172at_nat (lambda ((X4 tptp.list_nat)) (@ tptp.suc (@ F X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups4396056296759096172at_nat F) A3)) (@ tptp.finite_card_list_nat A3)))))
% 6.81/7.15 (assert (forall ((F (-> tptp.nat tptp.nat)) (A3 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) (@ tptp.suc (@ F X4)))) A3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A3)) (@ tptp.finite_card_nat A3)))))
% 6.81/7.15 (assert (forall ((S tptp.set_o) (T tptp.set_o) (R (-> Bool Bool Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_o T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_o T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_o) (T tptp.set_nat) (R (-> Bool tptp.nat Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_nat T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_o) (T tptp.set_int) (R (-> Bool tptp.int Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_int T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_o) (T tptp.set_Code_integer) (R (-> Bool tptp.code_integer Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_o S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T) (= (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((I4 Bool)) (and (@ (@ tptp.member_o I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups8507830703676809646_o_nat (lambda ((I4 Bool)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite4902975817058060853nteger T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_int) (T tptp.set_o) (R (-> tptp.int Bool Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_o T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_o T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (R (-> tptp.int tptp.nat Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_nat T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_int) (T tptp.set_int) (R (-> tptp.int tptp.int Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) T) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((J3 tptp.int)) (and (@ (@ tptp.member_int J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_int T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_int) (T tptp.set_Code_integer) (R (-> tptp.int tptp.code_integer Bool)) (K tptp.nat)) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite6017078050557962740nteger T) (=> (forall ((X3 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X3) T) (= (@ tptp.finite_card_int (@ tptp.collect_int (lambda ((I4 tptp.int)) (and (@ (@ tptp.member_int I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((I4 tptp.int)) (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((J3 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite4902975817058060853nteger T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_o) (R (-> tptp.code_integer Bool Bool)) (K tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_o T) (=> (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) T) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I4 tptp.code_integer)) (@ tptp.finite_card_o (@ tptp.collect_o (lambda ((J3 Bool)) (and (@ (@ tptp.member_o J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_o T))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_Code_integer) (T tptp.set_nat) (R (-> tptp.code_integer tptp.nat Bool)) (K tptp.nat)) (=> (@ tptp.finite6017078050557962740nteger S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) T) (= (@ tptp.finite4902975817058060853nteger (@ tptp.collect_Code_integer (lambda ((I4 tptp.code_integer)) (and (@ (@ tptp.member_Code_integer I4) S) (@ (@ R I4) X3))))) K))) (= (@ (@ tptp.groups7237345082560585321er_nat (lambda ((I4 tptp.code_integer)) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((J3 tptp.nat)) (and (@ (@ tptp.member_nat J3) T) (@ (@ R I4) J3))))))) S) (@ (@ tptp.times_times_nat K) (@ tptp.finite_card_nat T))))))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_set_nat A3)) (and (not (= A3 tptp.bot_bot_set_set_nat)) (@ tptp.finite1152437895449049373et_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_list_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_list_nat A3)) (and (not (= A3 tptp.bot_bot_set_list_nat)) (@ tptp.finite8100373058378681591st_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Code_integer)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite4902975817058060853nteger A3)) (and (not (= A3 tptp.bot_bo3990330152332043303nteger)) (@ tptp.finite6017078050557962740nteger A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite711546835091564841at_nat A3)) (and (not (= A3 tptp.bot_bo2099793752762293965at_nat)) (@ tptp.finite6177210948735845034at_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_o A3)) (and (not (= A3 tptp.bot_bot_set_o)) (@ tptp.finite_finite_o A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat A3)) (and (not (= A3 tptp.bot_bot_set_nat)) (@ tptp.finite_finite_nat A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.finite_card_int A3)) (and (not (= A3 tptp.bot_bot_set_int)) (@ tptp.finite_finite_int A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K5 tptp.code_integer) (F (-> tptp.nat tptp.code_integer))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A3) (@ (@ tptp.ord_le3102999989581377725nteger K5) (@ F I3)))) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.finite_card_nat A3))) K5)) (@ (@ tptp.groups7501900531339628137nteger F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (K5 tptp.rat) (F (-> Bool tptp.rat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A3) (@ (@ tptp.ord_less_eq_rat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_o A3))) K5)) (@ (@ tptp.groups7872700643590313910_o_rat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (K5 tptp.rat) (F (-> tptp.int tptp.rat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A3) (@ (@ tptp.ord_less_eq_rat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_int A3))) K5)) (@ (@ tptp.groups3906332499630173760nt_rat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K5 tptp.rat) (F (-> tptp.nat tptp.rat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A3) (@ (@ tptp.ord_less_eq_rat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.finite_card_nat A3))) K5)) (@ (@ tptp.groups2906978787729119204at_rat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (K5 tptp.nat) (F (-> Bool tptp.nat))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A3) (@ (@ tptp.ord_less_eq_nat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_o A3))) K5)) (@ (@ tptp.groups8507830703676809646_o_nat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (K5 tptp.nat) (F (-> tptp.int tptp.nat))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A3) (@ (@ tptp.ord_less_eq_nat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_int A3))) K5)) (@ (@ tptp.groups4541462559716669496nt_nat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_o) (K5 tptp.int) (F (-> Bool tptp.int))) (=> (forall ((I3 Bool)) (=> (@ (@ tptp.member_o I3) A3) (@ (@ tptp.ord_less_eq_int K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_o A3))) K5)) (@ (@ tptp.groups8505340233167759370_o_int F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K5 tptp.int) (F (-> tptp.nat tptp.int))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A3) (@ (@ tptp.ord_less_eq_int K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_nat A3))) K5)) (@ (@ tptp.groups3539618377306564664at_int F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat) (K5 tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((I3 tptp.nat)) (=> (@ (@ tptp.member_nat I3) A3) (@ (@ tptp.ord_less_eq_nat K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ tptp.finite_card_nat A3))) K5)) (@ (@ tptp.groups3542108847815614940at_nat F) A3)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_int) (K5 tptp.int) (F (-> tptp.int tptp.int))) (=> (forall ((I3 tptp.int)) (=> (@ (@ tptp.member_int I3) A3) (@ (@ tptp.ord_less_eq_int K5) (@ F I3)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ tptp.finite_card_int A3))) K5)) (@ (@ tptp.groups4538972089207619220nt_int F) A3)))))
% 6.81/7.15 (assert (forall ((N7 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N7) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N7)) N2))))
% 6.81/7.15 (assert (forall ((S 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 S)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) S))))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.81/7.15 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.81/7.15 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.81/7.15 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.81/7.15 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L2)) (@ (@ tptp.modulo364778990260209775nteger K3) L2)))))
% 6.81/7.15 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu2 tptp.nat)) true)) Nat))))
% 6.81/7.15 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu2 tptp.nat)) false)) Nat))))
% 6.81/7.15 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Y)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y))))
% 6.81/7.15 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.81/7.15 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X4 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa4)))))
% 6.81/7.15 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.81/7.15 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X4 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa4)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))))
% 6.81/7.15 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R4) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R4)) S6))) (= S6 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.81/7.15 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.81/7.15 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.81/7.15 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.81/7.15 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))))
% 6.81/7.15 (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_less_nat (@ tptp.code_nat_of_integer X)) (@ tptp.code_nat_of_integer Y)) (@ (@ tptp.ord_le6747313008572928689nteger X) Y)))))))
% 6.81/7.15 (assert (forall ((U tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) U) (= (@ (@ tptp.set_or8404916559141939852nteger tptp.zero_z3403309356797280102nteger) U) (@ (@ tptp.image_1215581382706833972nteger tptp.semiri4939895301339042750nteger) (@ tptp.set_ord_lessThan_nat (@ tptp.code_nat_of_integer U)))))))
% 6.81/7.15 (assert (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.81/7.15 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K3 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ 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 L2) S6)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ 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.uminus1351360451143612070nteger L2)) S6)))))) _let_1))))))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))))
% 6.81/7.15 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.81/7.15 (assert (forall ((K tptp.int)) (not (forall ((N5 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M4 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N5) M4) (= (@ _let_1 M4) (@ _let_1 N5))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N5) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N5) tptp.one_one_nat)) (not (@ _let_1 N5)))))))))))
% 6.81/7.15 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X23 tptp.nat)) X23))))
% 6.81/7.15 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (exists ((R2 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R2) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S))) (forall ((N9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N9) (@ tptp.finite_card_nat S)) (@ (@ tptp.member_nat (@ R2 N9)) S))))))))
% 6.81/7.15 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (and (@ _let_1 K) (@ _let_1 L))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.81/7.15 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.81/7.15 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (Q6 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q6)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q6) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.81/7.15 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.81/7.15 (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 ((R4 tptp.code_integer) (S6 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R4))) (@ (@ (@ 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))))))))))
% 6.81/7.15 (assert (forall ((K5 tptp.set_nat)) (=> (not (= K5 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.complete_Inf_Inf_nat K5)) K5))))
% 6.81/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.81/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.81/7.15 (assert (= (@ (@ tptp.times_times_assn tptp.top_top_assn) tptp.top_top_assn) tptp.top_top_assn))
% 6.81/7.15 (assert (not (= tptp.top_top_assn tptp.bot_bot_assn)))
% 6.81/7.15 (assert (not (= tptp.top_top_assn tptp.one_one_assn)))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.81/7.15 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.81/7.15 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.81/7.15 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.top_top_assn) H) (@ tptp.in_range H))))
% 6.81/7.15 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.81/7.15 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.81/7.15 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.81/7.15 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.81/7.15 (assert (forall ((P tptp.assn)) (@ (@ tptp.entails P) tptp.top_top_assn)))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num) (Q6 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q6)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q6)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.81/7.15 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn P) H) (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H))))
% 6.81/7.15 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (not (@ (@ tptp.rep_assn P) H5)))))))
% 6.81/7.15 (assert (= tptp.top_top_assn (@ tptp.abs_assn tptp.in_range)))
% 6.81/7.15 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.81/7.15 (assert (forall ((H tptp.heap_e7401611519738050253t_unit)) (@ (@ tptp.rep_assn tptp.top_top_assn) (@ (@ tptp.produc7507926704131184380et_nat H) tptp.bot_bot_set_nat))))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.81/7.15 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.81/7.15 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 6.81/7.15 (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))))))))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 6.81/7.15 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))))
% 6.81/7.15 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I4)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I4) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))))))
% 6.81/7.15 (assert (forall ((A0 tptp.int) (A1 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A1)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A1)))))
% 6.81/7.15 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.81/7.15 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.81/7.15 (assert (= tptp.top_top_set_o (@ (@ tptp.insert_o false) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.81/7.15 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.minus_minus_nat I4) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N5 tptp.num)) (= Xa (@ tptp.bit0 N5))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N5 tptp.num)) (= Xa (@ tptp.bit1 N5))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M5) N5)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5))))))))))))))))))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num _let_1)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N5 tptp.num)) (= Xa (@ tptp.bit0 N5))) _let_4)) (=> (=> _let_5 (=> (exists ((N5 tptp.num)) (= Xa (@ tptp.bit1 N5))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (=> (=> (exists ((M5 tptp.num)) (= X (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5)))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5)))))))))))))))))))))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N5))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit0 N5)) (not (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (=> (= Xa (@ tptp.bit1 N5)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5)))))))))))))))))))))
% 6.81/7.15 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))))
% 6.81/7.15 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))))
% 6.81/7.15 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))))
% 6.81/7.15 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.81/7.15 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y tptp.none_num) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.81/7.15 (assert (forall ((X tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa)) (=> (=> _let_1 (=> (= Xa tptp.one) (=> (= Y tptp.none_num) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit1 N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ tptp.bit0 N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit1 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit0 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) _let_1))))))))) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= X _let_1) (=> (= Xa tptp.one) (=> (= Y (@ tptp.some_num (@ tptp.bit0 M5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit0 N5))) (=> (= Xa _let_1) (=> (= Y (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5)))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))) (not (forall ((M5 tptp.num)) (=> (= X (@ tptp.bit1 M5)) (forall ((N5 tptp.num)) (let ((_let_1 (@ tptp.bit1 N5))) (=> (= Xa _let_1) (=> (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N5))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) _let_1))))))))))))))))))))))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ 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) (V2 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 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U2))))))) __flatten_var_0))) Xa) X)))))
% 6.81/7.15 (assert (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y3 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X3) Y3))))))))
% 6.81/7.15 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.81/7.15 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat)))))
% 6.81/7.15 (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)))))
% 6.81/7.15 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))) Xa) X))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))) Xa) X))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ 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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0))) Xa) X)))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ 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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0))) Xa) X)))))
% 6.81/7.15 (assert (= tptp.ord_less_eq_int (lambda ((X4 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y4) V2)) (@ (@ tptp.plus_plus_nat U2) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa4)))))
% 6.81/7.15 (assert (= tptp.ord_less_int (lambda ((X4 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y4 tptp.nat) (Z6 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y4) V2)) (@ (@ tptp.plus_plus_nat U2) Z6)))) __flatten_var_0))) (@ tptp.rep_Integ X4)) (@ tptp.rep_Integ Xa4)))))
% 6.81/7.15 (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))))))
% 6.81/7.15 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M3 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M3)))))))
% 6.81/7.15 (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) (V2 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 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0))))))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0))))))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M6) (= (@ tptp.gcd_Gcd_nat M6) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M6) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M6) (=> (not (= M6 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M6)) (= (@ tptp.gcd_Gcd_nat M6) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M3 tptp.nat)) (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M3))))) M6)))))))))
% 6.81/7.15 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_int_int tptp.abs_abs_int) K5)) (@ tptp.gcd_Gcd_int K5))))
% 6.81/7.15 (assert (forall ((K5 tptp.set_int)) (= (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (lambda ((K3 tptp.int)) (@ tptp.nat2 (@ tptp.abs_abs_int K3)))) K5)) (@ tptp.nat2 (@ tptp.gcd_Gcd_int K5)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) N2)))) N2))))
% 6.81/7.15 (assert (forall ((N7 tptp.set_nat)) (= (@ tptp.gcd_Gcd_int (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) N7)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat N7)))))
% 6.81/7.15 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.81/7.15 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X11 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X11 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X11)))))
% 6.81/7.15 (assert (forall ((S tptp.set_nat)) (=> (@ tptp.finite_finite_nat S) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S))))))
% 6.81/7.15 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N)) M3))))))))
% 6.81/7.15 (assert (= tptp.gcd_Gcd_int (lambda ((K6 tptp.set_int)) (@ tptp.semiri1314217659103216013at_int (@ tptp.gcd_Gcd_nat (@ (@ tptp.image_int_nat (@ (@ tptp.comp_int_nat_int tptp.nat2) tptp.abs_abs_int)) K6))))))
% 6.81/7.15 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.81/7.15 (assert (forall ((N2 tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D5 tptp.int)) (@ (@ tptp.dvd_dvd_int D5) N2)))) (@ tptp.abs_abs_int N2)))))
% 6.81/7.15 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.81/7.15 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.81/7.15 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M3)) M3))))))
% 6.81/7.15 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (@ tptp.finite_card_set_nat (@ tptp.collect_set_nat (lambda ((K6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat K6) (@ tptp.pow_nat (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (= (@ tptp.finite_card_nat K6) K3))))))))
% 6.81/7.15 (assert (= tptp.upto_aux (lambda ((I4 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I4)) Js) (@ (@ (@ tptp.upto_aux I4) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X4 tptp.int)) X4)) _let_1) _let_1))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 6.81/7.15 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.81/7.15 (assert (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa))) (=> (= (@ (@ tptp.upto X) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.81/7.15 (assert (= tptp.upto (lambda ((I4 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I4) J3)) (@ (@ tptp.cons_int I4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.81/7.15 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N7))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N7)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N7))))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N7 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N7))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N7) M)) tptp.one_one_nat)) N7))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X4 tptp.nat)) X4)) _let_1) _let_1))))
% 6.81/7.15 (assert (forall ((J tptp.nat)) (= (= (@ (@ tptp.upt tptp.zero_zero_nat) J) tptp.nil_nat) (= J tptp.zero_zero_nat))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 6.81/7.15 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat J) K)) (= (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.upt J) K)) (@ _let_1 K))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M) (@ _let_2 N2)) (@ _let_2 _let_1)))))))
% 6.81/7.15 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.last_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) tptp.one_one_nat)))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X4 tptp.nat)) X4)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))
% 6.81/7.15 (assert (forall ((Ofs tptp.nat) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) Ofs))) (@ (@ tptp.upt A) B)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat A) Ofs)) (@ (@ tptp.plus_plus_nat B) Ofs)))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (Ys3 tptp.list_nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.append_nat Xs) Ys3)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I2) K3) (@ (@ tptp.ord_less_eq_nat K3) J) (= (@ (@ tptp.upt I2) K3) Xs) (= (@ (@ tptp.upt K3) J) Ys3)))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.append_nat (@ _let_1 I2)) (@ (@ tptp.upt I2) J)) (@ _let_1 J))))))
% 6.81/7.15 (assert (= tptp.upt (lambda ((I4 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I4) J3)) (@ (@ tptp.cons_nat I4) (@ (@ tptp.upt (@ tptp.suc I4)) J3))) tptp.nil_nat))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.upt M))) (= (@ tptp.butlast_nat (@ _let_1 N2)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I4 tptp.nat)) (@ (@ tptp.plus_plus_nat I4) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))))
% 6.81/7.15 (assert (forall ((L tptp.nat) (H tptp.nat) (Is1 tptp.list_nat) (I2 tptp.nat) (Is2 tptp.list_nat)) (let ((_let_1 (@ tptp.upt L))) (= (= (@ _let_1 H) (@ (@ tptp.append_nat Is1) (@ (@ tptp.cons_nat I2) Is2))) (and (= Is1 (@ _let_1 I2)) (= Is2 (@ (@ tptp.upt (@ tptp.suc I2)) H)) (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_nat I2) H))))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X) Xs)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs)))))
% 6.81/7.15 (assert (forall ((U tptp.nat) (U3 tptp.nat) (P (-> tptp.nat Bool))) (let ((_let_1 (@ tptp.upt tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.filter_nat2 P))) (=> (@ (@ tptp.ord_less_eq_nat U) U3) (=> (forall ((I3 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat U) I3) (@ (@ tptp.ord_less_nat I3) U3)) (not (@ P I3)))) (= (@ _let_2 (@ _let_1 U)) (@ _let_2 (@ _let_1 U3)))))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.upt M) N2))))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa))))))))))))))
% 6.81/7.15 (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)))))))))))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa)))))))) (not _let_1)))))))))))
% 6.81/7.15 (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)))))))))))
% 6.81/7.15 (assert (forall ((B Bool) (H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn (@ tptp.pure_assn B)) H) (and (= (@ tptp.produc8586169260539613262et_nat H) tptp.bot_bot_set_nat) B))))
% 6.81/7.15 (assert (forall ((H tptp.produc3658429121746597890et_nat)) (= (@ (@ tptp.rep_assn tptp.one_one_assn) H) (= (@ tptp.produc8586169260539613262et_nat H) tptp.bot_bot_set_nat))))
% 6.81/7.15 (assert (forall ((P tptp.assn) (H tptp.produc3658429121746597890et_nat)) (=> (@ (@ tptp.rep_assn (@ (@ tptp.times_times_assn P) tptp.top_top_assn)) H) (not (forall ((H5 tptp.produc3658429121746597890et_nat)) (=> (= (@ tptp.produc1824681642469235216et_nat H5) (@ tptp.produc1824681642469235216et_nat H)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.produc8586169260539613262et_nat H5)) (@ tptp.produc8586169260539613262et_nat H)) (not (@ (@ tptp.rep_assn P) H5)))))))))
% 6.81/7.15 (assert (= tptp.bNF_Ca8459412986667044542atLess (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N2)))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_min_nat B) _let_1) _let_1)))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc A))) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_min_nat _let_1) B) _let_1)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q6)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q6))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N2)) Q6) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q6)) (@ (@ tptp.times_times_nat N2) Q6)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N2) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N2)) I2))))
% 6.81/7.15 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M7) N2)))) M))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M7)))) M))))
% 6.81/7.15 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.81/7.15 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.81/7.15 (assert (= tptp.ord_less_int (@ (@ (@ tptp.map_fu434086159418415080_int_o tptp.rep_Integ) (@ (@ tptp.map_fu4826362097070443709at_o_o tptp.rep_Integ) tptp.id_o)) (@ tptp.produc8739625826339149834_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))))))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0))))))
% 6.81/7.15 (assert (= tptp.ord_le3102999989581377725nteger (@ (@ (@ tptp.map_fu2496120808607739376eger_o tptp.code_int_of_integer) (@ (@ tptp.map_fu6957801986076833569nt_o_o tptp.code_int_of_integer) tptp.id_o)) tptp.ord_less_eq_int)))
% 6.81/7.15 (assert (= tptp.ord_le6747313008572928689nteger (@ (@ (@ tptp.map_fu2496120808607739376eger_o tptp.code_int_of_integer) (@ (@ tptp.map_fu6957801986076833569nt_o_o tptp.code_int_of_integer) tptp.id_o)) tptp.ord_less_int)))
% 6.81/7.15 (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)))))
% 6.81/7.15 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.81/7.15 (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)))))
% 6.81/7.15 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q6) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q6)) (@ (@ tptp.times_times_nat N2) Q6)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q6)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q6))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q6)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q6))))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q6 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q6) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q6)) (@ (@ tptp.plus_plus_nat N2) Q6)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M7)))) M)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M7 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M7) N2)))) M)))))
% 6.81/7.15 (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))))
% 6.81/7.15 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.81/7.15 (assert (forall ((N7 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N7)))
% 6.81/7.15 (assert (forall ((N7 tptp.set_nat) (K tptp.nat)) (=> (forall ((N5 tptp.nat)) (=> (@ (@ tptp.member_nat N5) N7) (@ (@ tptp.ord_less_eq_nat K) N5))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N7))))
% 6.81/7.15 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X4 tptp.rat)) (@ tptp.the_int (lambda ((Z6 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z6)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z6) tptp.one_one_int)))))))))
% 6.81/7.15 (assert (= tptp.ord_less_eq_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y4) (= X4 Y4)))))
% 6.81/7.15 (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))))
% 6.81/7.15 (assert (= tptp.sgn_sgn_rat (lambda ((A5 tptp.rat)) (@ (@ (@ tptp.if_rat (= A5 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A5)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.81/7.15 (assert (forall ((Q6 tptp.int) (P3 tptp.int)) (=> (@ (@ tptp.ord_less_int Q6) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P3)) (@ tptp.uminus_uminus_int Q6)))))))
% 6.81/7.15 (assert (forall ((P3 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P3) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.81/7.15 (assert (forall ((R3 tptp.product_prod_int_int) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R3) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 6.81/7.15 (assert (forall ((Q6 tptp.int) (S2 tptp.int) (P3 tptp.int) (R3 tptp.int)) (=> (not (= Q6 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R3) S2))) (= (@ (@ tptp.times_times_int P3) S2) (@ (@ tptp.times_times_int R3) Q6)))))))
% 6.81/7.15 (assert (= tptp.normalize (lambda ((P7 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P7))) (let ((_let_2 (@ tptp.product_fst_int_int P7))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.81/7.15 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 6.81/7.15 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N2)) (or (not (= M tptp.zero_zero_int)) (not (= N2 tptp.zero_zero_int))))))
% 6.81/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 6.81/7.15 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.81/7.15 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.81/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 6.81/7.15 (assert (forall ((R3 tptp.rat) (N2 tptp.int) (D2 tptp.int)) (=> (= (@ tptp.quotient_of R3) (@ (@ tptp.product_Pair_int_int N2) D2)) (= R3 (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N2)) (@ tptp.ring_1_of_int_rat D2))))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.81/7.15 (assert (forall ((D2 tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D2) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D2))))) (= D2 (@ (@ tptp.gcd_gcd_int A) B))))))
% 6.81/7.15 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X) Y))))))
% 6.81/7.15 (assert (forall ((R3 tptp.rat) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R3) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6))))
% 6.81/7.15 (assert (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R3)))))
% 6.81/7.15 (assert (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M) N2) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D5 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D5))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A5)) __flatten_var_0))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) B5)) (@ (@ tptp.times_times_int C4) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C4) B5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (= tptp.ord_less_rat (lambda ((P7 tptp.rat) (Q7 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B5 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C4) B5)))) (@ tptp.quotient_of Q7)))) (@ tptp.quotient_of P7)))))
% 6.81/7.15 (assert (= tptp.ord_less_eq_rat (lambda ((P7 tptp.rat) (Q7 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B5 tptp.int) (D5 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int C4) B5)))) (@ tptp.quotient_of Q7)))) (@ tptp.quotient_of P7)))))
% 6.81/7.15 (assert (= tptp.archim3151403230148437115or_rat (lambda ((P7 tptp.rat)) (@ (@ tptp.produc8211389475949308722nt_int tptp.divide_divide_int) (@ tptp.quotient_of P7)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A5)) __flatten_var_0))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int B5) C4))) (@ (@ tptp.times_times_int C4) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat) (Q6 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P3) Q6)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (C4 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B5 tptp.int) (D5 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A5) D5)) (@ (@ tptp.times_times_int B5) C4))) (@ (@ tptp.times_times_int C4) D5))))) (@ tptp.quotient_of Q6)))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P3)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P3)))) tptp.one_one_int))))
% 6.81/7.15 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.81/7.15 (assert (forall ((P3 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P3)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A5 tptp.int) (B5 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)) B5)) (@ tptp.abs_abs_int A5))))) (@ tptp.quotient_of P3)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N2)) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))))
% 6.81/7.15 (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))))
% 6.81/7.15 (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))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N2)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N2) M)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_nat)) (=> (forall ((A4 tptp.nat) (B4 tptp.nat)) (=> (@ (@ tptp.member_nat A4) A3) (=> (@ (@ tptp.member_nat B4) A3) (@ (@ tptp.member_nat (@ (@ tptp.gcd_gcd_nat A4) B4)) A3)))) (=> (not (= A3 tptp.bot_bot_set_nat)) (@ (@ tptp.member_nat (@ tptp.gcd_Gcd_nat A3)) A3)))))
% 6.81/7.15 (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)))))))))))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N) (not (= M3 N))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.gcd_gcd_nat M) N2) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X) Xa))))) (not _let_1)))))))))
% 6.81/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 6.81/7.15 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.81/7.15 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.81/7.15 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 6.81/7.15 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 6.81/7.15 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L)))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.81/7.15 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.81/7.15 (assert (forall ((B tptp.int) (D2 tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D2))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D2 tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D2)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int) (P3 tptp.int) (Q6 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A) B))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P3) Q6)) (= (@ (@ tptp.fract P3) Q6) _let_1)))))
% 6.81/7.15 (assert (forall ((P (-> tptp.rat Bool)) (Q6 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ P (@ (@ tptp.fract A4) B4)))) (@ P Q6))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ tptp.product_Pair_int_int P3) Q6)) (= (@ (@ tptp.fract P3) Q6) (@ (@ tptp.fract A) B)))))
% 6.81/7.15 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A) B)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.81/7.15 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.81/7.15 (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)))))
% 6.81/7.15 (assert (= tptp.ord_less_rat (lambda ((X4 tptp.rat) (Y4 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y4) X4)))))
% 6.81/7.15 (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)))))))
% 6.81/7.15 (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)))))))
% 6.81/7.15 (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))))))))
% 6.81/7.15 (assert (= tptp.inverse_inverse_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X4)) _let_1)))))))
% 6.81/7.15 (assert (= tptp.one_one_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))))
% 6.81/7.15 (assert (= tptp.fract (lambda ((Xa4 tptp.int) (X4 tptp.int)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= X4 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int Xa4) X4))))))
% 6.81/7.15 (assert (= tptp.zero_zero_rat (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.81/7.15 (assert (= tptp.fract (@ (@ (@ tptp.map_fu7831380289885515383nt_rat tptp.id_int) (@ (@ tptp.map_fu3424225382358772769nt_rat tptp.id_int) tptp.abs_Rat)) (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B5))))))
% 6.81/7.15 (assert (= tptp.uminus_uminus_rat (@ (@ (@ tptp.map_fu5673905371560938248nt_rat tptp.rep_Rat) tptp.abs_Rat) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X4))) (@ tptp.product_snd_int_int X4))))))
% 6.81/7.15 (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)))))))
% 6.81/7.15 (assert (forall ((Xa 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 Xa))) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.plus_plus_rat (@ tptp.abs_Rat Xa)) (@ 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 Xa)) _let_1)) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) _let_2))) (@ (@ tptp.times_times_int _let_2) _let_1))))))))))
% 6.81/7.15 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.81/7.15 (assert (let ((_let_1 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (@ (@ tptp.ratrel _let_1) _let_1)))
% 6.81/7.15 (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))))))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.uminus_uminus_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X))) (@ tptp.product_snd_int_int X)))))))
% 6.81/7.15 (assert (forall ((Xa tptp.product_prod_int_int) (X tptp.product_prod_int_int)) (=> (@ (@ tptp.ratrel Xa) Xa) (=> (@ (@ tptp.ratrel X) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_Rat Xa)) (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int Xa)) (@ tptp.product_fst_int_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int Xa)) (@ tptp.product_snd_int_int X)))))))))
% 6.81/7.15 (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)))))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X))) (=> (@ (@ tptp.ratrel X) X) (= (@ tptp.inverse_inverse_rat (@ tptp.abs_Rat X)) (@ tptp.abs_Rat (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X)) _let_1))))))))
% 6.81/7.15 (assert (= tptp.cr_rat (lambda ((X4 tptp.product_prod_int_int) (Y4 tptp.rat)) (and (@ (@ tptp.ratrel X4) X4) (= (@ tptp.abs_Rat X4) Y4)))))
% 6.81/7.15 (assert (= tptp.code_dup (@ (@ (@ tptp.map_fu2599414010547811884nteger tptp.code_int_of_integer) tptp.code_integer_of_int) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3)))))
% 6.81/7.15 (assert (= tptp.quotient_of (lambda ((X4 tptp.rat)) (@ tptp.the_Pr4378521158711661632nt_int (lambda ((Pair tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Pair))) (let ((_let_2 (@ tptp.product_fst_int_int Pair))) (and (= X4 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)))))))))
% 6.81/7.15 (assert (forall ((Q6 tptp.int) (P3 tptp.int)) (let ((_let_1 (@ (@ tptp.product_Pair_int_int P3) Q6))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q6) (=> (@ (@ tptp.algebr932160517623751201me_int P3) Q6) (= (@ tptp.normalize _let_1) _let_1))))))
% 6.81/7.15 (assert (forall ((R3 tptp.rat) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.quotient_of R3) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.algebr932160517623751201me_int P3) Q6))))
% 6.81/7.15 (assert (forall ((R3 tptp.product_prod_int_int) (P3 tptp.int) (Q6 tptp.int)) (=> (= (@ tptp.normalize R3) (@ (@ tptp.product_Pair_int_int P3) Q6)) (@ (@ tptp.algebr932160517623751201me_int P3) Q6))))
% 6.81/7.15 (assert (forall ((P (-> tptp.rat Bool)) (Q6 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.algebr932160517623751201me_int A4) B4) (@ P (@ (@ tptp.fract A4) B4))))) (@ P Q6))))
% 6.81/7.15 (assert (forall ((Q6 tptp.rat)) (not (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= Q6 (@ (@ tptp.fract A4) B4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (not (@ (@ tptp.algebr932160517623751201me_int A4) B4))))))))
% 6.81/7.15 (assert (forall ((Q6 tptp.rat)) (=> (forall ((A4 tptp.int) (B4 tptp.int)) (=> (= Q6 (@ (@ tptp.fract A4) B4)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (not (= A4 tptp.zero_zero_int)) (not (@ (@ tptp.algebr932160517623751201me_int A4) B4)))))) (= Q6 tptp.zero_zero_rat))))
% 6.81/7.15 (assert (forall ((R3 tptp.rat)) (exists ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int X3))) (let ((_let_2 (@ tptp.product_fst_int_int X3))) (and (= R3 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1) (forall ((Y6 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int Y6))) (let ((_let_2 (@ tptp.product_fst_int_int Y6))) (=> (and (= R3 (@ (@ tptp.fract _let_2) _let_1)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1) (@ (@ tptp.algebr932160517623751201me_int _let_2) _let_1)) (= Y6 X3)))))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.algebr934650988132801477me_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8699439704749558557nt_o_o tptp.ratrel) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3))) (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))))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8402795839162346335um_int (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3))) (@ (@ tptp.bNF_re1822329894187522285nt_int (lambda ((Y5 tptp.num) (Z3 tptp.num)) (= Y5 Z3))) (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3)))) (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N)))) (lambda ((M3 tptp.num) (N tptp.num)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M3)) (@ tptp.numeral_numeral_int N)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re157797125943740599nt_int (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (@ (@ tptp.bNF_re6250860962936578807nt_int (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) tptp.ratrel)) (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B5)))) (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B5)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4712519889275205905nt_int (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))) (lambda ((K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) K3))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) tptp.ord_less_eq_int) tptp.ord_less_eq_int))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) tptp.ord_less_eq_nat) tptp.ord_less_eq_nat))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re578469030762574527_nat_o (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) (@ (@ tptp.bNF_re4705727531993890431at_o_o (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) tptp.ord_less_nat) tptp.ord_less_nat))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3403563459893282935_int_o (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (@ (@ tptp.bNF_re5089333283451836215nt_o_o (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) tptp.ord_less_int) tptp.ord_less_int))
% 6.81/7.15 (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))))))
% 6.81/7.15 (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)))))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X4))) (@ tptp.product_snd_int_int X4)))) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X4))) (@ tptp.product_snd_int_int X4)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re7145576690424134365nt_int tptp.ratrel) tptp.ratrel) (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X4)) _let_1))))) (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X4)) _let_1))))))
% 6.81/7.15 (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))
% 6.81/7.15 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.81/7.15 (assert (@ (@ tptp.pcr_rat (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) tptp.zero_zero_rat))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re3461391660133120880nt_rat (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) (@ (@ tptp.bNF_re2214769303045360666nt_rat (lambda ((Y5 tptp.int) (Z3 tptp.int)) (= Y5 Z3))) tptp.pcr_rat)) (lambda ((A5 tptp.int) (B5 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= B5 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int A5) B5)))) tptp.fract))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X4 tptp.product_prod_int_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.product_fst_int_int X4))) (@ tptp.product_snd_int_int X4)))) tptp.uminus_uminus_rat))
% 6.81/7.15 (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))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re1494630372529172596at_o_o tptp.pcr_rat) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3))) (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))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re8279943556446156061nt_rat tptp.pcr_rat) tptp.pcr_rat) (lambda ((X4 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_fst_int_int X4))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ tptp.product_snd_int_int X4)) _let_1))))) tptp.inverse_inverse_rat))
% 6.81/7.15 (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) (V2 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 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U2))))))) __flatten_var_0)))) tptp.times_times_int))
% 6.81/7.15 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat)) tptp.zero_zero_int))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re6830278522597306478at_int (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) tptp.pcr_int) (lambda ((N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat N) tptp.zero_zero_nat))) tptp.semiri1314217659103216013at_int))
% 6.81/7.15 (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))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4555766996558763186at_nat tptp.pcr_int) (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat)) tptp.nat2))
% 6.81/7.15 (assert (@ (@ tptp.pcr_int (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat)) tptp.one_one_int))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))) tptp.ord_less_int))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re717283939379294677_int_o tptp.pcr_int) (@ (@ tptp.bNF_re6644619430987730960nt_o_o tptp.pcr_int) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))) tptp.ord_less_eq_int))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0)))) tptp.plus_plus_int))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0)))) tptp.minus_minus_int))
% 6.81/7.15 (assert (= tptp.complete_Sup_Sup_int (lambda ((X11 tptp.set_int)) (@ tptp.the_int (lambda ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) X11) (forall ((Y4 tptp.int)) (=> (@ (@ tptp.member_int Y4) X11) (@ (@ tptp.ord_less_eq_int Y4) X4)))))))))
% 6.81/7.15 (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) (V2 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 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _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) (V2 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 V2))) (@ (@ tptp.plus_plus_nat (@ _let_2 V2)) (@ _let_1 U2))))))) __flatten_var_0)))))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Y tptp.nat) (U tptp.nat) (V tptp.nat)) (= (@ (@ tptp.intrel (@ (@ tptp.product_Pair_nat_nat X) Y)) (@ (@ tptp.product_Pair_nat_nat U) V)) (= (@ (@ tptp.plus_plus_nat X) V) (@ (@ tptp.plus_plus_nat U) Y)))))
% 6.81/7.15 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.81/7.15 (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)))))
% 6.81/7.15 (assert (let ((_let_1 (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))) (@ (@ (@ (@ tptp.bNF_re8246922863344978751at_nat tptp.intrel) (lambda ((Y5 tptp.nat) (Z3 tptp.nat)) (= Y5 Z3))) _let_1) _let_1)))
% 6.81/7.15 (assert (let ((_let_1 (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.intrel _let_1) _let_1)))
% 6.81/7.15 (assert (= tptp.intrel (@ 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) (V2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat X4) V2) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))))
% 6.81/7.15 (assert (@ (@ (@ (@ tptp.bNF_re4202695980764964119_nat_o tptp.intrel) (@ (@ tptp.bNF_re3666534408544137501at_o_o tptp.intrel) (lambda ((Y5 Bool) (Z3 Bool)) (= Y5 Z3)))) (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ 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) (V2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat U2) Y4)))) __flatten_var_0)))))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ 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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) V2)) (@ (@ tptp.plus_plus_nat Y4) U2)))) __flatten_var_0)))))
% 6.81/7.15 (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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __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) (V2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X4) U2)) (@ (@ tptp.plus_plus_nat Y4) V2)))) __flatten_var_0)))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.81/7.15 (assert (forall ((N2 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) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ tptp.ord_less_eq_nat X4) Y4)))))) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))))
% 6.81/7.15 (assert (@ tptp.wf_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_nat))))
% 6.81/7.15 (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))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.81/7.15 (assert (forall ((S tptp.set_nat) (N2 tptp.nat)) (=> (not (@ tptp.finite_finite_nat S)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S) N2)))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.81/7.15 (assert (forall ((S tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.finite_card_nat S)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.infini8530281810654367211te_nat S) N2))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool))) (=> (@ P tptp.zero_zero_nat) (= (@ tptp.ord_Least_nat P) tptp.zero_zero_nat))))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 6.81/7.15 (assert (= tptp.complete_Inf_Inf_nat (lambda ((X11 tptp.set_nat)) (@ tptp.ord_Least_nat (lambda ((N tptp.nat)) (@ (@ tptp.member_nat N) X11))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (Q (-> tptp.nat Bool)) (M tptp.nat)) (=> (@ P N2) (=> (@ Q M) (=> (not (@ P tptp.zero_zero_nat)) (=> (forall ((K2 tptp.nat)) (= (@ P (@ tptp.suc K2)) (@ Q K2))) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat Q)))))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (= (@ tptp.ord_Least_nat P) (@ tptp.suc (@ tptp.ord_Least_nat (lambda ((M3 tptp.nat)) (@ P (@ tptp.suc M3))))))))))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or8404916559141939852nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or4266950643985792945nteger L) U))))
% 6.81/7.15 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (@ tptp.finite6017078050557962740nteger (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 6.81/7.15 (assert (forall ((L tptp.code_integer) (U tptp.code_integer)) (= (@ (@ tptp.set_or189985376899183464nteger (@ (@ tptp.plus_p5714425477246183910nteger L) tptp.one_one_Code_integer)) U) (@ (@ tptp.set_or2715278749043346189nteger L) U))))
% 6.81/7.15 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.81/7.15 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.81/7.15 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_atMost_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 6.81/7.15 (assert (@ (@ (@ tptp.filter3212408913953519116et_nat tptp.set_ord_lessThan_nat) (@ tptp.finite3254316476582989077op_nat tptp.top_top_set_nat)) tptp.at_top_nat))
% 6.81/7.15 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.81/7.15 (assert (not (= tptp.at_top_nat tptp.bot_bot_filter_nat)))
% 6.81/7.15 (assert (forall ((M6 tptp.set_nat) (N7 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M6) N7) (= (@ (@ tptp.image_nat_nat tptp.suc) M6) N7))))
% 6.81/7.15 (assert (forall ((X tptp.product_unit)) (@ (@ tptp.member_o (@ tptp.product_Rep_unit X)) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))
% 6.81/7.15 (assert (forall ((X tptp.product_unit) (Y tptp.product_unit)) (= (= (@ tptp.product_Rep_unit X) (@ tptp.product_Rep_unit Y)) (= X Y))))
% 6.81/7.15 (assert (forall ((Y Bool) (P (-> Bool Bool))) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (=> (forall ((X3 tptp.product_unit)) (@ P (@ tptp.product_Rep_unit X3))) (@ P Y)))))
% 6.81/7.15 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (not (forall ((X3 tptp.product_unit)) (= Y (not (@ tptp.product_Rep_unit X3))))))))
% 6.81/7.15 (assert (@ (@ (@ tptp.type_d6188575255521822967unit_o tptp.product_Rep_unit) tptp.product_Abs_unit) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)))
% 6.81/7.15 (assert (forall ((Y Bool)) (=> (@ (@ tptp.member_o Y) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (= (@ tptp.product_Rep_unit (@ tptp.product_Abs_unit Y)) Y))))
% 6.81/7.15 (assert (forall ((X tptp.product_unit)) (= (@ tptp.product_Abs_unit (@ tptp.product_Rep_unit X)) X)))
% 6.81/7.15 (assert (forall ((X tptp.product_unit)) (not (forall ((Y3 Bool)) (=> (= X (@ tptp.product_Abs_unit Y3)) (not (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.product_unit Bool)) (X tptp.product_unit)) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ (@ tptp.insert_o true) tptp.bot_bot_set_o)) (@ P (@ tptp.product_Abs_unit Y3)))) (@ P X))))
% 6.81/7.15 (assert (forall ((X Bool) (Y Bool)) (let ((_let_1 (@ (@ tptp.insert_o true) tptp.bot_bot_set_o))) (=> (@ (@ tptp.member_o X) _let_1) (=> (@ (@ tptp.member_o Y) _let_1) (= (= (@ tptp.product_Abs_unit X) (@ tptp.product_Abs_unit Y)) (= X Y)))))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat (lambda ((I4 tptp.nat)) (@ P (@ tptp.suc I4)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.81/7.15 (assert (forall ((F4 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F4) tptp.at_top_nat) (forall ((N8 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N8)) F4)))))
% 6.81/7.15 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X3) (@ P X3))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.81/7.15 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N8 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N) (@ P N)))))))
% 6.81/7.15 (assert (not (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) false)) tptp.at_top_nat)))
% 6.81/7.15 (assert (forall ((N2 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) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.81/7.15 (assert (= tptp.top_to1996260823553986621t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit)))
% 6.81/7.15 (assert (= tptp.bot_bot_Product_unit tptp.product_Unity))
% 6.81/7.15 (assert (= tptp.product_Unity (@ tptp.product_Abs_unit true)))
% 6.81/7.15 (assert (= tptp.sup_sup_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv2 tptp.product_unit)) tptp.product_Unity)))
% 6.81/7.15 (assert (= tptp.comple2584293577114468500t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))
% 6.81/7.15 (assert (forall ((Y tptp.product_unit)) (= Y tptp.product_Unity)))
% 6.81/7.15 (assert (= tptp.top_top_Product_unit tptp.product_Unity))
% 6.81/7.15 (assert (= tptp.uminus2952777764628376836t_unit (lambda ((Uu3 tptp.product_unit)) tptp.product_Unity)))
% 6.81/7.15 (assert (= tptp.comple4687483117567863418t_unit (lambda ((Uu3 tptp.set_Product_unit)) tptp.product_Unity)))
% 6.81/7.15 (assert (= tptp.inf_inf_Product_unit (lambda ((Uu3 tptp.product_unit) (Uv2 tptp.product_unit)) tptp.product_Unity)))
% 6.81/7.15 (assert (= tptp.heap_Time_wait (lambda ((N tptp.nat)) (@ tptp.heap_T6183433275982383450t_unit (lambda ((H6 tptp.heap_e7401611519738050253t_unit)) (@ tptp.some_P1914260805536162275it_nat (@ (@ tptp.produc7133225469290080770it_nat tptp.product_Unity) (@ (@ tptp.produc584006145561248582it_nat H6) N))))))))
% 6.81/7.15 (assert (= tptp.defaul566961228789861419t_unit tptp.product_Unity))
% 6.81/7.15 (assert (= tptp.log (lambda ((B5 tptp.code_natural) (I4 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (or (@ (@ tptp.ord_le1926595141338095240atural B5) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural I4) B5))) tptp.one_one_Code_natural) (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ (@ tptp.log B5) (@ (@ tptp.divide5121882707175180666atural I4) B5)))))))
% 6.81/7.15 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ tptp.log X))) (let ((_let_2 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_1 Xa) Y) (and (=> _let_2 (= Y tptp.one_one_Code_natural)) (=> (not _let_2) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_1 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))))))))
% 6.81/7.15 (assert (forall ((X tptp.code_natural) (Xa tptp.code_natural) (Y tptp.code_natural)) (let ((_let_1 (@ (@ tptp.accp_P8126237942716283194atural tptp.log_rel) (@ (@ tptp.produc3574140220909816553atural X) Xa)))) (let ((_let_2 (@ tptp.log X))) (let ((_let_3 (or (@ (@ tptp.ord_le1926595141338095240atural X) tptp.one_one_Code_natural) (@ (@ tptp.ord_le5570908160329646204atural Xa) X)))) (=> (= (@ _let_2 Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y tptp.one_one_Code_natural)) (=> (not _let_3) (= Y (@ (@ tptp.plus_p4538020629002901425atural tptp.one_one_Code_natural) (@ _let_2 (@ (@ tptp.divide5121882707175180666atural Xa) X)))))) (not _let_1))))))))))
% 6.81/7.15 (assert (= tptp.minus_shift (lambda ((R4 tptp.code_natural) (K3 tptp.code_natural) (L2 tptp.code_natural)) (@ (@ (@ tptp.if_Code_natural (@ (@ tptp.ord_le5570908160329646204atural K3) L2)) (@ (@ tptp.minus_7197305767214868737atural (@ (@ tptp.plus_p4538020629002901425atural R4) K3)) L2)) (@ (@ tptp.minus_7197305767214868737atural K3) L2)))))
% 6.81/7.15 (assert (forall ((X tptp.produc8731074985263844745atural)) (not (forall ((F2 (-> tptp.code_natural tptp.option6357759511663192854e_term)) (D tptp.code_natural) (I3 tptp.code_natural)) (not (= X (@ (@ tptp.produc2252593628808123835atural F2) (@ (@ tptp.produc3574140220909816553atural D) I3))))))))
% 6.81/7.15 (assert (forall ((X tptp.produc989692990947075319atural)) (not (forall ((F2 (-> tptp.produc4972180933644002618e_term tptp.option6357759511663192854e_term)) (D tptp.code_natural) (I3 tptp.code_natural)) (not (= X (@ (@ tptp.produc3831813291587773865atural F2) (@ (@ tptp.produc3574140220909816553atural D) I3))))))))
% 6.81/7.15 (assert (forall ((X tptp.produc7822875418678951345atural)) (not (forall ((B4 tptp.code_natural) (I3 tptp.code_natural)) (not (= X (@ (@ tptp.produc3574140220909816553atural B4) I3)))))))
% 6.81/7.15 (assert (forall ((V 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 V) _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 V) _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 V) 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))))))))))))))))
% 6.81/7.15 (assert (= tptp.split_seed (lambda ((S6 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V2 tptp.code_natural) (W3 tptp.code_natural)) (@ (@ tptp.produc8282080750456430313atural (lambda ((V3 tptp.code_natural) (W4 tptp.code_natural)) (let ((_let_1 (@ 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)))))))))))))))))))))))) (@ (@ tptp.produc4480994950612372183atural (@ (@ tptp.produc3574140220909816553atural (@ (@ tptp.inc_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 _let_1)))))))))) V2)) W4)) (@ (@ tptp.produc3574140220909816553atural V3) (@ (@ tptp.inc_shift (@ tptp.numera5444537566228673987atural (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_1)))))))))) W3)))))) (@ tptp.produc6591912806276919810atural (@ tptp.next S6))))) S6))))
% 6.81/7.15 (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 ((V2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.plus_p4538020629002901425atural V2) (@ (@ 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 ((V2 tptp.code_natural) (__flatten_var_0 tptp.produc7822875418678951345atural)) (@ (@ tptp.produc6639722614265839536atural (@ (@ tptp.modulo8411746178871703098atural V2) K3)) __flatten_var_0))) __flatten_var_0))))
% 6.81/7.15 (assert (forall ((K tptp.code_natural) (S2 tptp.produc7822875418678951345atural)) (=> (@ (@ tptp.ord_le5570908160329646204atural tptp.zero_z2226904508553997617atural) K) (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.produc497848011034438852atural (@ (@ tptp.range K) S2))) K))))
% 6.81/7.15 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le5570908160329646204atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ (@ tptp.ord_less_nat Xa) X))))
% 6.81/7.15 (assert (forall ((Xa tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_le1926595141338095240atural (@ tptp.code_natural_of_nat Xa)) (@ tptp.code_natural_of_nat X)) (@ (@ tptp.ord_less_eq_nat Xa) X))))
% 6.81/7.15 (assert (= tptp.ord_le1926595141338095240atural (lambda ((X4 tptp.code_natural) (Xa4 tptp.code_natural)) (@ (@ tptp.ord_less_eq_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa4)))))
% 6.81/7.15 (assert (= tptp.ord_le5570908160329646204atural (lambda ((X4 tptp.code_natural) (Xa4 tptp.code_natural)) (@ (@ tptp.ord_less_nat (@ tptp.code_nat_of_natural X4)) (@ tptp.code_nat_of_natural Xa4)))))
% 6.81/7.15 (assert (= tptp.ord_le5570908160329646204atural (@ (@ (@ tptp.map_fu6256889081107267320ural_o tptp.code_nat_of_natural) (@ (@ tptp.map_fu4892316939951275536at_o_o tptp.code_nat_of_natural) tptp.id_o)) tptp.ord_less_nat)))
% 6.81/7.15 (assert (= tptp.ord_le1926595141338095240atural (@ (@ (@ tptp.map_fu6256889081107267320ural_o tptp.code_nat_of_natural) (@ (@ tptp.map_fu4892316939951275536at_o_o tptp.code_nat_of_natural) tptp.id_o)) tptp.ord_less_eq_nat)))
% 6.81/7.15 (assert (forall ((N2 tptp.code_natural)) (let ((_let_1 (@ tptp.code_nat_of_natural N2))) (=> (not (= N2 tptp.zero_z2226904508553997617atural)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat _let_1) (@ tptp.suc tptp.zero_zero_nat))) _let_1)))))
% 6.81/7.15 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K) L)) (@ _let_1 L)))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat S2) T5) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T5))) tptp.fun_pair_less)))))
% 6.81/7.15 (assert (forall ((A3 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.total_3592101749530773125at_nat A3) tptp.fun_pair_less)))
% 6.81/7.15 (assert (@ tptp.trans_4347625901269045472at_nat tptp.fun_pair_less))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.product_Pair_nat_nat X))) (= (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ _let_1 Y)) (@ _let_1 Z))) tptp.fun_pair_less) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.81/7.15 (assert (= tptp.fun_pair_less (@ (@ tptp.lex_prod_nat_nat tptp.less_than) tptp.less_than)))
% 6.81/7.15 (assert (@ tptp.wf_Pro7803398752247294826at_nat tptp.fun_pair_less))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 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) T5))) tptp.fun_pair_less))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_strict) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y) YS))) tptp.fun_min_strict)))))))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat S2) T5) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat (@ (@ tptp.product_Pair_nat_nat A) S2)) (@ (@ tptp.product_Pair_nat_nat B) T5))) tptp.fun_pair_leq)))))
% 6.81/7.15 (assert (= tptp.fun_pair_leq (@ (@ tptp.sup_su718114333110466843at_nat tptp.fun_pair_less) tptp.id_Pro2258643101195443293at_nat)))
% 6.81/7.15 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (not (= X6 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_strict))))
% 6.81/7.15 (assert (= tptp.fun_min_strict (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_less)))
% 6.81/7.15 (assert (forall ((A tptp.nat) (B tptp.nat) (S2 tptp.nat) (T5 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) T5))) tptp.fun_pair_leq))))
% 6.81/7.15 (assert (forall ((Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) YS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat XS) YS)) tptp.fun_max_weak) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) XS)) YS)) tptp.fun_max_weak))))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (XS tptp.set_Pr1261947904930325089at_nat) (Y tptp.product_prod_nat_nat) (YS tptp.set_Pr1261947904930325089at_nat)) (let ((_let_1 (@ tptp.produc2922128104949294807at_nat XS))) (=> (@ (@ tptp.member8440522571783428010at_nat X) XS) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 YS)) tptp.fun_min_weak) (@ (@ tptp.member8757157785044589968at_nat (@ _let_1 (@ (@ tptp.insert8211810215607154385at_nat Y) YS))) tptp.fun_min_weak)))))))
% 6.81/7.15 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat X6) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) X6)) tptp.fun_max_weak))))
% 6.81/7.15 (assert (forall ((X6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) tptp.bot_bo2099793752762293965at_nat)) tptp.fun_min_weak)))
% 6.81/7.15 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_min_strict) tptp.fun_min_weak)))
% 6.81/7.15 (assert (= tptp.fun_min_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.min_ex6901939911449802026at_nat tptp.fun_pair_leq)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))))
% 6.81/7.15 (assert (= tptp.fun_max_weak (@ (@ tptp.sup_su5525570899277871387at_nat (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_leq)) (@ (@ tptp.insert9069300056098147895at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) tptp.bot_bo2099793752762293965at_nat)) tptp.bot_bo228742789529271731at_nat))))
% 6.81/7.15 (assert (forall ((Y tptp.product_prod_nat_nat) (Y7 tptp.set_Pr1261947904930325089at_nat) (X tptp.product_prod_nat_nat) (X6 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y) Y7) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_less) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat X6) Y7)) tptp.fun_max_strict) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ (@ tptp.insert8211810215607154385at_nat X) X6)) Y7)) tptp.fun_max_strict))))))
% 6.81/7.15 (assert (= tptp.fun_max_strict (@ tptp.max_ex8135407076693332796at_nat tptp.fun_pair_less)))
% 6.81/7.15 (assert (@ tptp.fun_re2478310338295953701at_nat (@ (@ tptp.produc9060074326276436823at_nat tptp.fun_max_strict) tptp.fun_max_weak)))
% 6.81/7.15 (assert (forall ((Y7 tptp.set_Pr1261947904930325089at_nat)) (=> (@ tptp.finite6177210948735845034at_nat Y7) (=> (not (= Y7 tptp.bot_bo2099793752762293965at_nat)) (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat tptp.bot_bo2099793752762293965at_nat) Y7)) tptp.fun_max_strict)))))
% 6.81/7.15 (assert (= tptp.euclid3395696857347342551nt_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K3)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.81/7.15 (assert (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (Z4 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z4))) (=> (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A3)) (@ tptp.set_ms8126754132646256062at_nat B3))) tptp.fun_max_strict) (and (= A3 tptp.zero_z1048942125864253310at_nat) (= B3 tptp.zero_z1048942125864253310at_nat))) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A3)) (@ _let_1 B3))) tptp.ms_weak)))))
% 6.81/7.15 (assert (forall ((A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat) (Z4 tptp.multis2468970476368604999at_nat)) (let ((_let_1 (@ tptp.plus_p7104986032573967614at_nat Z4))) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A3)) (@ tptp.set_ms8126754132646256062at_nat B3))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ _let_1 A3)) (@ _let_1 B3))) tptp.ms_strict)))))
% 6.81/7.15 (assert (@ tptp.fun_re7357418987779152907at_nat (@ (@ tptp.produc5245064249948416855at_nat tptp.ms_strict) tptp.ms_weak)))
% 6.81/7.15 (assert (= tptp.ms_weak (@ (@ tptp.sup_su3035147773818789531at_nat tptp.ms_strict) tptp.id_mul2649389997224486051at_nat)))
% 6.81/7.15 (assert (forall ((Z4 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z4) Z9) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A3)) (@ tptp.set_ms8126754132646256062at_nat B3))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z4) A3)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) B3))) tptp.ms_strict)))))
% 6.81/7.15 (assert (forall ((Z4 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat) (A3 tptp.multis2468970476368604999at_nat) (B3 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z4) Z9) (=> (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A3)) (@ tptp.set_ms8126754132646256062at_nat B3))) tptp.fun_max_strict) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z4) A3)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) B3))) tptp.ms_weak)))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)))))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat) (X6 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X) Y)) tptp.fun_pair_leq) (=> (@ (@ tptp.pw_leq X6) Y7) (@ (@ tptp.pw_leq (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X) tptp.zero_z1048942125864253310at_nat)) X6)) (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y) tptp.zero_z1048942125864253310at_nat)) Y7))))))
% 6.81/7.15 (assert (= tptp.pw_leq (lambda ((A12 tptp.multis2468970476368604999at_nat) (A22 tptp.multis2468970476368604999at_nat)) (or (and (= A12 tptp.zero_z1048942125864253310at_nat) (= A22 tptp.zero_z1048942125864253310at_nat)) (exists ((X4 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat) (X11 tptp.multis2468970476368604999at_nat) (Y8 tptp.multis2468970476368604999at_nat)) (and (= A12 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X4) tptp.zero_z1048942125864253310at_nat)) X11)) (= A22 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y4) tptp.zero_z1048942125864253310at_nat)) Y8)) (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X4) Y4)) tptp.fun_pair_leq) (@ (@ tptp.pw_leq X11) Y8)))))))
% 6.81/7.15 (assert (forall ((A1 tptp.multis2468970476368604999at_nat) (A23 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq A1) A23) (=> (=> (= A1 tptp.zero_z1048942125864253310at_nat) (not (= A23 tptp.zero_z1048942125864253310at_nat))) (not (forall ((X3 tptp.product_prod_nat_nat) (Y3 tptp.product_prod_nat_nat) (X14 tptp.multis2468970476368604999at_nat)) (=> (= A1 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat X3) tptp.zero_z1048942125864253310at_nat)) X14)) (forall ((Y9 tptp.multis2468970476368604999at_nat)) (=> (= A23 (@ (@ tptp.plus_p7104986032573967614at_nat (@ (@ tptp.add_ms2612439473150266591at_nat Y3) tptp.zero_z1048942125864253310at_nat)) Y9)) (=> (@ (@ tptp.member8206827879206165904at_nat (@ (@ tptp.produc6161850002892822231at_nat X3) Y3)) tptp.fun_pair_leq) (not (@ (@ tptp.pw_leq X14) Y9))))))))))))
% 6.81/7.15 (assert (forall ((Z4 tptp.multis2468970476368604999at_nat) (Z9 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq Z4) Z9) (@ (@ tptp.member6689249552917799696at_nat (@ (@ tptp.produc4348348721325984599at_nat (@ (@ tptp.plus_p7104986032573967614at_nat Z4) tptp.zero_z1048942125864253310at_nat)) (@ (@ tptp.plus_p7104986032573967614at_nat Z9) tptp.zero_z1048942125864253310at_nat))) tptp.ms_weak))))
% 6.81/7.15 (assert (forall ((X6 tptp.multis2468970476368604999at_nat) (Y7 tptp.multis2468970476368604999at_nat)) (=> (@ (@ tptp.pw_leq X6) Y7) (exists ((A8 tptp.multis2468970476368604999at_nat) (B10 tptp.multis2468970476368604999at_nat) (Z10 tptp.multis2468970476368604999at_nat)) (and (= X6 (@ (@ tptp.plus_p7104986032573967614at_nat A8) Z10)) (= Y7 (@ (@ tptp.plus_p7104986032573967614at_nat B10) Z10)) (or (@ (@ tptp.member8757157785044589968at_nat (@ (@ tptp.produc2922128104949294807at_nat (@ tptp.set_ms8126754132646256062at_nat A8)) (@ tptp.set_ms8126754132646256062at_nat B10))) tptp.fun_max_strict) (and (= B10 tptp.zero_z1048942125864253310at_nat) (= A8 tptp.zero_z1048942125864253310at_nat))))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.order_2888998067076097458on_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.81/7.15 (assert (forall ((N2 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) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ 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) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.81/7.15 (assert (= tptp.bNF_Cardinal_cone (@ tptp.bNF_Ca7083678892733797993t_unit (@ (@ tptp.insert_Product_unit tptp.product_Unity) tptp.bot_bo3957492148770167129t_unit))))
% 6.81/7.15 (assert (and (not (@ (@ tptp.member444158400953824016od_o_o (@ (@ tptp.produc763777882069021527od_o_o tptp.bNF_Cardinal_ctwo) tptp.bNF_Cardinal_czero_o)) tptp.bNF_We2654380646378065620so_o_o)) (@ (@ tptp.bNF_Ca8331644756375544342r_on_o (@ tptp.field_o tptp.bNF_Cardinal_ctwo)) tptp.bNF_Cardinal_ctwo)))
% 6.81/7.15 (assert (@ (@ tptp.member4095101504841534314at_nat (@ (@ tptp.produc8517790099723286449at_nat tptp.bNF_Cardinal_ctwo) tptp.bNF_Ca8665028551170535155natLeq)) tptp.bNF_We8182288985678559134_o_nat))
% 6.81/7.15 (assert (= tptp.bNF_Ca8665028551170535155natLeq (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o tptp.ord_less_eq_nat))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.order_underS_nat tptp.bNF_Ca8665028551170535155natLeq) N2) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2))))))
% 6.81/7.15 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.inf_in2572325071724192079at_nat tptp.bNF_Ca8665028551170535155natLeq) (@ (@ tptp.produc457027306803732586at_nat (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))) (lambda ((Uu2 tptp.nat)) (@ tptp.collect_nat (lambda ((X4 tptp.nat)) (@ (@ tptp.ord_less_nat X4) N2)))))) (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((X4 tptp.nat) (Y4 tptp.nat)) (and (@ (@ tptp.ord_less_nat X4) N2) (@ (@ tptp.ord_less_nat Y4) N2) (@ (@ tptp.ord_less_eq_nat X4) Y4))))))))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.assn) (Y tptp.assn)) (= (@ (@ (@ tptp.if_assn true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.code_natural) (Y tptp.code_natural)) (= (@ (@ (@ tptp.if_Code_natural true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (@ (@ (@ tptp.if_set_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_o) (Y tptp.option_set_o)) (= (@ (@ (@ tptp.if_option_set_o false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_o) (Y tptp.option_set_o)) (= (@ (@ (@ tptp.if_option_set_o true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_int) (Y tptp.option_set_int)) (= (@ (@ (@ tptp.if_option_set_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_int) (Y tptp.option_set_int)) (= (@ (@ (@ tptp.if_option_set_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (@ (@ (@ tptp.if_option_set_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.option_set_nat) (Y tptp.option_set_nat)) (= (@ (@ (@ tptp.if_option_set_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (@ (@ (@ tptp.if_mul8430962117462786573at_nat false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.multis2468970476368604999at_nat) (Y tptp.multis2468970476368604999at_nat)) (= (@ (@ (@ tptp.if_mul8430962117462786573at_nat true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X) Y) Y)))
% 6.81/7.15 (assert (forall ((X tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X) Y) X)))
% 6.81/7.15 (assert (forall ((X tptp.option8963830502488799655at_nat) (Y tptp.option8963830502488799655at_nat)) (= (@ (@ (@ tptp.if_opt7704869406773131885at_nat false) X) Y) Y)))
% 6.81/7.15 (assert (fora/export/starexec/sandbox/solver/bin/do_THM_THF: line 35: 12817 Alarm clock ( read result; case "$result" in
% 299.79/300.14 unsat)
% 299.79/300.14 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.79/300.14 ;;
% 299.79/300.14 sat)
% 299.79/300.14 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.79/300.14 ;;
% 299.79/300.14 esac; exit 1 )
% 299.79/300.15 Alarm clock
% 299.79/300.15 % cvc5---1.0.5 exiting
% 299.79/300.15 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------